\n",
" \n",
"## Introduction\n",
" \n",
"As you know, a new epidemic has overwhelmed the world, COVID-19 jeopardizes people and changes our habits. It is easy to realise that knowing how illnesses spread is vital to our own protection. How can we predict whether a disease will cause an epidemic, how many people it will infect, which people it will infect, and whether or not it is dangerous to society as a whole ? Also, how can we determine which techniques to use in fighting an epidemic once it begins ? One way to answer all of these questions is through **mathematical modeling**.\n",
"\n",
"In this work you will have to review different epidemic modelings relying all on the representation by graphs of a human network called a **contact network**. A vertex in a contact network represents an individual and an edge between two vertices represents a contact between two individuals. The disease only spread from individual to individual if they are in contact, so through the edges. This representation is actually really common in research, and a lot of state-of-the-art modeling are built over it. From these different models you will be asked to draw conclusions from experiments on varying contact networks.\n",
"\n",
"For readability and ease of use, this project will be carried on a Jupyter Notebook, hence code and question answering have to be written in this unique file. This is a **DUO** project, no group of one person will be accepted, the duo has to be composed of same TD group students, if the number of students in the TD group is odd we will accept one group composed of three students. It will be coded in Julia using the LightGraphs package. **BEWARE:** \n",
" \n",
"- If the code does not provide good results, its readability as well as its comments are essential for the corrector to potentially find some notation points.\n",
"- The specifications of the functions have to be strictly respected.\n",
"- Do not neglect written questions they stand for an important part of the notation, you are not only evaluated on the coding. Also, even so a written question may not ask you directly to code or provide results from code, support your arguments when possible with a runable example is very welcome and sometimes even expected.\n",
"- Any initiatives and additional efforts bringing contents and thoughts out of the question scope may result in bonus points if pertinent.\n",
"\n",
"Deliverable: You will deliver your work on moodle before **23.01.2022** in a **.tar** containing the notebook with your codes and your written answers, and the different graph figures in .png you will generate. The corrector will use the student N7 computers for running your code, so take care of verifying that your work is running as expected on these computers !\n",
"\n",
"LightGraphs documentation: "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"## Environment and packages installation\n",
"\n",
"**mathematical modeling**: For evaluation, coding questions have to run with no additional packages ! Only the ones present here ! However if you want to use another package to go further in your answer and add bonus contents, take care of separating the cells and precising which packages you are using."
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [],
"source": [
"# Import originaux, qui ne fonctionnent pas avec toutes les version de Julia\n",
"# De plus Lightgraph est déprécié, depuis genre 2 ans\n",
"\n",
"# using Pkg\n",
"# Pkg.activate(\".\") # Path to Manifest.toml and Project.toml\n",
"# using LightGraphs\n",
"# using GraphPlot\n",
"# using Colors\n",
"# using CairoMakie\n",
"# using StatsBase\n",
"# using Plots\n",
"# using JLD2\n",
"# using Compose"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `~/Documents/Cours/ENSEEIHT/S7 - Graphes/projet`\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Documents/Cours/ENSEEIHT/S7 - Graphes/projet/Project.toml`\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Documents/Cours/ENSEEIHT/S7 - Graphes/projet/Manifest.toml`\n"
]
}
],
"source": [
"# Import packages\n",
"# Marche en Julia 1.8.0 et sur les machines de l'enseeiht\n",
"using Pkg\n",
"Pkg.activate(\".\") # Path to Manifest.toml and Project.toml\n",
"Pkg.resolve()\n",
"\n",
"# Remplace LighGraph\n",
"using Graphs\n",
"using Graphs: smallgraph\n",
"using Graphs: stochastic_block_model\n",
"using Graphs: barabasi_albert\n",
"using Graphs: random_regular_graph\n",
"using GraphPlot\n",
"\n",
"using Colors\n",
"using CairoMakie\n",
"using StatsBase\n",
"using Plots\n",
"using JLD2\n",
"using Compose\n",
"using Random"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"## Part 1 - SIS model\n",
"\n",
"SIS is a compartmental model, ie a model where the population is divided into subgroups that represent the disease status of its members. SIS stands for Susceptible $\\rightarrow$ Infected $\\rightarrow$ Susceptible where the susceptible group contains those who remain susceptible to the infection, and the infected group consists of those who not only have the disease but are also in the contagious period of the disease.\n",
"\n",
"\n",
"Combine with a contact network approach, this model can capture contact patterns (family, company, friends). Each vertex represents an individual in the host population, and contacts between two individuals are represented by an edge that connects the two. The probability of transmitting the disease from an infected to a susceptible individual along one of these edges or contacts is $\\beta$ (=**mathematical modeling**).\n",
"\n",
"In order for a disease to begin spreading through a network, the disease must be introduced into the population, either through infecting a proportion of the population or through infecting one individual. As time moves forward, the disease will spread away from those initially infected, and two things may occur simultaneously at each time step $t$. First, each infected individual will spread disease to each of its contacts with a probability $\\beta$. Secondly, each infectious individual will recover at a rate, $\\alpha$, at which point the individual will then no longer infect any of its contacts. After the disease has run its course, we can determine how the disease affected the network by calculating various quantities that help us better understand the outbreak.\n",
"\n",
"###### P. Van Mieghem, J. Omic, R. E. Kooij, _“Virus Spread in Networks”_, IEEE/ACM Transaction on Networking (2009)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"### 1.2 Introduce the infection\n",
" \n",
"We denote by `state` a vector containing the disease status of each vertex where Susceptible=0 and Infected=1. Then `state` is an `Array{Int32,1}` of length the number of vertices. This array in addition of a graph (represented internally by an adjacency matrix or an adjacency list) will be the data structure of our model.\n",
" \n",
"In `Array{Int32,1}`, `Int32` refers to the kind of data in the array, here 32 bits integers, `1` refers to the dimension of the array, here we have a 1-dimensional structure so a vector"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 2 (written): What do you think/predict about the influence of the initial number of infected people and their locations on the evolution of an SIS model epidemic ?\n",
"\n",
"> Plus le nombre initial d'infectés sera élevé, et plus l'épidémie va se propager rapidement. De plus, plus la répartition initial des infectés dans la population est uniforme, plus la propagation de l'épidemie sera rapide."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"### 1.4 Simulate and understand the epidemic\n",
" \n",
"In the SIS model of this project, every disease is characterized by:\n",
"\n",
"* The infection rate $\\beta$ representing the chance of infection when being in contact with an infected individual.\n",
"* The curing rate $\\alpha$ representing the chance of being cured of the disease.\n",
"* The effective spreading rate $\\tau=\\frac{\\beta}{\\alpha}$ representing the capacity of the disease to spread. More the disease infect easily ($\\beta$ high) and less it is cured easily ($\\alpha$ low) more $\\tau$ can be high.\n",
"\n",
"We are now willing to understand what are the influences of these parameters as well as the contact network shape on an epidemic."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 4 (written): The function `SIS` you implemented launches one run of an SIS model on a given contact network. As it makes use of randomness, one run of spreading is stochastic. Then what simple method can you propose to provide a prediction of the disease spreading on a given contact network ?\n",
"\n",
"> Pour obtenir une prédiction d'un modèle SIS, on peut simplement executer la simulation un grand nombre de fois et ensuite tracer la moyenne de ces simulations."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Question 5 (code): Implement the function `Simulation_SIS` (respect the header and the specifications).\n",
" \n",
"###### The corrector should be able to write `predictions, taus = Simulation_SIS(net, nbinf, betas, alphas, t, nbsimu)` with your code."
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Simulation_SIS"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\"\n",
"Take a contact network, different diseases (defined by different parameters alpha and beta), a number of initial infected people and process nbsimu simulations of SIS over t time steps. You will provide the prediction of the percentage of infected at each time t as well as the spreading rate of each disease.\n",
"\n",
"* PARAMS\n",
" - net (LightGraph): graph representing the contact network\n",
" - nbinf (Int32): number of infected at the start of each simulation\n",
" - betas (Array{Float64,1}): array of infection rate on edges\n",
" - alphas (Array{Float64,1}): array of curing rate on vertices\n",
" - time (Int32): number of time step\n",
" - nbsimu (Int32): number of simulations\n",
"\n",
"* RETURNS\n",
" - (Array{Float64,2}): the prediction of the percentage of infected at each time step and for each disease. The first dimension contains the time steps and the second contains the diseases\n",
" - (Array{Float64,1}): effective spreading rate for each disease\n",
"\"\"\"\n",
"function Simulation_SIS(net, nbinf, betas, alphas, t, nbsimu)\n",
" taus = zeros(length(alphas))\n",
" prediction = zeros(t+1, length(taus))\n",
"\n",
" for (i, (beta, alpha)) in enumerate(zip(betas, alphas))\n",
" taus[i] = round(beta / alpha, digits = 2)\n",
" for _ in 1:nbsimu\n",
" state = new_state(net, nbinf)\n",
" _, X = SIS2(net, state, beta, alpha, t)\n",
" prediction[:, i] += X[:, 2] ./ nbsimu ./ length(state)\n",
" end\n",
" end\n",
"\n",
" return prediction, taus\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 6 (written): Run the 2 scripts below and describe what you see. Conclude on the influence of $\\tau$, $\\beta$, and $\\alpha$ on an epidemic we can model with SIS.\n",
" \n",
"> Il semblerait que plus $\\tau$ est élevé, plus la limite du pourcentage d'infectés sera élevé.\n",
"> De même le rapport entre les valeurs de $\\beta$ et $\\alpha$ semblent impacter la forme de la courbe, pour de petites valeurs la courbe sera plus \"douce\" que pour des grandes valeurs (cf les coubes de même $\\tau$, mais de valeurs $\\beta$ et $\\alpha$ différentes)."
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"data": {
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UqCDOwrBmmtHTwcSGIFIFSHGkKUcf09NgzNQ23bOHjh2iYMOAwquqCBVeRSoypGs5S+g5OAAACKl1ZZvKji2vK9sUmzY2s+fkuJSrfCWM/YDbedKrjedM3XTBJBr80pGKJK8iueTg96sIqio2tkYED9iUdYK/cvBXAACwJlqf+uu3YGWFBslx1NNwzOuvFMzd9QRNSMHWBa/CGGjWSFMa8tf8RFJNWUpL0TqKNdKsib68uh2UoeiURbcsuRTBKQUzrhJQG5MuryoBNXj/QetoKEPJq+gSOF0yp0/ScFaG4iiCBLSOAgTBGijWfN4L+9sZFeQpCfir+GBNUeGhKkKCANpETpfIBdtpfH5fi/UIEUS+ct5d5HcX+QN1oi6RC146fapGY2V5uxRMooFaQXQpuiTOmKE1ZOj0SVxjhVhBYoMkOmU5oMbkGlrTQiM4JNcpH2OgtYmcNo4NHqd///4fd4GFeQt6Fqx9dhtSUf+ncxhjW9bicCJsG+4if8nqWtCsfUJyy7pkTcqYWGsvY8dt3A8W2cFUpwiQ5shgMQcI4PP59Ho9QVzO74ZUpAhQFVQQTDwA0Drq3NTehoIFVsNJnxJQYgtM5u76c2+6L0zhVcklsyYmfO3JIfG+muLDH5cd+0JrSM4suDu95xRBIs5dHjbclIDqKvQhCLgYhothWBN94WQfAVCCckBVeJWkSU0sE4F4Qi7M2x50kUTYp0+furq6cBwcN422AW8Zf/Ljipxbk5saOUH4S/bIIEiC1lLg0p+CXOSwFMHoKSaCGYUgCWOWzpilu+wjBOs9bRjSRTmq95w5+EF92eaM/NuvunW5KbZncLsgeSMZRhCto+L6myN/3gsgWZJjyQtUozGslXAivFL+auHEh2U97k615rfHW0Wsw4FQrixcfWb/Yln0dB/w0KBr3sY9P7EOR5blysrKhIQEvT70tLSCIOzdu9doNLaHiixOhFeEt4nHFpdl35KMsyB25RTJV3Lk/04f+I8xpnv+iGcSs8bh6T2xjmjChAlbtmyRZfnrr78OOel2SUnJ7373u8zMzNra2tzc3FWrVtF0NJMR/md2+QSHdHRhabcbEttbkxHW4YgB2/Edb6/7cJitctvwG5aMvu2LpG7X4CyIdVAvvvhiVVVVz549z7fD3LlzJ0+evGnTpoMHDxYVFa1atSqS4Z0L1wgvk+xVji4sTZ+YED/IEu1YsA7J7y531OxtqN7rqN7t91RkFtw17p4fdKa0aMeFYVdqzJgxF95hxYoVP//8MwBAq9XecccdK1asuOOOOyISWmg4EV6msrV1sX1NScNjoh0I1sF4HIWlx5ZVnPqWAMCaPDg2ZUhGr9ssCX1JCnf6wNqM4qiVK05H5lxc3iBScwnd0Fwul9frzczMDP6YlZUVTIpRhBPh5QjUiY6j3kFzor+wMtZRKJKvsvC70qOfB7yVmQV3jb1jhcGSHe2gsE5LbagNHNwcmXOx3fLBpSRCnudBs0m3OY4LbokinAgvR8l3tekT4iPcmR7roJx1h0uOfFpZ+F1MYv/uA2ekdr+OIPG/Oyy8uB79uR79ox1FaAkJCRRFORyO4KTbdrsdT7rd8bjP+Pl6sdeDGdEOBGvXJMFddXp10aGPoCJkFtx97QNbOV18tIPCsOijKGrQoEGbN2/u3r07AGDz5s3Dhw+Pbkg4EV4iBEq+q826ISn0JJwYBoDIN5zY+feKkytSciYNGPdGbEqUZ9bHsAj7/PPPy8vLHQ7HqlWrCgsL77vvvtTU1CVLlixdunTbtm0AgGeeeeaJJ57QaDSlpaXr16//xz/+Ed2AcSK8NPX7XAQF4vriRd2wEFRFOHNgyel9C1O6Xz9x2mZcBcS6Jq/X63Q6H3zwQQCA0+lUFAUA0Ldv33vvvTe4w5133smy7MqVK41G49atW1NSUqIZLk6ElwQqqGxtXc/70jvu3KFYmCAEy49/dWzH32KTB1199/cGS7doR4RhUTNjxoxzNw4dOnTo0KFNP06ZMmXKlCkRDOpCcCK8BNWb7YZ0ranb5c9XiXVK1UXrjm17k9VYhk/+jzV5ULTDwTDs0uBE2FqKX63a6Oj7R3ynj/3GUb3n6NbXJcHZa/gzabk3RjscDMMuB06EreU46jF312vj293Ch1hU2Kt2ndg1P+CuyB/5XFruTXg6NAxrzu/319XVJSYmnm/Sba/Xu23bNrPZPGzYsODKplGEE2Fruc/4Lbl4EYCuDiFYU/xj4Z73RKGh5+A/ZObfiQcFYlgLV1111Z49e1RV/eqrr0JOul1YWPi73/2uf//+VVVV8fHxa9asaRpfHxX4Nra13EV+S4/QtzZYVwChXHrs858+GXtq9z96DJo5cdqWrN734CyIYeeaP3++w+HIzc093w6vvvrqnXfeuWbNmt27d9fW1q5YsSKS4Z0rjP+MRVE8efJkUlJSYmJiyB0URSkqKgIA5OTkRHcNjovibRIAQBPb4RfaxS6PvWr3wfWzOV38gPFvxaeNjHY4GNauDRlykbGzq1at2rhxIwCAZdk77rhj1apVU6dOjURk5xGu9LN///4bb7wxNTW1uLj4j3/848svv9xihxMnTtxwww0WiwUA4HK5Vq9enZ+fH6Zgrpz7jM/cHVcHuyJJcJ3Y+U7V6TUFo+Zk5kdzgnwMa70aX92phjOROdeQ5AF65hL60judTr/fn5HRODlXRkbGunXrwhNaa4UrET799NNPPvnk//zP/5SVlfXp02fq1Kktqslz586dOHHiwoULAQCzZs2aO3fu8uXLwxTMlXOf8Vvy8APCrgUhWHp02bHtb2X0un3iA1toBt8JYR1Gja9uQ9nWyJyrd1zeJSVCURQBAAzTuNwKwzCCIIQlslYLSyKsrq7eunXrypUrAQCZmZkTJkz48ssv//KXvzTfR1GUptkEUlJSbDZbOCJpK+4if+bk0A28WKcU8FTu/fEpqEqjb/vSHNcr2uFg2KUZmNR3YFLfaEcRWnx8PEVRdrs9OOm2zWZLTk6ObkhhSYQVFRVmszk2Njb4Y3Z2dnl5eYt9/vrXvz700EM+nw8AsHHjxqVLl57vaAihM2fONC1YFR8f369fv3CEfT6BOpGkSY0VPyDsKioLVx/c8EJ232m9hj9NEHiNEQxrSxRFDRs2bMOGDT169AAAbNy4cdSoUdENKSyJ0O/3c9xv4+20Wm1VVVWLfRwOh9/vD9aRA4GA3W4/39EghOvXrw92qwEADBs2LDv7t4XcJElCCEmS1Ja/wNnsR726LNbr9YbvFB2R3++HEBJEp5puTuIdx7e+GPCUD5i4xBSX7/MFoh1RCMHbRyzy2u2VhxBGO4Sz/Oc//ykuLq6vr//000937dr12GOPZWZmLlq0aPHixfv27QMAPPfcc9OnT6coqqSkZNu2be+//35rDosQuoxyWKfTUdRFbmfDkggTExNdLhdCKFhKOhyOc5ebeuyxx5599tkHHngAAPDJJ5889thjx44dC3k0iqJmzJjx/PPPh3w3mAib5902V1XpjOttMRqN4TtFR0QQhF6v70yJsLpo3YFfZmcV3D3q5g/b+Xrx+G9jtLTPKx/1AektGI3GmJiY5557LvhjcFDA0KFDmwYLTpkyRafTrVixwmQy7dix43wjC1ogCCJM1z8siTA7O1uj0ezfv3/QoEEAgO3btz/77LMt9nE6nU3ZMZg4wxFJG0DAXRzodnOUm7CxsFJk/6GNL9kqtw+/cUls8uBoh4NhHVvIsRADBw4cOHBg048TJ06cOHFiBIO6kLAkQq1W++ijj86aNev1119fv3693W6/7bbbAABbt2596KGHCgsLAQBTpkx54YUXKIoiCGLOnDntZxryFvy1Aq0hOUu7rh9gV6Kh9sCetY9bkwdec+9PNIv7BmNYlxOu4ROvvfba/Pnz33nnnbS0tE2bNmk0GgBAfHz8jTc2Tkz897//fdGiRYsWLQIATJs2bebMmWGK5Aq5z/jN3XHh2DkhqJzYNb/kyGcDxr2Z0v26aIeDYVh0hCsR0jT93HPPNbURB/Xs2fOdd94JvuY47sknn3zyySfDFEBbcZ/xx/U3RzsKrO0FvFW7//sYzRrG3/uTRp8Q7XAwrBOy2+1lZWUFBQXBulALZ86cOXDgQPfu3QcMGBD52JprX49Y2x0EPMV+PKdM51NT/OP6ZdclZIwZNeUznAUxLBwghLfccsvgwYPPHT4HAPjoo49Gjhz57bffTpkypcUo88hr1zN8Rp2vWmAMNGvEV6nzQFA5sevdsuNfjLjxg9iUi8yIiGHYZXv33XcHDx68dWuICW4kSZo9e/bnn38+fvz40tLS/Pz8WbNmNU2xEnm4RngheIrRTsbvLt+w/Aa3/fj4e3/GWRDDwqekpOTDDz88d5bpoJ07d0IIx40bBwDIysoaPHjwmjVrIhvgWXBd50Lcp/0JQ2KiHQXWNmpLftn749N5Q5/oPuBhADrP8EcMOxdfL7qL/JE5V1x/M609a8Q6QmjGjBl///vfDYbQPQ2rqqrS0tKaRiGnp6efO+lKJOFEeF4IIk9JoMfdqdEOBLty6NSe94oOLcXNoVgXIftVX2WEZrK2FpiA9qwtCxcuTEtLmzhxoqIoIT8iy3Lz2V5omg7r7GAXhRPhefmrBM7CMAZ8iTo2SXDtXjtLlflxU9fifjFYF2HqpjN1u4QVIdrW66+/PmLEiEcffTQ499tLL730xBNPjBz520KeycnJzRdaqK+vHzw4mhNZ4GeE5+WvFvRpIbr8Yh2I23Zs/bJrzbF5Y27/CmdBDIuM119/fcKECYMGDQpOLlZQUBBcg0GW5WAdcdCgQfX19WfOnAEABAKB7du3jx49OooB4+rOefE2SRsfxilMsXCzVe7YtWZG/9/9b1ruTdGOBcO6kPvvvz/4QlGUxx577K677gquR3vHHXfk5eW9+eabVqv10UcfvfPOO2fNmvX111+PGjWqf//+UQwYJ8Lz4u1i/AA8lL6jqin6Yd9Pzwy57r3EzLHRjgXDuiiSJN988824uLjgjw8//LDVag2+fueddz799NO9e/dOnjx5+vTp0YsRAJwIL0CwSdo4XCPskMqOf3ls2xtX3fq5JaFPtGPBsK6LJMnmCwc1TbEZfGvatGnTpk2LRlwt4UR4HggIDkkThxfj7XhO7flXyZFPx9yxwmDJvvjeGIZ1eTgRhia6ZUpDUhzuTNSRIKQe3PCXhuo9V9+1GneNwTCslXBBH5pgxz1lOhhFDuz47iGfs3jMHStxFsSw9qCqqurnn38OBAIh3z1y5MhHH320ffv2CEd1LpwIQ+NtIm4X7UAEf/3mr25ltTGjbvmM4UzRDgfDMKAoyu233z5hwoTKyspz3120aNGECRN27tx5//33P/PMM5EPrzmcCEPjbZI2HifCjsHjKNyw/IakbtcMnvguSeIllDGsXZg3b97YsaH7bIui+OKLL3711VeLFi3atGnTwoULKyoqIhxeczgRhsbbRNw02iHYKrdv/vr2gpHP5494NtqxYBjW6NSpU8uXLz/f+ko7d+6kKOqqq64CAKSmpg4dOvS///1vZAM8C+4sE5pgl7S4abTdqzz17cGNfxl2/aL49FHRjgXD2hFvwxl71c7InCst96YWzyMghNOnT58/f37I9XgBAFVVVSkpKU2TbqemplZXV4c90PPDiTAUBIQGGT8jbOfOHFhcuPffV9263BJfEO1YMKx9EfkGZ92hyJwrOXtCi0S4YMGC/Pz8cePGnW/SbVVVSfK39kiKomRZDm+UF4QTYQiCU2L0FMngduN2Cx3d+npN8Y9X3/29zoiXB8GwluJSh8alDo3W2efNmzdmzJhLmnR76NCoRQtwIgxJsOOeMu0XVOW9PzwZ8FSMvfMbVoNXi8SwdmfRokWiKAIAVFVdsmTJyJEjg6vPe71eiqJ0Ot2QIUMcDsfJkyfz8vJ8Pt+2bdvefvvtKAaME2EIfL2kwZOrtUuqwm//7kGGNY6+/WuKxt8RhrVHN93UOIdIKX4AACAASURBVM29oihTp06dNGlSVlYWAOD3v/99cNJts9n8+OOP33HHHY888siqVasmTJjQu3fvKAaME2EIvF3ENcJ2SJEDO757gNPFD7l2AUHiv7oY1t6RJPn+++8nJiYGf5w1a5bFYgm+fuONNwYPHrx379777rsv6jOO4tIkBN4mWXoYoh0FdhZF9m//5n6DpduAa/5GEPjxLYZ1ACRJzpgxo+nHiRMnNr0mCOL222+//fbboxFXS7hACUHANcJ2RhY9W1bcZbTm4CyIYVibw2VKSwgi0SlzVpwI2wtJcG7++vbYlMEDxr+FsyCGYW0ON422JDbIrIkhaSLagWAAAKBIvq0rpyZmju191Z+jHQuGYa3l8Xi+++47SZImT57c9IywiSAIW7dubfqxe/fuwd400YITYUu8TdTgdtH2Aaryzu+nxyT2xVkQwzoQh8MxZMiQ/v37WyyW559/ftu2bbm5uc13sNlskyZNuvXWW4M/Tp06FSfC9gVPt91OIAT3rHucojX9x70R7VgwDLsE77//fl5e3sqVKwEATzzxxLx58xYvXtxiH47jvvzyy2hEFwJ+4tISbxe1eBBhO3B40ytiwD70+kUEQUU7FgzDLsHatWtvueWW4OspU6asXbv23H0ghGvWrPnxxx8dDkdkowsB1whb4m2StZcx2lF0dSd2vmOr2Db2zlV41DyGXYbDbvfamrrInOuR7KxY9qxWtOCc2sHXqamptbW1qqpS1Fl3tOnp6R999FF9ff2RI0eWLVs2adKkyEQbEk6ELQk2vDZ9lJUc+az8xIqr7/oWL7GLYZdHVKEzUtNYqwi12IIQalpZgiAIhBA6e5+0tLTCwsLg63/961/Tp0+P7nqEOBGeBalI8shcDF7cNWrqSjcc3/H21Xd+w+niox0LhnVUQ6wxQ6xRm4k3OTm5rq6xPlpXV5eQkEDTZ+WapjQJALj11lv/+Mc/Op3OmJioBYyfEZ5FcEhcDENQeOxEdHgcp/b88OTwGxbrLVnRjgXDsMt0zTXXND0XXLt27fjx44Ova2pqeJ5vsfOuXbssFkvT1GtRgWuEZ+FteLrtqBH8ddu+ua/f2FdiU4ZEOxYMwy7fzJkzBw4cOHPmzJiYmIULF27atCm4fciQIfPnz7/jjjvmz5+/a9eu/Pz8mpqaZcuWzZs3r3kdMfJwIjwLb8OTq0WHqvA7vnswu++09Lxbox0LhmFXJCUl5cCBA8uXLxdFce/evd27dw9u/+c//zlo0CAAwF133WU2mysqKgoKCnbs2JGfnx/VeHEiPBtvk/TJmmhH0eUgpO7+7yxTXK+eQx6PdiwYhrWB5OTkp59+usXGpjEVKSkpDz30UMSDOi/8jPAsgl3UJuAaYaQd3vSKqvADxr8Z7UAwDOuKcI3wLLxN0sThRBhRZce+qCvd8Lup/yVJ3FkXw7AowInwN1CGsl/lLLg4jhxH9Z6j214fe+cqPGQQwzoTu92+YsUKSZJuvvnmjIyMFu8GAoE1a9Y0/di7d+9evXpFNsCz4ET4G8EuaawMQeKxExES8Fbt/H76oAl/N1iyox0LhmFtpr6+ftCgQVdffbXFYunfv//WrVtbdIdxOBxTp05tmnSbpmmcCNsL3oHbRSNHVYSdqx/uOfgPSd3GRzsWDMPa0qJFiwYNGvTpp58CAFiWnTdv3tKlS1vsgyfdbqdkj8KacbtoZKC9Pz5lis3tPnB6tCPBMKyN/fDDDzfeeGPw9Y033vjDDz+cuw+E8Msvv1y1alXTHDRRhGuEv5G8CmvEFyQSTu5awHurx9z+dbQDwbDOSSmpl/ecicy5NJMGECZt8y3V1dXJycnB1ykpKXV1dYqitJhlrVevXmvXrq2trZ02bdpnn3120003RSbakHC5/xvZp+iS8CDCsLNVbCs69NH4e38gKdwQjWFhQdAUoY9UaXZOv4rgRNvB18EJuFtMHJOenr5///7g68WLF8+cORMnwvZC9ipMD3xBwksM2Pes++Pgaxdo9InRjgXDOi0qPZZKj43W2ZOTk2tra4Ova2trExISWqzB1NzkyZNnzJjR0NBgtVojFWBL+Bnhb3DTaLgFF53PLLgrMXNstGPBMCxcJk6c+P333wdfr169euLEicHXxcXFPp8PANB8VaYtW7ZYrdYoLj0BcI2wOdmnMga8GHoYndr9D1UR84c/E+1AMAwLo5kzZw4aNOj++++3WCyfffbZli1bgtvHjBkTnHT7nXfe2bJlS25ubn19/cqVK9977z086XZ7IXsVBtcIw8ZetbPo0Efj7llHkPgiY1hnlpiYePDgwZUrV0qSdOjQofT09OD2JUuW9O3bFwAwbdq0jIyM8vLyvLy8l156KScnJ6rx4kT4K6ggqEBag2uEYSHyjt3/nTX42ne1hqRox4JhrdIgghJvYwuengYsBbw+QhGRXwGCCtwSognQw0z0NBMMfsR0jri4uBkzZrTYOGnSpOCL+Pj4O++8M+JBnRdOhI1wdTCc0N4fnsrIvyMx8+poR4JhoQUUcMaDTrrQoQZ0yIEONwCPjLKNjTNN+RUgqQAh1qpRdTTQUMDCEhIEp9ywzIdyjERBDJFnATEsYeGAmQUWljD+OiZZVEFAARQJrFzwD6E/f0kTPBGvoiTteSe5ggg4JeAUkVMETgm4JeSV2/pytEsqAj9XIQDAmGSCbdObD1z0N8KJMHxKjvyf4K8bcdOH0Q4Ea6f8CvDKIEl78T0vQIGg1IfOeEC5D9kEYBeQXQB2AYkqMLKEkQEmBphYYGEJl/RbTw27AM540Gk3aBBRjonoaSb6WolH8oh+VqKbsWUi8nq9RqOxxUZRBSdc6LgLnXKhYi9yOYBLAm4J+n5NThwFdDRQIGgQg3+QioDunMImmC91NOAowJHAKYEsA5FjAjkmIl1P2AVU4QflPlTmA7U8MjEghiNiWBDDAQtLSOoVXbqOQlLBW4dVAMCAODq2TRdQx0V/I8mnsAZ8Ndqe311+bNsbY25fgReXwM61x4aWnIJfl0CGBE4RpOiJND1I1xNxGmCggZklzCwwMEBFoDYA6nhkE0Adj3gVBB9ixLAEAMCvoNMeUOFDyTqiuwlkGIhELcgwEAPjQCxHsiTwK8grA48EPDLwySj4qaAcI7gnh+xuAumGy+ytwVGgfyzRP/YSPi2ogFdCHKd5dhRUUOxFRR5U5AE1ARTDEX2tINNAZhhAio6gz64P9e8a45+1NPjpurCU0rjob4RrhOGAENz341N5Q58yxeVFOxYsjMp96HAD4CiQZwHp+rNSglMEBxzooAMJamPbYKyGsLBgZz1acgp6ZfBwT/LobUyyDogqqAqgKj+o8COHALwycEqo1Ae8MqAIkKABaXpiQByI15AGGggqAAA4JQQA0FBEDxORbbpAc1n7mklfQ4GL9kbQUCDfQuRb2lfknRUu+hvJPoXBNcK2Vrj33wjBnAEPRzsQrG34ZGATgg2PwC6g4y6034722xFLgX5WQobguAv5ZZBnIfIshEcCBxuQQ0D9YokBsYSBBmW+YNsgdEkg10y8PYwal/JbPYyjQLaRyDaCS8lbOE9gbQAX/Y0kr6Kx4hm/2pLHUXh6/3/GTf0vQeBOdR2YBMEvVWhVGfy2DPplEKchErQgTgPiOCLXTDzZmxwYSyTrftvfJYGTLnTKjXQ0mBdL5piiOkAMw1oBJ8JGsk8xZuguvh/WOhDKe3/4Y5/Rf9GZ0qIdC3YWjwwqfKjSD6oCqMIHFIQMdGOqijm7A4KKwNZatLYSFsQQt2SSL9xEZ53Tf+RcFhYMTyCGJ+D0FzkajWbBggUJCQnRDiSMAoFA+A6OE2Ej/IywbZ3Y8Y7WkJKZ346GCnVWXhnwCvApqMV2HU1wJIAAFHmC4wHQ4QZ0xIlkCDL0RJoepOqJDANgSSL4pA0hUOxtefAxycTfhzOJV9afEwu3Tz75ZNWqVdGOIlxUVUUIxcTEvPPOO2E6BS76G+GJRtuQs+5w6bHPr7nvl2gH0glBBA47idM18KgTHW5AR53IIwEdDYxMyxqYX0ESBAQA3YxEXyvR10pMySL7xxJt2+8caw9yc3Off/75aEcRLrIsq6qq0YSxaywu+hvhiUbbCoLK/p+f6Tv2FU4XF+1YOg+PDH6qhGsq0H8roIVhhySgPlbimVy+oPhH9uhmyprApeWxWb2YtO4E3ThMBUmi6rKpPjeTkkVq9NGNH8OuFEKq16W67dDj4PIGE1RbJi+cCAEAAEGk8CpzgfkesFY7setdrSE5vect0Q6kw2sQwc56tKsebq1De21oZCJxQwb54gA6Dvg0Aad/y3eB/Zs0eYN0198PvS6p9IR/73qlvpJJTEeyqLocCCqUOY7UG5Xacjo5S5M3SNNzEJuRC8iL912Cfo9iq1bs1ZQljk3vQXDhbRtFsqQ4amHAA30e6HOpPjdBUZQ5jrImUOZYyhxH0AwSecj7oeBHvA8hQOqMpM5I6o3BAlH1OtWGOqWhTm2oQ7JExyZRsUm0NYkyxwIAVKdNriuXa8uUugoki1xuf03uACrmEp6oQSEgHN8tFB0jEtPouBQ6LpmKTWqzshghxV6tuhtUtx16naqnAfrcgGYAAASrISiaoGk6MYNJ6UbHp17gpKrHKVcXy7VlBEmRemPjJdIZod+rep2qywa9TtXdAGia1BpIrZ7UGkitgdBoCYomNDpAkKTWQBpMLW6bkCSIJcelM0fEkmNI5IMbCYYFNEtbE9hu+WxmLyYxHTTvFAVV1esCqkpodKTOcNkXBvI+4fhu/8GtcsVp5HWSeiNpiqXMcWxWPqE3XfZhz/XbNV22bNnjjz9+0Q80NDS04enbCdmvMjoK98S+cm778eJDH42/76doBYBURamvVOw1qqNGcdQqjloAVSatO5uaw6Tl0HEpIGQfRghlW6VcVaw665EkIEUBAEDBT2oNml6DuW75gDx/awFCiqNWri5RXTZSb6TMcaTRQpmspPYS/v17ZVDuQxV+UOlH1W7JW1NZ5BACAT7PQvSKIV4xKgVWDxNwwzMu9aDbX1/la6jVj7w+cfb7lKlxCTfd4HEAACQJcnUpodFS5timAJAiS8XHhFP7nF/9U22oY1K60QlpdEIak5hOxyYjWVRcdrWhTnXbVadNsdco9ioAQLC4V5x2ubqYjklgM3KZzJ50bDJljqVMVrLVxRCSJSRLSBYJmmnxKbm2TDi5Tzy5Tyw5TlniKL2J1JtJvYk0WpCoytUlqtOmuu2qy46gSrAaUqMjtXpCowcEAQNe6PfCgJdgWABVgtPS1kTKmkhbEwmGFU7tVxx1akMt9HsASZI6I5OYQSdlBO8DxFMH3KuXklq9pudANqsXQTOAokhOCwAgtAaS1RAaHanREZwWBnz80R38oW1S0WE2uzeRkqPUVwjHdyv2GtVtJ/UmgmZJrR7QDMFwJKcFFEXqjARJEpyOYDk6PpWOT2US0lrcSSCRVz0NUuUZueK0VH5KriwiDWbKHEdZ4kiDhTLH0kmZQJEBAFASgKogWeIPb/Os+0x11tMJaUxSZtMBCYYDBKHUlslVxQiqTGo2k5wFIIRl3qZLROpNlCmGMseRJivbrRdSFcT7YcCrOGphwItEAakKEgIAQRjwQb8bIUTHxFOWeNJkVWxVcnUJm5rD9ehrnHA3qTM2fa1AkeT6KvH0Ie9Py6Hfy2b1Imi6MZ373KTBDCgK8QHI+0iNjtDomNQc3YCx2j4jLnpfpThqxVP7+cPbpNITXPe+moLhuusf0CWktG0tsLnf1hHeu3fv119/3RiHonzwwQc0TV933XXJycn19fW//PKL3W6fPn36ggULwhTK+cyePTsmJuZ8LeCSJCGEOO6Knnv4q4XCZZUDnu1+JQfpanw+n16vb754CoLKhuU35PR7MLPgrjY8kWKvUT0NBMOSOgPBaAiWIzVn9e9FsiSVnRKLDotnjkjlpyhLPB2XTMcm0bHJdFwSAIRUWSRXnZEri2DAS8UlkzojqdERnI7U6JAiy1VFcm05ZbIyqTl0XBLBagmaBgCQGr3qaRCO71Ya6jQ9B2oKhrEZudDvhX6X6nMH/8HL1SVydQmpNzLJ2XRsIvR7VLdd9bqh2wEFf/MgCYalE9OZxAwmOYtOylStqce91AE3u8fJHGhAdr80HhUN54/39hxLcRWL5iROq9HptMGLS9A0qTdTBjNpsJAGs8RoLf1GXF6hAP0euaZUqa+U6yuVunLFUUuwHGWOp4N1r5h4OjaFjk85K2NBVa4plcpOSRWn1YY61e1QvU4k8qTBQlA0kgSkysHCtOkTwUoAUlUk8gTNECxHMBySRSgEKL2Z1BtJvVlx1BIUrckbxOUN0uT2v0jhiFDoOxgAoBAgSIpgQ5cASJEBVAn2nMdLCMnVxcKpA3JVMVJloCpQFAAAiPdBkUciD4UAEnlSo+NyB2j7XaUpGEZqdGdNsQZV1e1AqgJ5P1AkJEtQ4AFUYcCLoBo8gmKrUmzViq2S1OgpSxyShGByAjRDGSxMajabkctm5DLpPVp524RkSa4tU2rLkSz+ukUEgKDjU5iUbMrSNg8jkMgrTpvqsqluB21NZLN6EcxFhpZBn0sqP41UmTJZKUs8ZYxp3vAABT/i/WLx0cD+zVLREa7nAN3AsUxadwAAEngEVQCA6rLJFaelitNSeSHBsFx2b23fUZr8IQSricAzQqL5AolN/vCHPxQVFa1cuVKnayxxZFl+5JFHXC7Xt99+G75oQopAInSd8lVutPd+NOtKDtLVnJsIT+5eYKvYNvq2L658mDMUAuLpg+LJ/cKpfcGWLiiJiPcjSQiWp+DX0pZgNZD3M8mZXE5fLqcPm13QIk2eddiAT3HUIN4HBR4JfigEAEWxKdlMSrcLFMSq2yEc3y0c3y1Xl5J6I2mMoQxm0hhDWeKYpCwmtdsFSrGAAtwScEvI4RWry8p8VWWgvtzYUJYYqNIRUA8kDZAoAlAkyaRmc9m9uewCNjPvwlkh5IyXEYYUGfpcSFUIRtOY6ujfptCDAR8AgKColr8IVFWfB/rd0O+hzLF0fGqEw740CAGEmhfol33lVZdN9TgJlgu2VTa/Vl0NDPj4I9v4/ZsUew0AgNBoCZICAJDGGDYjl03vwaTnUqazFumNTiLkeT4mJmbLli1Dhgxpvr2qqiotLa28vLxpcanIiEAirN/ncp305d6LR7xdghaJ0Oss2vTllHH3rNMZL7F0QwjyPrWhXrZVKnUVSn2FXF+p2Kq5bvlc3iBNz4FMclbIzwVLWySLpM540TvWyCjxor12tNeG9tjQMRdyioAmgZkBZpaI1YCeZqKnmehpAb0sRLbx8tfuaQ+JsGvCVz4qotNr1OVyiaJ47nrBwS11dXURToQRgAcRXiGE4L4fnsof8dyFsyBSZLnitFh6Qio5rjTUId4HAz7I+0idgYpJCD5N0RQMN/wujUnKvGhu+/Uh/OU/im8TXhmsq4TflKIfq6CGIobEE4PjiNn9yb5WwsqBtl0sBsOwcAhR+ickJCQlJb388ssrVqxoSsKKorz44otarbZnz56tPPS+fft27dqVkZFx/fXXk6E6qiGEfvnll8LCwvj4+AkTJlgslsv+Na4QToRXqPjQUoKks/v+vmmLXFOq1FXAgBfyfsj7YMAr15TJVUVMYjrbLV/bfzQdn0rqDKTWeCWdyqKoJgC+L4fflMGttWhUEjElk5w3jE7R4Q5XGNbxhCj9KYr65z//effdd2dmZl533XVJSUl2u/3nn38uKyt77733WtkysGTJkhdffHHq1KmLFy9evnz5Z5991mIHSZJuueWWsrKysWPH1tXVCYLw+9//PuShIkDyKbqkrrGQSRgEvFUndv597J3fAECoXie/b4N/909ICDDpuaSusZc2FROvGzCWzewZottCh3LAgb4vR6vLYZEHXZtGTutBLh9HGrvuEx8M6wxCV4Nuv/32rVu3/u1vf9u8eXNVVVViYmKfPn0WL148YcKE1hxUUZSXX375k08+mTBhgsvlysrKOnr0aO/evZvv8+677zocjn379l3h4702gWuEV+Lghj93HziDsXntK16RSo5qe4+w3DqLy+l9vm5+HY6ggq21aHU5XFWKaBJMSCVeHEBem0biZk8M6xzOW/oPHz585cqVl3fQQ4cO+Xy+cePGAQAsFsvYsWPXrl3bIhF+9dVXTzzxxJEjR+rq6oYOHRofH39552oTOBFetvKTKwPOsp6+fFfxP00T74m9//lwD76OmHoefF8Bvy9Hv1TBfrHEjRnkj9eReXh9OAzrdC5U+kMIy8vLPR5P3759L+mgwUokRTWOQU5JSamurm6xT3Fx8b///e+YmBij0fjAAw988803o0aNOl8YGzZsUFU1+GOPHj2mTJnS9K4sywihkM8gW0/0KqQWyLJ8JQfpamRZ9nvrD6//S4+GHNCdtT61gOC0CgCgg1/GE27wfTn4vhKcdIPxyeCmdPDv4SCWQwCooH38crIs47+rUYGvfFQEe402JZRLRdP0uX0/W+4TciuEcO7cufPnz/d4PKmpqZWVlQCAJ554QpKkRYsWXfTECKHmJyZJEkLYYh9Jknr06PHJJ58AAN58883Zs2dv2bLlfAfked7pdAZfe73e5keDECKEzj3+JUBADaikBlzRQboelfcf+25arNeUeutLTE5fBADqyBewOgA+PE0sKyFUBCanoRf7gqsSUVPjZ7v6zSCE+O9qVOArHxXwV+E7RehE+Morr7z11ltPPPGE1Wp97733ghuvueaae++99x//+AfLXqRfe3AymqZ0WFtbO3To0Bb7pKSkjBgxIvh65MiRb7/99vmORpLk9ddff75xhARBXOE4QiWgkiyp0XXsThyRAKFcXyGXF0qVZ6TyQpvjoDu+ZuIftjKGDjy5NgLglyq06CTcUA2n5pArriH7x7b3xk9JktrDk/UuCF/5qCBJUlXVsF75EC2KiqIsWLDgjTfemDdv3siRI5u2DxgwwOfzVVRUXPSg/fr1Yxhm+/btAIBAILBx48bx48cDAHieb2ojnThx4okTJ4Kvjx8/npWVdcW/y2XCCzBdFFIV39bVNX/9veODucKp/bQ1UT/5ntIMz+Cb3++gWVBUwYYa9Oe9at5XyrO71AmpRNndzL9GUu0/C2IY1uZCJID6+nqPxzNp0qQW24Pj/BoaGnJyci58UI7jZs+efe+9986YMeOHH34YOXLk4MGDAQBr1qx58sknq6qqAABPP/30yJEjaZo2m83/+te/li5d2ja/0KXDPWUuBCH+0Fb39x9S1qTYR15m03ODmw9u+EtsyoiEjDHRje5SlfnQl8Xo5yq4ox4VxBDjU4iPx1J4LXUM6+JCJACj0UiSZG1tbX5+fvPtx44dAwAkJSW15rh/+tOf+vXrt3379kceeeTuu+8Obhw2bFhTQ2t2dvb+/fu//PJLCOHmzZt79ep1Rb/HFZB9CmPAiTAE/tBW938/pgyWmHue5bILmrY31O6vPrNmxK3fRzG2S7WjHs0/AtdXw7tyyMfyyS/Hk+Z2MSkbhmHRFzoRjho1au7cucOGDWvq8+LxeJ5//vm+ffu2fn618ePHB1tEm6Snpzf/eEpKylNPPXW5kbcZ3DR6Lrm6xLVyIeR9lltmavIGNX8LqvK+H//U7+rXGM4crfBaT4FgRSmcfxQ6BPBEAfnhGMaAB79jGHa20AlgwYIFY8eOzcvLKygo8Hg8Dz/88Nq1axsaGn76KWrrzIUPbhptDgZ8nnWfBvZvNE2Yahh907mLuJ7cNV9vzkjtMdnn80UlwtbbZ0ePbFGNDJjTj7wxgyRxCyiGYaGEHn43YMCAvXv3jh49es+ePV6v94svvhg4cOC2bdtGjx4d4fgiADeNNkLIv21N7euPAAiTXlhiGDvl3Czotp8oPvzxgPF/i0qArccrYPYe9bp1ymO9yE030Ddn4iyIYdh5nTcB5ObmLlu2DABwJSMZOwTcNAoAkCoKXV/9i2C4+FlvMCndQu6DEDzwy/MFV72gNbTqOXG0bKpBM7aq/azEsduZeDwoBsOwiwldI5w+ffqpU6eCr5uyYGFh4Z133hmhuCKoi9cIIe9zrVxof/8l/fBJ8Y//7XxZEABQdOADkmK79b4nkuFdkqNOdNvP6oOb1X+MoL4cT+EsiGFYa4ROhKtXr3Y4HC02OhyOr776KvwhRZrsVRljZ67yXkBg3/q6N2YAqCb9eYl+5PUXmCab91af3P3uwGvmXfnq8+FQ4kWPblWv+a8yNJ44dht9bVp7DBLDsPbpEmpCVVVVsbGx4QslWiSfwna9GiGSJdfX70llJ2Onv9I0OvACDm74c86ARwyW89YXo6XUi17eD9dVwqd7U0V3Mfou901iGHalzio21qxZ8/HHHwMA3G73iy++2DztiaK4devW5hPNdA6qCAkCdLUFdVRnvWPp/9LxKQl/WtCaBQJrS9d7GgqHXn/xaWYjySOD1w+qH5yCfyygTt/JmPC4CAzDLstZidDtdhcXFwMAVFWtqqpyu91Nb2m12rvuuuuFF16IdIBh1gUfEArHdjV8Pt/4u1uN41v1xFdV+IPr5wya8A5Ft5dZFiECn52Bs/eo16SQh29lknXRDgjDsI7srBxwzz333HPPPQCAYcOGLVy4cODAgVGKKnK6VpdRhNxrPgrs3xA3469sRs9Wfuj4jrfjUofFp18V1tBaCQHwfTl8YQ9M1IK1k+h+VvwsEMOwKxU6B+zatSvCcURL1xlNjySx4bO/wYA38Zl/kXpTKz/lsZ8sO/7VhN+vD2tsrQERWFkK//cgJAB4fQh5Y0bXas3GMCx8QueAt99+m6Kop59+uvnGjz/++MyZM6+++mpEAouQLtI0qnqcjiUvM0mZ1mlzCKq1vy9CcP8v/1Mw8nlOF80lJhQIlhfD1w9CMwteG0xdn36xRTYxDMMug+5WpgAAIABJREFURYjbaoTQ66+/fu7k2jk5OW+99ZbH44lIYBHSFZpG5doy27tPafKHxkz9U+uzIACg9OgyBJWs3lPDF9sF8Ar4rgw+vFlNWSZ/eAr+YwS14yZ6Ms6CGIa1tRDFot1udzqdffv2bbG9T58+siyXlpae+1bHJXsVXVJnHnctnNzX8Nk8y60zdQOvvqQPSoL72Pa/jb5tOUFEuhHypyq06AT8uQoOjiemZJIvD6QzDDj9YRgWLiESYXDFCafT2WJ7Q0MDAABCGIGwIqZzN43yR3e6vlwQ9/BLbLf8i+99tuM75qX2mGyOu+QPXgmnCJ7eqW6pRS8NJBePZqztpZsqhmGdWYib/bi4uIyMjCVLlrTYvmTJEp1O17Nna3sbdgiSV2U76bQywsl9ri8WxD7y18vIgt6G05Wnvskf8Vw4AjufNRWo30qFo8ChW+lpPUicBTEMi4zQlaE5c+Y89thjbrf7wQcfzMjIqKmp+eKLLz799NM///nPWq02wiGGVWftNSqc3Of8v7djp7/CZlx81phzHdr0ct6wJzmttc0DC8kmgMe3q4cc6PNx1KhE3AqKYVhEhc4BM2fOdLlcr7322jfffBPcwnHcs88++/LLL0cwtkiQfZ0wEYqFBxo+fSv24ZdaP1iwudqSXwKeiux+D7R1XKFtr0N3rVfvySE+HktrOmflHMOwdu28OWD27NkzZ87csWOHzWazWq3Dhw+Pi4tmH/pwgAqCMqS5TlX6isVHHZ+8Ffvgi1x278v4OILKkS2v9h37V5KMxJRl/zkJ/7xXXTyampKJxwViGBYdF6oMWSyW6667LmKhRF5jT5lO1BQnV55xfPhq7IN/4XL6XN4Rig4u1egTk7LGtW1g5xJUMGubesCBdt1MZxs70XeAYVhHc97b8BMnTjz++OPjxo276qrGubUWL17cyZZh6mQPCFW3w/7BXMutj112FpQE18k9/+h39dy2DexcZzxo2LeKisD2G3EWxDAsykInwo0bNw4aNOi7775TFKW0tDS40e/3z5kzJ3KhhV9nGk2PZMnxwV8NV91wqeMFmzu2/a30nlNMseHtGPxtGbxqtTKzF/nxWErbSS4/hmEdWOhE+Ic//GHChAmFhYVz5/5WObj22muLiopqamoiFVvYKX6V1nWKB4QINXzyJpOc1coFJULyOAqrTn/fa/gzbRhXCyoCr+xXn9gBv5lAP9YLPxTEMKxdCHFD7nA4jh8/vnTpUo1GQzSb0Co9PR0AUFNTk5ycHLkAw0kOKJ0jEbq/XQwDXusDV7RI1uHNr/Qa9hSrsbRVVC3YBHDvBkVFYPfNdGKnGoODYVjHFuKuXFEUAADLsi2222w2AADHdZ5xzgoPO0Ei9O/8gT+6I/ahFy9pHtEW6su3BNzl3fre34aBNbetDg1cpYxKJH+6DmdBDMPalxCJMCEhISUlZcWKFeDX6daCli5dajabc3MvZ4B2+6QEVFrbsROhVF7o/n5p3Mz/bf3KSudCSD286eU+Y14O05CJtRXo1p+VxaOplweSJO4Zg2FYOxN6rtE5c+Y89dRTgUAgIyNDUZQtW7Z88cUXCxcunDt3LsNEYnhZZKh8x06ESBIaPn3LcttjdFzKlRyn5PBnrNaanD2hrQJr7rsy+OhW9ZsJ9IgEnAMxDGuPQjemPf74416v97XXXgsEAgCAMWPGMAzz9NNPz549O7LhhZfCd+zOMs6v3+O699UNGHslB1Ek34nd7466+ZO2iqq5/zsD/2c3XHcdXkoew7D267xPlebMmTNz5szt27dXVVVZrdZRo0Z1mj4yTTp00yh/aItUfCzxufeu8Dgndr2b3G28JeEyhx5ewKIT8LWD8MfrqIIYnAUxDGu/fkuES5cuffvtt48dOwYAeO6552bOnJmTkzN58uToxRZ2HbdGqLpszq/ei5vxV4K7op4nfnd52bHPr/n9+rYKrMmbh+AHp+DWG6gsPF7+/9k77/CoqvSP33un95LeSQIE0nuB0JuggoIFK1ZUBBFxUXEX0d11WRsWXFG3uIv7W1csawXpkIT03nvvyfS5d2ZuOb8/JgbEACkzyZTzeXh4MnfOPXPmZnK/877nLRAIxLG5FCzD4/FIkrT+fOTIkf7+/hla0vThrBYhAKpPX5OsuH1yNbUvpyr7j7MTtvJFPjZZ1yj7S+gjjcyFm9hQBSEQiONzySKcPXt2S0vLP//5z+joaJIk6+vrx8yUSEpKmsbl2ReKoNkC50vr1v30b5TFkSzdOMV5VH0lw71FyWvescmqRtlXTH/ZCk6tY/sJbTsxBAKB2IVLQpiamrp58+YHHnjA+vChhx4a8wQAwDQsaxpgSAZBEIzjZEJIdrcYc37w/s37CDpVY6sq+9WojD0sNt8mC0MQBCDI7jz6XC84fxPb02azQiAQiH35RbDMp59++vLLL3d0dGzatGn//v2RkRPubO5EUATjfH5RADRffyBddz9LOtWWub0tJyyEKjjyNpusC0EQgCBP59I5/eDUOjZsLg+BQJyIK6NGw8PDw8PDN23atGbNmogI+xZfnlmcMVLGWHASmM2i9BumOA8AdFX2qzGL96Goba4AySCPZdONOnDmRrbUdRJNIRCIWzB2+sTHH388zeuYfpwuUobBDbof/uHxyP6pO0Xbqj/jCZS2ajqotSC3naaEbPT4DWwR7CYBgUCcjavet5qbm7///vu+vr4rNgUPHDhg/1VNB05nEWp/+IcgNnPqkaI0ZarNeyv9xo9ssqouI7j5BL3YF30rncWCIaIQCMQJGVsIP/jgg507d5Ik6e3tLRaLL3/KdYTQqSxCS2ejqTLX53kbqFdj8Yee/qlKPxtE/xYMgo2nmOfjsB1RThZzBIFAIKOMIYQAgBdffHHVqlX/+Mc/vL29p39N0wNF0CxnEUIANF+8L7v5IUwovv7ga2ImVE2lHy3d/P3UF/VdF/Z0Mf2Pxex1QdAShEAgTswYQjg4OKhWq/ft2+fCKog4lWvUePFHlMUSJq+Y+lR1+W8HzdsolodOcZ4vWplnitnH17ASPKEKQiAQ52YMj5ZcLpdIJAaDYfpXM51QuHNk09PaYe2xI/Lbd0w9Rsagbums+2pe2tNTnOd/7cy2HProIjLeA6ogBAJxesZQAi6X+9xzzx04cIAgiOlf0LThHBYhAKp/vy5evIHjN2vqk5WffykiZQdP4DGVSY53gcez6R9vYMcrXaS0AgQCcXPGDpbRaDRlZWVz585dsmSJSCS6/KkPP/xwWhZmd5wiWEZ36jOEpqUr75z6VAMdWXp1U8bNf5vKJCe6wQPnqe9Ws5M9UVd3GUAgEHdhbCG8cOGCVCpFECQ3N3d61zN9OH5lGUtHg+H8Nz6730WwqbpwAUOVn9sXt+QVjMWd9CQnusF956hvV7FTvKBHFAKBuA5jC2F+fv40r2P6cfD29IzJqPrnq4o7d7IUNghZaqn4J0/oOZUe9N91MI9k0V+vZKfBRvMQCMS1cN9CIA6+R6g5eog/P0UQkzH1qSwmbW3+O4s2/XfSM3zWzOzMo79dBVUQAoG4IJeEkCAIrVYrkUhEItHg4CBN02Oe4OvrO11rsy+OvEdozP+J7G7x3v2eTWaryX0tcM5NMs/5kzv9X43M3iLm5Fp2rBKqIAQCcUEubT599tlnfn5+7777LoIg0dHRfldh5pZqSwANGBqwuI6YPkHrVNpv/6Z8YC/Kmfx+3ih6VWNX/TfzM56d3OmHapiXSpiz61hQBSEQiKtyySJcvHjxJ598Yu27+95777l+7oSAhTjkvV1/5gthykqOb4hNZqs4v39e2k6eYDJtm14pZf7TzGTdxAoUOeSVgkAgEFtwSQitDZisP99xxx0ztJ5pwmH9ooxRhxee8tnzgU1mG+zKNWhaM+I+mcS5B8qZz1uY8zeyvQU2WQsEAoE4KG4aLEMRNFvoiH5R/ZmjwqRlLNmUct5Hqbn4WmTGsxg24Q6Bh2qYv9Uz529iQRWEQCAujyOKwTTgmEmEjFFnzD0uWbrJJrP1tZ6ymDSBEbdM9MRPGpjXK5iTa1n+QugRhUAgro+7WoQO6RrVn/tKmLCEpbRJrXNQffHPUQufQ9GJfdf5opV5sYg5cyNrlgSqIAQCcQvc1iJ0OCFkTEZj7jHxitttMltXw3coyvYPXzOhs75qY57KpU+uY0XIoApCIBB34ZIQDg8PV1dXz+BSphMHzKY3nPtaEJ3BVvpMfSoA6JrcN6Iz9yITiYvNGwCPZ9M/rmFHyqEKQiAQR6TfOHCs5TTFjJ3mPmkuCeG33347GiyalpZWUlJi21dyKBzNNcqYcEPWtxIbmYPtNZ/zBB7ewYvGf0oPDu44Tf91EQt2VoJAIA5FPz54ruvi6/mH7vpm62PHny3sLTWQNi75f2mPUCwWG41G68/t7e0mk8m2r+RQUAQt8ObN9CouYTj/P0FUGtsrYOpTMTRZl/9OytpD4z+FoJBbTtI7orD1IW7qKodAIA4CA0C9qrF6sL5V296iaW/TdgjZwrmKsGT/+NvmrZ8lC0LtkAB+SQjj4uI6Ozsff/zxuLg4giC++eabqqqqX5+wdetWmy9i+nEo1ygwE4asb713vmmT2Vor/yX1iPDwSx7vqyPIQ1n0PBn6m1ioghAIZGbQWfSFPaV5PcUFPSUKgTzeOzpCOfuGsOWhshAeyqVpms/n2+/VLwnh3Llz33nnnT/+8Y/WjoOvvfbamCe4iBA6kmvUmPcTb3aMTcxBmiLqCg9l3vLp+E95uYRu14OzN7pp/DAEApkpTJSpYrCmrL+qtL+iXduV4BOT5p/0SNy9PiKvy4eRJGnvlfzi9rd9+/bt27cbjcbQ0NAjR46kpqba++VnCgeyCBnGcOEb5X3P2WSylvJ/efqnyLyixjn+aCvzSQPI38DmOcbFgEAgLk+/cfBk2/m87sImdetcZXiCT+xjCQ9EeURwWBMu/WErxrADRCLRvn37oqOjFQrF9C9oeqBwmi1wCE8gUZ7NknlwZ82b+lQ0ZW4sObzw1n+Pc3zBIHgyhz6xlu0Dy8dAIBA7Y7AYz3XknGw916btXBqy8MHYu6M85/HZDhGrMbZDbPv27QiCkCTZ3t7e1dXl5+cXGhrK5dqgGYKD4DgWof78V5IVd9pkqpbyTzz8U2SekeMZ3KYHt56kP4ZhohAIxJ6YaUtud+Hptgsl/RXJvvF3zL8l1T+RgznWXszYqwEAvPHGG6+++qpGo7EeEYvFO3bseOWVV9hsx3oDkwAwgLEAR/AGmluqGKNeEJ0+9akmZA7qSGT9Sfr5OGwDDBOFQCB2wEJbCnvLzrRn5fUURXpELA/JfD5jp4gjnOl1jc3Yqvbmm2/u2bNn5cqVmzdv9vX1HRwc/Pbbbw8cOGAymd56661pXqLNoU0Mi4c5Qg8mw9kvxUtvRVAbLGX85iDJILedolb4ozuioApCIBDbgJNEs6a1QdXSqG5pVLV06rrme8xdPmvRjuRH5DzZTK/uOowhhDRN//nPf962bdv7778/evCBBx549dVXX3755f3790ul0mlcoe1xEL8oNdhtbqm2SZjMhMzBHRdpLoa8kTbzVwACgTgvBouxbrixUd3SoGpuVLcM4sOhsuA5yrAoz4hb5qwNk4dwWU6zmzaGEA4MDAwNDT3yyCNXHH/00UdffPHFxsZGa/Ne58VBcicM574WZ96Ecm2QHDN+c/DVMqZoCJy/ic1yAIMYAoE4HZ267ovdhRe7ChrVLXOU4XMVYRkByfdH3xEsC2ShM39fnRxjCKFAIEAQZHBw8IrjAwMDCIIIheNy8prN5vfee6+kpGT+/PlPP/20RCIZcxgA4MCBA15eXr/WXfvhCBYhg+vx0vM+z3809anGbw4e6wQf1DIFG9gip9/nhUAg0wdAQN1w4/mOi9ld+QRlWhCQsjlyY6JvLM95bL5rM8YdUS6Xp6am7tq16/vvvw8NDbUe7O/v37ZtW3BwcERExHjm3bp1a0dHx/bt2z/99NPbbrvtp59+GnPYxx9//NZbb8XHx0+rEDqARWjI+k4Qu4AltUGCyjjNwU4jeOgC9fkKtp+DbldDIBDHAiCgZqj+XMfF8x0XeSzu0uCFv1u4e64y3B5FzmaWsU2D999/f8WKFXPnzk1OTvb39x8YGCgqKgIAfPPNNxh2/QiLnp6ezz77rL293dfXd926dd7e3uXl5XFxcVcM6+7ufv/993ft2nX27FkbvJVxM+MWIaBIY873ntv+NPWpaIpoKP4gc+N/rj2MZJDNZ+jfxLIW+braJxgCgdgWGtDl/dVZXblZnfkijmBpcOafl/4uVB4y0+uyI2MLYXJyckVFxcGDBy9cuFBWViYWi7ds2bJz58758+ePZ9KioqLw8HBfX18EQQQCQVpaWm5u7q+F8NFHH/3973/f1tY2tbcwYShihrPp8YKTnMDZHF8bfLBayv/l4Z8s87zO7+XpPNqTj+6KgWGiEAhkbIbw4aqhutzuwtzuIj+xz+KgjLdWvBIsDZzpdU0HV90sCgkJefvttyc3aV9fn4eHx+hDT0/Pvr6+K8Z88skncrl8/fr177777rVno2n6yJEj+fn51oeJiYlPP/306LMWiwUAMKFidLjGxBZgBoONG3mMF4bRnfpcdNv2qS+ApswNxR8krvn42lN92YEd72BnrSGNBjDFV7wco9EIAEBtkfsBmRBGoxFe9hnBxa68iTI3aVvr1U11qsYGTQvFkHPl4YnecXctudVTMHIDn7H75GWQJEnTNEVRkztdKBRe15Fpl6gJgUBwuTKZTCZrAM4ovb29f/zjH3NycsYzG4ZhcXFxGzZssD708/O7PGCHzWYDAHi8CdTpQSmtQMYfZ9SPzSGKz7IVXpJ5iVOfqrn0/xS+CT5B1wrirdeCPaXMj6sxX5mNf9cMwwiFQle6LzgLNE3P1KfXzXGBKz9EqCoHa6oG62qG69u0HWHyWZEec1eELt7u8Yif2AZdwe2BVQgn3X1iPNt5dhHCgICAjo6OUXOho6Pj9tt/0XI2Jyenr68vIyMDQRCtVovjeFRUVHV19ZizoSgaGxs72jT4CjAMAwCM562OQhMMR8ie0Ck2AwDDmaOyDY9O/dVpytxY8kHG+k+uMZWJRm47TR1IYSV52f7NYhiGYRgUwunHeuVnehXuiPNe+SFCdb4j52x7doeuO9Y7Mspz3vJZiyKU4U6R6jeJm/xEsYsQZmZmMgxz6tSpVatWVVZWNjQ0rFu3DkGQpqampqamG264Yf369R0dHdbBH3300bFjx/73v//ZYyVjMoPBMkRVLoKx+BE2MAdbK48ofOIVPlfuvF7O3kI61gN9cK5T/ulCIJApMogPZXXmn+3IbtN2LAxMuz/6zkTfODbmrNl+9sMuQsjlcg8ePHjXXXelpaUVFha++uqr1kYWJ0+e/PDDD2+44QYulztawlsgEHA4HLlcbo+VjAlF0Gz+zHwU9KePSlffNfWaagxtaSj6S8b6v19jTE4/ONoKyjbCnEEIxL1o03Zmd+Zd6MrtMwwsCEi5O3JTsl+8o9W5dijsdWnuuuuu5cuXV1VVRUREBAaOxB3dd999t9xyyxUjt2zZcoXj1N5Q+MxYhOaGUoYwCGIXTn2q1spP5d4xCp/4qw0wUsgD5+nDmSwPh2hyAoFA7IuRxEv7K4t6ywp6SyiGzgxMeyLhwTjvKAyFDqHrMy4h1Gq1CILIZBMrnOrj4+Pj84vdV7FYLBaLrxgmk8kmOvMUoYiZSajXnfyvdMUdNjEH6wsPXdscfCaPXuqH3hgEN/AgEFemWdOW05Vf0FPapG6J9IxI8Ut4ZdFzsxVhM70uJ+M6Qpidnf3YY4/V1NQgCBIdHf3hhx8uWLBgWhZmNwBCmxjWtOcRWjrqqcFuQdKyqU/VWvV/Mq+oa5iDJ7vBiW5QDp2iEIgrwgCmYqA6uys/uysfRdDMwLQtMXfGeke5TMGz6eda90ocx2+99dZHH330yJEjCIIcPXr01ltvbW9vn3QYqyNAmWmMi6LYdJtK+hP/kay8A2VNVZwYmmwoPJR208dXG6CxII9k0R8vYkk5U3wpCATiQDCAKe2vPNOeldWZ5yv2zgxMe3XJb8NcuuDLtHHpvqzT6XJzc9esWTN6pKGhwdvb+9VXX7U+TExM/N///tfQ0BAbGzvdy7QdM1JolBrosnTUK7fsnfpUbdX/kXrOU/omXG3Ajov0hhB0dQB0ikIgrgAN6IqBmnMdOec7LvqKvJeFZH689qCPyGum1+VSXBJChmHuvffeJUuWHDx4MCgoCEGQ4ODgjo6OY8eOrV27FkGQH3/8sbOzMzg4eMYWawsogpn+SBlj3nFh6mqUM1XHBcOQ9YWH0m48fLUBxzpB3gB0ikIgTo/apMnrKc7vKS7qLfOX+C4NXvjBmtcdNufd2bl0x5TL5fX19Xv37o2Kitq7d+8zzzyjVCpff/31jRs3WpOmAQBvv/32dOY52AN6+iNlGBovPuu1/bWpz9RW9ZlEOVvpO3YaIk4h2y/SH2ayhFAHIRAnhAGgQdWU212U11PUre9N8o1L90/ambxVwXfuu67j84tbplKpPHz48MMPP7xt27Z//vOfhw4devzxx2+55Zbi4mIURRMTE611tJ2a6XeNElX5bC9/tlfAFOdhGLKh6FDymveuNuB3xfRiP3QldIpCIE6FzqIv6avI6ynO6y6S8SQZASlPJDwQ4x3pvH1unY4xbIeUlJSCgoIjR45YM+Lff//9G2+8cfpXZiemv6yMMe+4KO2Gqc/TXv1fsTzMMyB1zGfLVeD/mpiKTTBCBgJxAiy0pXKwtrivvKivrEvXE+MVmR6QtCX6Tuj8nBHGdqKhKHr//fffdNNNL7/8cnR09DPPPLN3797RWjBOzTRbhLR22NJW6/HAi1Och2HI+sL3rmYO0gB5+AL9ehrLy4njeSEQ10dFqC92F+R0FZYNVIbJQ5J8455MfDjKcx4sezaz/EII1Wr1/v37T5w4QRBEQkLCK6+88s4779x1113btm374osvDh06tHTp0hlap82YZovQWHBCmLAE5U61vkt7zedieejVzMGDVYyUg9wzG5aQgEAcDoCARlVLfk9xTldBt6E31S9xVeiS3y58RsRx7kYWrsQvhPDee+8dGhrasWOHSCQ6derUihUramtr09PTCwsLDx8+vHHjxnXr1h06dMip42UoghZOW4YdAHj+SeWWF6Y4DcOQ9QXvJa95Z8xn2w3gtXI6dz0b7g1CII6Dzqwv7CvL7yku6CmRcMXpAcmPJWyJhTt/DsklISQI4uzZs4ODgyKRCEGQLVu2rFy5MicnZ/369SwW68knn7z99tv37NlTU1Pj1MVlKIJmC6fJcjI3VaBcHjdozhTn6ag5KpKFeAakjfns49n0s7GscCnUQQhk5jFRpqyuvBOt56oH6xJ8YlL9Ex+KvdtX5D3T64Jci0tCyOPx2Gx2bW1tcnIygiBarba9vf1y48/b2/uTTz4BwJZdzqef6dwjNOb9JMpYO8VJAEPVFbybvObdMZ/9TzPTRyDPREOnKAQyk5AMVd5fdaLt3MWugmiveTeErfjD4r2w5pmzcEkIMQzbv39/RkZGUlISn88vKytLS0vLzMy84gRnb8Q6bXuEjMloqi2Qb3piivO0134hkoWMuTuoMiO78+kvV7LZUAchkGmHAaBJ3VLSX1HcV149WBciC1o5a/ETCQ8q+NPaRQAydX6xR/jMM88sWrTo9OnTBEHs3Llzw4YNTtqO+RpQODM9FiFedIY/PwUTSqYyCQB0fcF7SavfGvPZPQX0HWFYhrdzfzWBQJwLE2Uu7C250JmX11Ok4MuTfGPXz16zb+GzEu6VrXUgzsKV6RMpKSkpKSkzspTpYdosQmPecfmGR6c4SXvN50JZ0Ji7gxf6wPEuUL0JVpGBQKYDFaHO6swtHCov6Suf5zFncVDGY/H3ewo9ZnpdDoqZYXCKvvyImM3iOKpl5Xa3UYqgWfZvT092NQHCyJsdN5VJGIasy39nzGBRC4M8nk2/vwCTwT0ICMRu6Cz68v6qkv6K0r7KIUIV4zF/WWjmc+k7oPF3BQBB2ox4pVZbpdWVa7WVWl2bEeezfiF7JpqZJ5HEyaVxclmcTBYlk3rzHKVvuHsJIW1mUBaK2T/RwJh/Qpi6aoo9eDtqjorls8Y0B18toyMV6IYQB/16BYE4LxRDVw/VFfaWFvaWduq6o73mJ/rGvrDg6TmKMKPBKJFMabNjGiAZxkDRCIJQgNFTlPWghWGMFI0gCIogERKJiD0ZY4BkGB1FaUlSS5IGitaTZLPRWKnVVWp11VqdnMuJlkpj5bIN/n6/nT9vnkR8hf1H0HS1Tleq1pZrtV929dTq9BQAc8TiORLRXLHYg8cdtSDVJIkgiJ6kKMCoLaSFprkoGqWQR0jEERLxXPEk138N3EsIp6c3PaApvPS89663pzIJw5B1Be+OaQ42aMEHtUzJLe71u4NA7IqRxLM687I6c0v7K4OkASl+CdsSH7puzRcaAC1JakhSbbH+b1FbSJXForJYNCQpZLF5LAxFEDmHgyCIkabNNK0hSRPNEDQt43AUXI6cw5FzOSIWW0eRKgup+nkGM8OMvgoXw7x4XG8ez5fP9+bxvHhcI01bBUlLUlqSHDCZe02mfpO532zSWEgJh40gCAtFpWzO6AxW8aABaDIY4+WyZd5ey7w8MzyUfNZV36CWJOv0hhK1plSjKVFranV6Posl53CkHLaYzZaw2bNEwkS5/P6Q4GiZ1Poer4GAxUpWKJIVitEjKoul0WBs0OubDMYmg1Hw80rkHA6KIEECAQfD5BwOChiDhWw2mb7q6qnXGxoMhtZ1q31t2hbXvW6m0yOEpqpcjl8o28NvKpNczRxkAPJoFv1SAitABGNkIK4MTtODZnOfyTxkNlMAKDgcOZej4HATcMbfAAAgAElEQVTlXA4ASDdB9JhMPQTRQ5jUJGmmGZymEATRkhQDAIIgPBYmZLEQBJFyOAlyWZJCMUcswn7lpCFpMr+35GTrucLe0gSfmOUhi55Lf0rKG8Ps6zeZ63W6TrWmTqdvMBjq9YZWo9FA0TIO27oqOYej4HIUHK6Sy1FwuWFiEUHTZpoBP5s4QhZLxOWGi8U8DBOyWRoLqSZJjcXSRRAmmhGyWUouN1QkTFJwlVwu/zJzyswwg2ZLn8nUiRMlas2g2Sxis2UctozDkXE4QQJBkkLux+f78Hk+PL4n7zr7JThNXxwaPjs49NuqmjKNVsnlClgsKYctYrO5GGamaZWFHLZYVBYLF8PmSsSJcnmCQvbgrJBYmcy2ppiSy01TctOUimsPI0mSpunRhvAMAL/+PU4RNxNCfDoiZYz5J0Rpq6cyw8/m4Bi5gx/UMhRAHp8PnaKQmaQdxwtV6i6CsN7N1RZSbbFIOOxAgSBQIAgRCQMEfBogQ2bzkNkyZDEPmS0AQSRstojNErPZMg4HQRC1hTRQlJGiDBSlspBq0qKykGqLRWUhh8xmgCCePK4Pj+/N57FRVG2xWA0vLUmyMdSXz/fj8wMEAn8BX8Hh8PiYkMVGEETGYVvvkmaawWkaQZBhi+Xr7t7fVdUOms3xclmERIKhCAPAEDHca+jrN/b78ATxntGbUzeFiOR8Fuv8sHHArOo1maxmVg9BdBOmXpNJzuH4crnz5bIIifgWf/+5EnGYSKTgOl+ZeyGLtdLHe6WPN4IgJpoeNFtMDK0jKQNFkQzDxTAll+vB4yq5XJ5DxrbYXAURtxNCgmYL7PurpXVqS1udxwO/ncokV6ss2qYH+0vo8zexMWgNQqaXdhyv1uqK1ZoClbpQrWahaKpSESwUKjicMJFIoeAoOFwdRXbhRJPBeHpgsNdkAgDx4nE9eTzr/xiC6Clq0Gw2UJSOpBAEkXM5YjZbxGIpudxwsVjJ5Si5XAWXo+RyPbk8m+8DqS1koVp1rru+XtXcpGlV8uVxyvBZIXEmwBkyW77tHR4095pp2pvP8+bx/Pj8ORLRIi8Pfz4/UCjw5fN5GKbX6x1/j3BC8FmsIKFgplcx87iXENKE3ZMI8cKTgrjMqVTZZhiyvuDdlLXvX3EcIMjWbPq5OFakHMogZMIwANTpDcVqdb/JrKcoA0XpKUpjIa8YxsEwMZtl3dySsNntOF6l1VXrdBI2J0oqSVLIHwoNOZwUHyBwprsnyVBFvWXnO3JyugtCpIF3BWcuWXCzl9BzptcFcRTcSwhJnOKI7CuExoJTys1PT2WGjtovRPJQD7/kK47/pYbRkcguWE0Nck0GzGYDRWkspIlhcIoasliqtLq8YVWhWu3D4ycr5f58gYTDDhAIxGz2rz171phDI0VZGEZLkoly+X0hwdFSqTP6ABkASvrKf2o9m9ddNEsevDR4wcNx90D9g/wa9xJCykizhXZ8y5a2OoShubPmT3oGAOj6wkNJq9684rjVKXruRjYLWoMQBEEQhKDpfpO512TqNZka9YZ6vaFWr6/X662xgjIOR8DChGy2gsOJlEp2R8xJVSo8XKKl6HgYJtTHmk/90HxSzBWtDVv5WMIWT4FyphcFcVzcSwhJnBb52fGLrbHghCht9VTSBzvr/icQ+XgGpF9+ECDIY9n0b2JZUQoogy4IDYCOpERsFvdXsQn9JnM7jnfgeDdh6iaIXpOpEyd6cLzPbKEA8OHzrLGCc8TihZ4eD4eGzJNK3Eftfg1BmQp6Sk62nS/vr1oSvGB/5p4Ij9kzvSiIE+BeQkjhtP1co4C0EOXZPr+5cm9vAjMApr7wUNzSV644friW0ZLI7hjoFHVKOnA8X6Wu0GhJAJCR1GaKBqDfZO4xmXoJ05DFImazDBTNxzAPHteLx5Ow2T2EqQ3HpWx2sFAYIhIECAQBAkGsTBYoFEhoaq6np4TtXn+812AQH7rYXZjdlV89WBflNW9p8MIXF+wSsG2ZZwZxbdzrb4ky2jF9gqjI4QbPZcm9Jj1Dd+MPbI7QO3jR5Qe7jOClYvrcTdAp6hxYa01V63QVGm2+Sl2gUqMIkuahSJDLxRiGjESjsFko6s3j+Qv4/gK+N4/HQlEEQXQkZc00MFCUL58fKhIKxkp21uv1UAURBOkx9J3vuHiuI6fX0J8ekHxT+OpXFj0P9Q8yCdzrz4nCKfsJoTH/hHhK3QdBfeF7UQueu+LojovMjigYKTqT0AD0mUztONFLmGgANCQJEGCNtzTStIVhEAQxUJSepGr1+hqdzpPLmy+VxMqk94UEHUqIG394upTDlnLYYSKRHd+M89Nj6DvTnn2+I2cQH1octGBr/P0JPjEYCv0lkMnjXkJI4jRHZJe3TGsGye5mfnT69YdehZ7mnxAE+IYuv/zg121MrQZ8tnyaOglDRqnU6o52dZ8bGGzHiT6TyZPHDREK/fh8NoZaS0kpuFwEQUQslojDQRAkSCAQsdnbZofNl0ikHPf6s5oeBvChs+3ZZ9qz+o2DS4IXbEt8KM47CuofxCa411+s/SrL4EVnBHGZKGfycQp1+e/MT9+NIJcsPx2JPJ3H/Hspiwd1cLqo0Gq/6Oo52tltZujbAgNejpofKhIFCPgO2z7G5TFYjKfbL5xsPd+u61wclAHtP4g9cCMhBDRgKMDi2uVPCC85J9+0bdKn97edpSnCL+wXhdn2FtI3BKKZvtApai8MFNWJE6UaTalGW6rWlGg0Cg73tkD/f6UmpVyv/iHErlhTAI+1nM7rKUrxS7g7alOKXwIHc6P7FWQ6caMPFmmkOUIWYgdZIfs6GNzAC4ue9Ax1BW/PT9uFXvY9t3AQfN0GqmDfXRuB0/TZgcFjff2lao2aHKnxz0ZRfwE/QS5PUMifjZiTIJf78B2lQZrb0mPoO95y+njLGTlPdkPYip0pW6Vcl6pqBnFA3Og+a0+/6Glh0tJJpw8OtJ83E+qAuTeNHqEY5LFs+mA6poC35SnQZzI1G4xFas2xvv6LQ8PJSsVaX5/NQYGjBS0ds6awe2KmLec7Lv7YfLJV07EydPGflv4uXD5rphcFcRfcSAhJI8W2R6QMAETpeY+H9k16gurc1yMznkXRSyL9RiXjI0DuCIO36QnQZzIVqjQFKlWlVtdiNDYbjGI2O0wsipVJHwubdTQjFaYcOCA6i76otyy/p/hiV+F8z7m3zF23MDANukAh04wbfeAonObYwSI0t9YgbC4nIGxyp/e2nKQsxoA5l8zBJh14q5Iu2OBGv5rJQQFQqtZkDw3nDA8XqjRGikpVKlKUivtnBYeLRGFiEVQ+h6VB1ZzbXZTfU9ym7Yjzjk7zT3wk7l5YBRQyU7jRnYLCabYdysoQxWdFycuvP25sQG3eW1ELnxvdHQQI8kQOvTeeNUsCY2TGgKDpQpU6a2g4a2g4b1gVLBQs8fLcFBDw55jocDFMv3NoGACqh+oudOZe6LjIxtgLA1Mfjrsn1iuSw3K+ct4QF8ONhJC0xx4hQxMVOV5PH5zc2d1NxxCE8Q9fM3rkozpGTyI7oqBT9BJqC3l+cMhq+VVotLFyWaanx5PhYf9JS3HGlgjuBgNA1WDNmfbsC50X5TzZ4uCMPy39XZg8ZKbXBYFcwo2EkDLa3jVqqitmefqzPXwncS4ATG3eW9GZe0dzB3tx5KVi+vQ6WE0NQRDESNHf9vR+1tl1fnBogYdyoafHgZioFKVCOFbVMYgDUjvccKY9+2x7tpQrXj5r8XurDgRI/GZ6URDIGLiTEOIU38PG3UTx4rPCpGWTO7er4VsM4/jOunT6thx6W6S7t5ggGeZYX///dXQd7+tf6OmxOSjg07RkuNvnLDCAqRysze7My+rK42DsZSGL3lz+cogsaKbXBYFcCze6v5C4jZsRAovZVFMov/WxyZwL6Nq8t+KX/XHUHPysmWnWg/+ucF9zJ29Y9e+Ozv92ds+XSu4JDno/Mc6dOwo5F0YSL+mryO0uzOkq8BZ5Zgamv7rkt9D/CXEW3EgIbd6Diai8yA2dj4nlkzi3o/ZLnkAx2mhi2Iw8k09/uZJtn7o3jgsNQIFK/WNv3+dd3RiC3hMSVLBi6SyRcKbXBbk+FEPXDNUV9ZUV9Za3atujPOdlBCRvibnTR+Q900uDQCaGOwmhrXswTdovyjBkbf7B5NVvjx55Ope+OxzL8HYXp6jKYvmxt//Hvr4TfQOBQsFaX58jqcmpsKqZM2CwGPN7irO78gt7S/0lvsm+8Q/H3RPjNZ/LguY7xFlxIyG0bdQoY9RZWms8trwwiXM7ao6KpMGeAWnWhye7wcV+UOke1dQaDYaDDU2fdXYt8/Ja6+fzemx0gMDGG7cQe2CwGE+1nb/QmVs33JjgE7MgMPWp5K0Kvmym1wWB2AC3uPlasW1CPVGWxZ+fhPImfBMHgK4vfD9p9ZvWh2Ya2XGRfieDZdPtS0ekWK15p7H5h96+e0OCKlevgPrnLFQN1n3XdDy7Kz/NL/G2eTcn+cbzoPEHcS1c/e77M4yFQQDAbLcFh5eckyzfNIkT22s+F0oDPANGOhceKGeilehNwS7rFO0zmT7r7PpXW6eRpnbNmX04KR7mPzgFBovxp9Yz3zWdoBnqptlrtiU+JONJZ3pREIhdcBchJHHahoVGae0w2dfOi0ia6IkA0PUFh0bNwWYdeK+aLrrFBX8LBE1/3d3zaXtnnkq1wd/vjbjopV6e2GTrkkOmk5qhhm+bjmd15qb5Jz2d8licdxRqj6YtEIjD4IK34DGxrV8ULzkniFmAsidc1qSj5guBxG/UHNyZS7/gctXUugjiUFPL31rbUpXK+0KCv1yQJoAmoDNgbYH7XeNPOEXcPHvN4+sPy3lwCxDiFriRENqw0ChRcl5280MTPQsAuq7w3cSVb1gfHm1l2g3IUy5UTa1ErXm7sfmH3r7bAv2zly2JkIhnekWQ68MAUNxXdqzldH5PcYpfwuMJDyT6xkHbHeJWuIsQkrbLnaCGein1AG92zERP7Kj9iifw8ArMQBBETyLP5DGfLmVxnF8HSYb5qrvn3cbmXpPpqTnhhxLipBx3+Vw5Ne3azhNt535qOeshUNwQtvzplMdgC1yIe+IuNywKp2zlGsWLzwoTlyDYxGYDgK4veCdh5WvWhy8V02sC0SV+zv29e8hs+bi17S/NrbPFot0Rczb4+7GgJeHwqE3aM+0Xfmo9O0yoV81a8vry/aGy4JleFAQyk7iPENosWIYoPa/Y/PREz+qs+5orUHoFLkAQpFwF/q+ZqdrkrJ0TGADODQ79van5h4GhjYH+P2RmxMnhZpKjYyTxnK6CM+0XqgbrFgSmPha/JcEnFrpAIRDEfYSQxGmO2AZvluxpZcwEN2TehM4CgK7LfzthxQEEQRiAbMuh/5jM8uRPfTnTTYVW+2l75386unz4vNt9vd9KjPfmO+HbcCfMtCW3u/B024XivvJ4n+iVs5bsz9zDZ8PfGgRyCXcRQgqnhd68qc+Dl5wTJi5FJvg9urPua57Q0ysoE0GQv9YzNEAenOtke4NnBgafq6gespjvCQ46sXjhfKnEYDCIeDa4pBB7oDFrc7sKc7oLS/rKIz0jVoQsei79KTEX9i6GQMbAbYTQRsEyRFmWx4O/ndApDEPW5L2ZtOpNBEGGzchLxfTxtWzMeTxSdXr9noqqGp3+QEzUpsAA51m4OzJMqE+0ns3uymvXdiX7xS8JztiTvh2GwEAg18ZdhNAmhUYtbXUIi8UJCJvQWe3V/xXLQqy7g7vz6HtnY3FK51CTYYvl9frGT9rad82Z/Xl6Kh+mAzoqDGDye0p+aD5R3l+9ODjjwZi743yiOZi7/HVDIFPEXf5UKCPFmXKwDF56Tpi4dEKnMLSlNv9g+o0fIQiS3QfO9oJqZyiuPWg2v9nQ9NeWtntDgmrWrFTCvoCOSo+h73jLmR+bT3kJPW6avfrFBc8I4P4fBDJBnOCmbBOoqVuEABBlWV7bX5vQSS0V/5R7xyj9kigGefIi/XY6JnbsWNFBs/n9ppb3m1vW+vrmr1gaLoa7So4IQZnOdeQcbz7drutcMWvx68teCoVdcCGQyeI2QkhMVQjNTRWYRMH2Chj/KTRlaij6YMEtRxAEeaOS8Rcit85y3BiZQpX6X+0d/9fRdU9wUOmq5YGwO4RDUjlY87+6Y/l9xbHekbfNuzk9IAW6QCGQKeIWf0K0mUFZKMae0s4cXnRGlLx8Qqc0lf7Vwz9F7hXVbgBvVtIFGxzxatfo9J91dv2noxND0buCAitXr/AXQN+aw6E2aawuUAxFVwYu3p7ysIIvn+lFQSAugiPemm0OaaSmaA4C0kJUXpSuu3/8p1Cksan048W3fYEgyFO5zK5oVqiDFdc+1te/r6q2z2S6Myjws/TUJAW8sTocJsqc11N0qu18WX/V4qCM5zOeivKcp9frJXwYCAqB2Ay3EMKpt54wVeVxg+eyZB7jP6Wx+LBPyBKJcs6xTlCnAZ8vd6CQywKV+rmKqn6z+dXoqPX+vrC8iKNB0mR+b8mZ9qz8nuJIj4jlsxbBKBgIxH64ixCyp9YAHi8+I0yagF/UYtI0l/192eYfCArZfpH+eBGL5xg6WK83/LaqJm9Y9VLUvAdnhcDSoA4FDeji3vLT7RcudhWGK2YtD1m0M3krbIcLgdgbtxHCKfRgYnC9uaVKed9z4z+lruCdgLk3i+Sz9hbSGT7ocv+Z15uzA4PvNjXnDKl2z539r9Qk2CPQcaAYumqw5kx79vmOiwESv+Uhi7bGb/EQKGZ6XRCIu+AWQjjFHkx4yTl+ZCrKG28UJa7r7Kj5fOV9Zxu04K/1TNnGmbzIZob5b2fXm/VNJobeFh72aWqKiA0lcOax0Jaa4Yby/qrygeq64cZAqf+SoAUfrn3TV+Q900uDQNwOtxDCKe4R4kVnpGvuGf/4qpwD4QmP8EXeT/xI7Utk+QtnxhzsxIm/NLf8rbU9w0P5VnzMcm+vmTdL3R4LbcntLjrVdr6oryxUFhLnHXX7vA2x3pEijnCmlwaBuC92FMK//vWv77zzDkmS995774svvoj+cjuqvLz8jTfeKC4uxjBs9erVL7/8skRir0A4Cqe48knmsVNDvfRwHz8iYZzjNYPVQ10XE1e+/mkTo7UgT8yfgcTBYrXmnZ87xZ9fumi+FEYYzjAUQ5f2V5xuu5DTVTBHGbZy1hJYAhsCcRzsJYRZWVkvvPDCd999p1Ao1q9fHxgY+MADD1w+oLa2NjU19YUXXqBp+oknnnjqqaf+8Y9/2GkxpJEW+k8y4g4vOi1IXDr+NryVF16Zn/6sAQifK6C+XsViTa8VVqHVPlpUqiHJ7bPD3k+Mk7DdwuJ3WIYIVX5PcV53UUl/RbA0cHnIokfj74ebfxCIo2GvG+Xhw4cffvjh9PR0BEH27Nnz4YcfXiGEmzdvHv35N7/5za5du+y0EmTENTrJd4oXn1Xe//w4B/e1niYMPbOi7nw0h944C02dRmckDcAb9Y1vNTS9Fht9X0gQzIiYKQACGlTNOV35OV2FA/hgil/CoqCM3Wnb5DzYuxgCcVDsJYTV1dW33HKL9eekpKSnn75WS/ecnJyYmBg7rQSZQusJS1sdgmHcoDnjGQwAU53zp5hFvzvbxzrdQ1dMY4xMmxF/oLCYAuDi8iWwOuiMQDF0+UBVVmdeTlc+n81bGJi2K+XxSM+5GOq4RfUgEIgVe92sh4eHpdKR/CeZTGYwGEwmE3+sbubnzp376KOP8vLyrjYVRVEvv/zygQMHrA9Xr179t7/9bfRZi8UCACBJ8hqLsRhIEjUbDMxE3wWR9xM7NtNgMIxncHfDFyhLyPJY+Mgx8mAShZpNBvNEX3DCMAB80tX9+4bm34SHPjErGEXAOFc7dYxGIwAAdW/T00Aai/rL8vtKSgYqAsX+Gf7Jv894PlDsb30WN+L2eFGj0ejml32mgFd+RiBJkqZpiqImd7pQKMSw63wftZcQyuVyvV5v/Vmv1wsEgjFVMD8//4477vjiiy/mzZt31SWy2Xv27Nm5c6f1IYfDEYvFo89ahZB3zVbpDMFIPSUc8QTfLEPra/K8dh5kX/ZyV4OmTM0l76Xf9NeXqvlL/ZFb5kxH36J8lfqp0nI2il5YtnhGImJEIpEb3hdoQNcPN5X0VRT2lTWqmhN9YxcEpT6Tvk3BnybnJwBAPI7PJMTmwCs/I1iFcEwFsRX2EsLZs2fX19dbf66trQ0PD//1mOLi4g0bNnzyyScrV6689mwCgUChmGyIAUAogpmEa5SoKWR7BrA9fMczuLH4sIdfcj0W/3U7XWl/p2ivybS/uvbH3v7fRc57JDQE7gjaG4CAZnVrcV9FaX9FxUCNn9g30SfmrshbE31iuSzYrBECcW7sdcvesmXLM888s3XrVrFY/O67727ZssV6fN++fRs3boyPjy8vL7/hhhtef/31jIwMtVqNoqhcbpeiz5SJZnExFJuwVOB5x4Vpq8cz0owPNpV+vPD2HzLP0u9mYIprWadThQLgrYam1+sbHgmdVXvDSjGMC7UnA/hQUW9ZUV9ZSV+5mCtO8o1bG7Zyb8YuKQ9mpEAgroO9bqMbNmzIycmZPXs2giDr16/fsWOH9fixY8dSU1Pj4+NPnTollUp///vf//73v0cQhM/nV1dX22Mlk6uvRuvU4y+rVpVzICTqrj+3BEUrkY327DjYZDDeV1AkZbPzlsOWufaCYuiKger8nuK8niKNSZfkG5vkF/9Y/BYfkddMLw0CgdgFewkhiqKvv/76gQMHaJrmci/5jgoLC60/7N69e/fu3XZ69cuhJlVfDc//SZCwZDxl1bRDNb0tJ31vzvrkLFOx0Y7t5//V3rG7vPLZuXN+EzEH+kJtTr9xsLC3JL+npKS/IlgakO6f/ELG03OVs+GlhkBcHvs61lgsFmumizuTOM2ZqEUIgDH/hHLLuNIHKy+8EpG2a3OB6I00zNs+Td0HzeatxaVNBuOpxZlxcpiOZjMstKVsoKqwp7Sgt0Rr1qX4JSwOzng27UnY8AECcStcf4eJwifcldfcVI5yedygudcd2dd6Ctd3fw7u9hEg9862i1P0s86u3eWV9wYH/Tc9lXu9IGDIeBgm1LndBbndRaX9leGK0DS/xL0Lds1RhEPjDwJxT1xfCEnjhJsRGnOPizLWXncYAHRl1h88kvYdLMUKb7G94dtoMDxZUj5oNn+ZkZbuobT5/O5Gk7o1p6sgpzu/V9+f4he/LCTzuYynpFwY9gKBuDuuL4QTbT3B4HpTbZH8tu3XHdlScYQr9NzVtuyVJCxUYktjwsIwBxuaXqtv3DE77MX5ERxoCE4Wa8GXnK6CnK58DMUyg9KfSHgw1juShcJeVBAIZAS3EEK+xwQyvfDC0/yoVEx4nbRZ0qyryz/YGfcp1Y88btMWE1lDww8VFsfL5RWrlwcI7LPr6Opozbr8nuKL3YVFvWVBUv+FgekHlu0LlQXP9LogEIgj4vpCSOK0OHgCX/+NBSfktz5+3WG1eW9KAlf9rnHe+ZtYE89RHBsTTf+2qvY/nZ2HExNu9h9XIj/kcvqNg2c7srM6c1s1HUm+cRkBKTuTtyr4dslPhUAgLoPrCyFlpMbvGrW01wETwQu/TgVw3XB9R91X/wo+/UwMK1JuGxms0GrvLyieKxaXr1rhyYPFSibAMKE+15F9tj27U9ezKCj9wZi747yjOCw7prJAIBBXwg2EEJ9AsIwx7ydRxg3I9aIHy86+aAjf3ahX/jvGBk5RCoA/1NQdbml9Oz52c1Dg1Cd0EwbwoazO3AsduS2a9gWBKfdF35HkG88ed+dICAQCseL6QkiOO6EeWExEebbPc4evPayz7iuC0D5r2fzNahZnyjrYgeN35xdJ2OzSVcv97FlV1mXo1vde6My90HmxW9+3IDD1zshbU3zjof0Hgbg4DGD0BNATQEew5/ohbFt+5XV9IaTGnVCPF5/lhcewZB7Xms1iqMz6ww9+h+/z4SR5TtUp+k1P79ai0ifCQ/dFzoNJbNemXtWU3Zmf1ZWnN+sXBqY9EndfvE80DP6EQFwGYCIBYQGEBRBmoCWYIR09qBv5X20kjGZMKkDFfFQiEO9Yi4qhEI4bwADazLAF47pkhpwf5OsfvvaYmrw3LZ5LTxGJZQlT+jWYGWZPRdU33b1fL0xfAHMErwJBmUr6Kgp6S3K7C7ks7qLA9D1p2+d5zIVfGiAQ5wIQFqDDGYMZGE3AaAIGM2MggNrIaHBGbQBanNERKJeNCriogIsKuahUiHlKMS8JZ14AIxcAqYDvKbvuptWkcXEhpAiGxceQcVw9c0sVMBO8OfHXGKMbbmir/u9vpac+XsESTOHKVWl19xcUh4tFZauXyznQp3clTerWvJ7iwt7SBlVTpGdEil/C68v2h8iCZnpdEAjkqgALBXQ4ozYyaiNQGxm14ZLIDesRDENlAkzER0U8VMxHRXxMIsDCfTlyISYXoTIhJhUiV4m/t/YjtJ8KIq4vhDg1Tr+oMes78aL1177WZWdfrPDZvcTXZ7HvJH8lFob5U13DX5pa/hQT9VBoyOQmcUkAAuqHm853XDzfeZEBTGZg2j2Rm2K9o/hseza1gkAg4wOYLEBvYjRGoMUZtZHRGBm1EeiJkX07vQlhGFQmxBRiTCFC5SJMKeYEe2JKMSoTYkoxynPob/yuLoTji5ShdSpTfYn8zqeuMaa95qjaoPmId29F8iSdouUa7UNFJb58ftHKZUFCmCmPIAhipi3l/VV5PcXZXfk8Fmdx8IL9mXvmKsdo4wyBQOwBICyMFreKGaMngMEEDCZgNAGjmTGagZ4ABhNjMKEsDJXwR6w3pRiTCTmRgahEgEr4mFSAigUo36Gl7tq4uBCS48udMF78UZiwBONftcMfYeiryHrloOhfH2Ry5RPP8TPR9L7q2vqFZhsAAB2eSURBVCPtnW/FxdwVDBMkkA5dV2FvaV5PcdVg7VxFeKp/4p+X/i5UDk1kCMR2AMDoCGAwAT3B6Aigwxm9CeiJkYcG04jCsTFUKsSkAlQiwCQCVMxHRTzMR4aKeJiIbw1OQcV8lOPKgWkuLoTjKjTK0Ma8456P/eHqI0DxyWfqPB4O8oy9MWjCTtEStea+gqIYmaxi9XIvnvs6+noN/aX9lSV9FSX95RyMk+wXf/PsNfsz94g4wpleGgTilADCwmiMIx7L0W05lR7oCUZvAgYTKraaa3xMIkBlQlQiYPkrULG/VfZQMd/lFW6cuLgQWnQkV3qd90iU57A9/Tl+s642oLns70N6/V+4T5RkTOwTQwPwRn3jmw1Nf4iO3Bp21fldGCOJl/SVF/aWFfaWmmlzgk9som/sQ3F3+4thATkI5PoAMwlwCzCamGE9M6hnhvXMkI4Z1lv35xAWZg0zuXJbzmrbSfh2DTBxJVxcCIl+izTsOgaHIfs78eL1V3vWqGmrznv7ZeFXnyzhKiZizrUa8S0FRTwWq2TVskA3q53dpu3M7szL6ylq0bRHec1L8Uu4NeJGWPMaAvkFFG31VTI6fMRdqTIwWmIk0tJoArgFxVBUyENFPMxDgnlKME8pZ5YX5iHB5CJUKkC5Ln4DnzZc/DriAyafDMU1BpB97dRQDz86Y8xnAUMVHHvygnzXhrlhS/wm8N3q763tz1dWvxQ5b9vsMPf5SlavarrQmZvVmUeQxKKgjAdj747xms9lwbqpEHcBmEdTwi0AN1uNucv/ZwwmgJuBwQwMJkDRmJiPSvioRIDJhJhUiCrFnFlemEKMSoWoiIeJeLatnwK5Gi4uhMSAReh1LTvOcOEb0YIbUdbY16G+8FCPRZQlvy87frwfRwNFPVFSVqzWnF6SGSOTTnjFzsYwoS7uKy/pKy/qK+exuIuDMvZmPB3hMRsdT/ImBOJcmCkG1zI6HBhMjBYHWpzR4YzKALQ4ozIwOgJlYaiQhwq4KJ+Dinio8Od/Ih7mKUVFPFTEx8Q81BqEIoDfER0FVxZCi45C2Sj76nmEjMlIlF7wef7DMZ/VDFTVlf7tFeGP3y9lj7OmaI1Of0duQaJCXrhimch1v8oRlKm0vzK3o7BiuFpFaBJ8Y5J84+6Jui1IGjDTS4NAJgMgaaAngBZn9ATQj4RTAgMBdARjTScwmBiDCcFQvdV0kwowiQCVi1h+Ck5UMCoTYAoxJhMiLNhD2ylxZSEkBsxC72uZg8bc4/zIlDGLi9IUkf/jts+F+363IGCObFzGzeHm1n3Vte/Ex7pkgoQ14T2/p6Sor6xR1RzpGRHrEflC+tNzPWbDgmcQRwYYTYwGZ9RGoDUyGhzocEBYgNEMCAtjNAPcDHQ4oJiR/AFrSpyEj4n5WKAHKhFgEj4qHgmwNJhwiUQy028IYntcWQjxfrPA56pCCGjKcOEbz4f3jfls+bl9zew4NGDjvbOv/xVv0GzeWlzagRM5yxfPEV+ntb1zwQCmfKD6QufFrM58IUeQ7p90X/TtsV5RfDbPYDCIRCIUqiBk5gAWCqiNjJ4Y2ZOzKpyesGYRMBojUBkQLhuTizC5CLVW85KLMH8lKuBaXZeYkItKheP1Uprs/H4gM4QrC+G1LUK88DTHN4QTOPvXT/U0H29vyXpbcix/wfXdmyf6Bx4uLNkY6P9ZeioPcxHHiIpQF/eXF/WW5XYX+Yq9FwcteGvFK8FSF7R0IQ4O0BH0oHZE7fQmxkAAgwnoCGtNS8RCogoxJhGgQmuxZh4q5KESASfYE/OQYHIhqhDD0ErIdXHljwjeb1bMv4ofAwD92S8Vt+/49TOEoa/41HNvCj76aKn82vkSBE0/X1n9TXfvkbTkpV6etljyTGKmLaX9FUW9ZUV95UP4cIJPTJJv3EOx9/iIvGZ6aRCXBVgoZlgPNEZGbwK4GVh9lbiZ0eLMgJYZ1CEcFstTiirFmJiPSoWYUoKFeKFSIaYQYXIRKoYtPCE2wJWFkBgwC6/iGiUqsjGegDc75orjADBFPz1VINmydG7y0mvmS5RqNHfnFaUoFeWrl8ucuYOEilBf7C7M7S4s7a+cowhL8Ut4Ln1HhHI2hrqIdQuZSWiG0RNWAw7ocEaLMzoc6ExAh1urNiMUjSnFqFyESQU/x1hyMaWYExWEecswLykMrYRMAy4rhLSZoXCaJx9bovRnv5Ss2vzr4w1Ff+nWm4/Ln8xJvJZT9OOWtherat5NiN0c5JTewmFCXTVYWzlYUzFY06PvS/FLWBqy8LmMp6RcGAgAmRQUzehNzJCO6dPQ/VqmX0P3a4HGyBhMmESASgWYQoRKBNiISeeNSgWYUozJRajIfYsOQhwHlxVCYsAs8OaNmcxmbihlCKMgOv2K46q+0triD/cLv/9mGZd7FXOIoOmnSiuyh4bPLs2MkjpTmmCnrrtisKZ8oLpyoMZgMUZ7zYv2mr898eFIz3lszGUzPSBTBFioyzyWFmD4OZ1Ad6n/DqPDgYnEJALMQ4L5yFi+ck5SGN9HjirFmFQIE0ohjo/LCiFuFcKx0J36XLryziuq8JmM/bnfP3JU+udnk4IirpIvUa833J6bHy+XF610gjRBiqGb1C3VQ/UVA9UVgzUcjBPnHRXnHXV35KYQWSBMeHdbgIUCBhMwmoGBYIyXtuV+roTy889GMzCaEAQZTQlHhTxUzB9JLQjxYltz6UbLWkIgTovLCiHRbxZ6j7G7QHY3UwNdgsSllx+kKXPudw+XSe41e655JGJsY/CTto49FVV/iol62IEb6hpJvLivvHKwtnaovknd6i/2jfKatzAwbVviQzDmxeUBJstI7S7czFwWeAJ0hLXhnLUYCgLASGUTMR8V8zHRzztzvooRwRNdpnww5BLiBrjsp5wYMHsmyH59XHfiP5Llt11RU63s7N4mi8/38u2nloxh56kslseKy+r1+jNLMqMdsmpat77XGvBSO9wQ4xUZ6x31SNy9ER5zBGz4Pd0loBlgNDOjhtqwxmwBjNrIaEfahQODiTGaUTY2onAjGXJWMeNiod4cmdBa0BKVCaG2QSBX4LJ/Enj/GEmE1GC3paVaec+zlx9sKP6gsaPifelXZ9ZwRL+6HqcHBh8sLF7r65O3YqmQ5UDuUK1ZV9pfWdZfVdxXZiTxjICUjRE3JfvG89kw+sA5ACYLwC2XMsFN5KUfCDPQmRiNEehwRocD3IIKuaiQjwm5qIjP8Fi0hxSTiziBSlQmwhQiVMTDxHxYoBkCmRyuKYSAASYVyf9VuW3dsSPixRtQ7iU7qb/9fGXBR3+SfPPtWrHyl8NNNL23quZoZ/c/UhJX+nhPw7Kvi8asrRyoKRuoKu2r7DMOxHlHxfvE7Mv8zWxFKNzzcxwAYQE6grFWqhwpzUwAHQ6M5pGaXkYzwM0ojz2SAy7gjvwbrdfsIcFCvTG5CJUKManwih04vV4vhIW+IBDb4ZpCaBq2cGVsjP0LbSB7Ws1N5Yo7d44e0asac37c8YbgwyPrgkLEvxh8YXBoa3FpnFxWvnq5kjtjmUwAAd363trhhsqB2vKBqiFCFeM1P9Y76tm07REe4SwUWgAzBEXTgzpm2ADUBmbYwKgNjNrADBuspZlRNguV8EdKM8uEqEzI8pOjc/1Q0eiGHA8V8RAMfneBQBwC1xTCMf2i2m//KllzD8ob6ZGL6zrPHL3rH9zfvrUuPVZ56ZakJcl91bVfdvW8HR9zW+AMtFOw+jzrhhvrVU31w01SnmSex5wYr/nr56wJk8+Cee7TA6MxMoM6RmMcCTkhLAC3AIOJGdIxQ3rGYMI8xJiHBFOKMQ8JK9SbkxiKKaydwaGLEgJxMlxTCH9dU8bcXEkNdovSbxh5iA+dPnrXf7GHt62+PcP7kgp+19O3vbR8iZdnxfQaggwADaqm/J7ivJ6idm1XvE90pEfE3ZGbIpSzpTzoBLMLgLAgDABGE6M2MkN6Rm1gVAZmSM8M6ZgBLSrkYZ5STCGy9o1DhVzMV46KeZinFPOUYnIRdEVDIC6Diwphv0UaJrz8iPa7v0tvfMAaLEqadaePbv6KuW3DisfWBo3cz4bMlidLyyo0un+nJWd6jtGYyeboLPq64cbaoca64cbqoTqlQJHun/Ro3P0x3pEczDV/L9MDsFBATwA9wehNQE8weoIZ1gMNzqgMjNpozShAEAQVcBEMRYU8q1WHKcUsfwUnJhjzkmJeUpTnxGXzIBDIhHDNGy4+YPbJUIw+JCpygMUkTFiCIAhF4me+vPcnS3rm4qfuDBtxM/7Q2/d4cdk6P5/iVcvsFxpqsBjrVU0NquYGVXO9qklj0kZ4zJ7vMXdd+IrdqU94CqdDfZ2dkUhLoxkYTcBoZowmYDQDHWEtXAm0RkZlRBhmJENOJkTFAlTKxzwkWJgvphRjCtHI/hwEAoH8jGsKITFgFo6GjDKM7sd/ym55DEFRmjKd/fK+s/qweYtffjgCQxBEQ5LPVVSdHhj8d1ryYjt0kOjW91YMVJcNVFUO1qpNmtmKsLnKsIyA5C0xm4OlgW7b0haQNGKhLj3EzQgAI1txBAlMFmAwMXoCaPCRks0Gwlr3BOWwLhU6EfNRIQ8T81GJgBPogSlEqFyEKUSwTDMEApkQLiiEFh2FslC2aMSwMxacxEQy/rwkmiLOff3ABa2vV8YbT8xnIQjyTU/vkyXldwYFVK5eIbCRITiID7VqOpo1bY3qlvL+KhTFEnyiY72j7orc5PLKB0yk1VADBhNjNIERz6QJGEwjNSpxCyDMALcgCILyLn32UCEPQRBUxEf5HFTARflcVMzHpHws3IcjE6Ji/mhrAoQFY4UgEIiNcUEhvDxSBpAW3U//9tjyAkXip7/akq3xEqQe3B3LHrZYdpZWFKjUn6WnTGVHkAGgU9dVr2puUDU1qJpbNO0cFidUFhyuCE3zS3w07j4/sY+N3tZMQDOMwQT0BDCYrDW6fs6BszC4mdLjejONmElg/UdYUA57pECXiI+K+ZiYj0oFLC8pGuaNSgQjUSfWbDkOjKuEQCCOggsK4eXltvWnPuMGzUH9Ak78984zxoiABQd2xbB/7O17rLhsnZ9P6arlE62dTQO6TdvZqGppVDc3qlqa1P/f3r0HRXHlewA/Pe8HM8yMAzJC5CUQHoIIAUJMpLi8xISQSIjWFi+tvFaSypZ5aKJlJdFKTKhYqRhiyp1AklvZRCKQ3MkVQQO7VTwiiIZEREYRJYy8GZhh3t29fzTOcvfqbu5F0kz37/PX6Z5GvmDbP/v06XOuKUWKCFVo+Io1qf5Jocogb+FynIMNuXDSemsSE5uTtLtIu5O02JHdRcxRd2w2wmSlXhVATpx0ukirAyHEoQoYNbGyXIxJhZhCylml4kmFJEaIVXJMJMAEPEwkwER8uF0DAHgiBhZC6+j8HaG9//xcxylF+cGTXz15xhqXmnUw3d/1hx8vdE5N/+U33wjOOkxXpwcHjIMDxuv66YHrM0Mrpb5hypAwVcgD/skRK9ZI+ZJ//6csDdLmIK1O0uogZy3E9Bw5ayVm5gijhbQ55t97s9hJq520OhFCmJiPiQTz3Y9CHibkYxIhEvI4EhFnlWp+dImXCJMKEY+LCXj/trA5zGauVIoxurMXAMAGDCyEllG7MlKGT49N/ee70q3Pnvyu7L/xzJycXd2mvp0Ng2XBgRey0u80NNSJOwdnh64Zrw8Yr181Dl4z3rA4LSGKoBBFYIRqTW5oRqgiSLT0M1n/Y44u6jGb2UbOWAjTrU2qi9Jix4R8TCTAJAJMLuEopZhczPGW8lepbvVACjCxEJMIMLEAXvEGAIA7YWAhtI7ZxSu4k1UHHEnr/9byp3pBmToh6489Z3L8Vp7NSAuRShcePGOfvTJ9TT89cGXq2pXpAYN5ZJVME+K9OkQZ/Fh4bogiyE9612YZpQZDUrNwkWZqzkkb1Rs5v9jprU8xPg+TiThyMeYlxrxEHJkIk0v4/ipMJsZkIo5MjElFmESA4G4MAAAWjWmFEHcQLgtubf7zdfFkx+A57coDQwKUT86d/Y+0IKkEIWRymPunrl6a1F+e1F+eujLntKxRBK9RBSdo4rZG5Qd5B95xuXYXPj+y34Uju5N04qTDhVw4aXchgiBtTuTEqSGR84/iqKdxNif1NI60OTE+F/MSYVIRRybCpPNr5WByMUej5FMvA9zqn4QbOAAA+N0wrRBax+x8qbF++L/+rHroglfhIxrpn1Q4cvb/pedvBvOowXTT6rJFydesFQfnihLK79msxCWkzYGmnORNF2kZcVhvOAiSxAlkdyKESKuDMNlIs5U020gnPt/lyOUgkQDjczEBD/E4mJCPOBxMxEc8LiYRYHIxx09BrXQ633Up4mMSISbkQXkDAIBliGmFcOjy1dOonTAVPmU0qxwXfJBIRoolhECES/hEKNcWgjlcGAfDvLiY1xQmtTi9REjEx0R8TMjHpCLOChnicjAuBwn5CCFMLJgfQuIlgte0AQCAkZhWCCPTY37u/GtkgMpXFalQqDlSISbkYyI+EvAxPhcTC5CAByt0AwAAcGNcScBQ4e6ddIcAAADgMeANaAAAAKwGhRAAAACrQSEEAADAah5fCD/88MODBw/SnYKNSkpKmpqa6E7BRpGRkXNzc3SnYJ2enp7c3Fy6U7DRsWPH9u3bt6TfwuMLodVqtdvtdKdgo7m5OafTSXcKNjIajSRJ0p2CdXAcn52dpTsFG9lsNpvNtqTfwuMLIQAAALAYUAgBAACwGrb8+1gOHz6s1Wo1Gs1tPzUYDC6Xa/Xq1b9zKtDX1+fn56dQKOgOwjpdXV3x8fHcO6ygApaIxWK5evXq2rVr6Q7COiMjIzabLSgo6P/35UePHg0NDf3Xx3hAISQI4ocffqA7BQAAAM+TnJwsk8n+9TEeUAgBAACApQPPCAEAALAaFEIAAACsBoUQAAAAq0EhBAAAwGqevQyTyWRqaGjAcTwnJwfG8S8pgiA6OzsvX76sVqvT09NFIhG1v62tzWKxUG2VSrV+/Xr6MjJTZ2fnzMwM1ZbJZMnJyVTb5XKdPn16dHQ0LS0tMDCQvoDMZDQau7q6Fu6JjY319fU1GAy9vb3unUlJSXK5/HdPx0A4jl+6dGlkZCQ9PZ3D+ccd2vDw8JkzZ1asWJGVlcXn86mdJEm2tLQMDg6mpqZGREQs/rt78KjRsbGxlJSUmJgYoVDY0dHR3t4eEBBAdyjGysvLu3btWkJCgl6vNxgMra2tq1atQghFRER4e3t7e3sjhOLj49999126kzJNamqq1WpVq9UIodDQ0KNHjyKECILYtGnT9PR0bGxsXV1dTU1Neno63UkZ5eLFiy+++CLVtlqtra2t7e3tKSkpn3766e7du+Pi4qiPjhw5clcuxCz3yy+/pKSkiMXiiYkJi8UiFoup/R0dHZs3b3700Uf7+/s5HM6ZM2eoWlhcXNzd3f3AAw/U1tZ+9NFHhYWFi01Aeqz9+/fn5+dT7aKiol27dtGbh9muXLnibmdkZOzZs4dqh4eHt7W10RSKFe6//36dTvdPOxsaGoKCgiwWC0mSlZWVqampdERji+rq6vDwcIIgSJLUarXuyw64W8xms8FgGBwcRAhRZzUlOzv7nXfeIUnS4XBER0fX1NSQJPnTTz8pFIqpqSmSJOvq6kJDQ3EcX2QAD35GqNPpCgoKqHZBQYFOp6M3D7MtnJpBo9E4HA735s8//9zU1HTz5k06crFCX1/fqVOnhoaG3Ht0Ol1ubi71H+eCgoK2trbJyUn6AjKcVqvdsWMHhmHU5szMTENDQ3d3N47j9AZjDKlU+r/nDrPb7U1NTVu2bEEI8fn8vLw86iKv0+nS09OVSiVCaPPmzQaD4dKlS4sM4MGFcHh42N/fn2r7+/sPDw/Tm4clLl68+N133xUXF1Obcrn8xIkThw4dCgsLq6iooDcbI0ml0oaGhvfffz8qKmrv3r3UzoUnv4+Pj0AggPN/ifT393d0dBQVFVGbGIZNT09XVlYWFBQkJiaOjIzQG4/Bbt68SRCE+4GX+yI/PDzs3snn8318fBZ/8nvwYBkcx93PVLlcrsvlojcPGxgMhvz8/AMHDsTGxlJ7Ojo6qEkvOzs7H3zwwby8vPDwcFozMk1DQwP1G+7r60tISMjLy0tKSlp48iM4/5dSVVVVbm6u+36luLi4rKwMIeR0Oh977LF9+/YdO3aM1oCMRd1wu2/E3Sc5juPuUTMIIR6Pt/iT34PvCDUazdjYGNUeHR2lxm6ApTM2NpaRkbFjx47y8nL3TvfUz/fdd19wcHBPTw9N6RjL/Ru+9957161bd/78efQ/T/7Z2Vmr1Qrn/1JwuVyff/759u3b3Xvcfx18Pv+JJ564cOECTdGYz8/PDyE0Pj5Obbov8gtPfoIgxsbGFn/ye3AhTEtLO3XqFNVubGxMS0ujNQ7DTUxMZGRkbN26dffu3bc9YHx8fGho6J577vmdg7GHyWTS6/XUQitpaWmnT58mCAIh1NjYGBkZuXLlSroDMtDJkydxHN+0adNtPz137hyc8EtHKpUmJSU1NjZSm+6LfFpaWnNzMzVMoa2tTSqVRkVFLfJ7eXDX6AsvvJCYmKhSqQQCgVarbW1tpTsRkxUVFRkMhuHh4WeeeQYhtG7duueee66rq+uNN95ITk4mCOKLL77IzMxMSkqiOymjDAwMPPvssxs2bOByuV999VVMTExWVhZC6PHHH3/rrbe2bduWlJRUUVFRUVHh7kECd5FWqy0tLV3YEVdWVqZSqTQaTXd3t06na25upjEeYzidzvLycrPZjBAqLy/38vL64IMPEEKvv/769u3bJyYment7R0ZGtm3bhhB66KGHwsLC8vPzMzMzjxw58vLLLwsEgkUG8OD3CBFCAwMDX375JUEQTz75JLzNs6Rqa2snJibcm0FBQVlZWWazub6+/vLlyzweb/369Q8//DBcju8uu91eV1dHDYqLjY3Nz893d80Zjcbq6uqJiYnMzMyNGzfSGpOxqqqqsrKy3OOSEEKdnZ3Nzc1TU1MBAQFbtmy50zqp4P8Ex3GtVuveFAgEpaWlVLu9vf37779XKBSlpaXU27QIIavVWlVV9euvv27YsCE3N3fxATy7EAIAAACL5MHPCAEAAIDFg0IIAACA1aAQAgAAYDUohAAAAFgNCiEAAABWg0IIAACA1aAQAuAZvv7663PnztGdAgAGgvcIAVgW1q5dOzc3d6dPf/zxx6ioqJKSEljiA4C7zoOnWAOASYqKityrPFJTxrz00kvuT8Vi8WuvveZe9AMAcBfBHSEAy05GRoZer79+/fpvOXhyclIikVCL9CKESJKcmJhQq9W3ne7OZDLNzc35+vouXMUJAJaDfwwAeIaYmJg333yTaldWVqpUqrNnz8bFxanVaplMtnPnThzHjx8/HhAQ4Ovrq1Qqq6urF355S0tLYmKiXC7XaDQajebjjz+m4WcAYFmCrlEAPMPo6Ojs7CzVttls09PTxcXFu3btio+P//bbbw8cOGCz2To6OiorK/38/A4dOvTUU09t3LgxODgYIdTa2pqdnZ2Tk3P48GFvb+/jx4/v3LlTIpGUlJTQ+jMBsCxAIQTAU+3Zs4eqZImJiTU1NZ999llvb294eDhC6JNPPqmvr9fpdM8//zxC6NVXX42Ojj5x4gSPx0MIxcbG6vX69957DwohAAgKIQCeKzs7290OCwtzuVxUFUQI+fj4KJXKoaEhhJDJZGpvb9+6dWtLS4v7eF9f39raWofDsfi13ADwdFAIAfBUSqXS3RYKhQs3EUICgYAahjo+Pk4QRH19/cmTJxceIJPJJicnYUU9AKAQAsBwcrkcIfTKK6/s37+f7iwALEcwahQAhlOr1dHR0XV1dS6Xi+4sACxHUAgBYL633367p6ensLCwp6fHarXeuHGjpqZm7969dOcCYFmAQggA8z3yyCPffPPN+fPn4+LiJBJJYGDg008/DZNpAECBmWUAWHYIgkAI/dPkLwRBYBh22/lifiOSJPV6vdFoVKvVq1evpl6lAABAIQQAAMBq0DUKAACA1aAQAgAAYDUohAAAAFgNCiEAAABWg0IIAACA1aAQAgAAYLW/A4NE9Jv/bGPZAAAAAElFTkSuQmCC",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Script launching predictions on different diseases on karat7 and printing the precentage of infected at each time step.\n",
"betas = [0.05, 0.1, 0.01, 0.4, 0.04, 0.05, 0.005]\n",
"alphas = [0.05, 0.1, 0.01, 0.1, 0.01, 0.1, 0.01]\n",
"\n",
"predictions, taus = Simulation_SIS(karat7, 2, betas, alphas, 100, 1000)\n",
"plot = Plots.plot(predictions, label = taus', xlabel = \"Time\", ylabel = \"% of infected\")\n",
"png(\"img/q6_1.png\")\n",
"display(plot)"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Same as before but applied on n7_2A.\n",
"betas = [0.05, 0.1, 0.01, 0.4, 0.04, 0.05, 0.005]\n",
"alphas = [0.05, 0.1, 0.01, 0.1, 0.01, 0.1, 0.01]\n",
"\n",
"predictions, taus = Simulation_SIS(n7_2A, 100, betas, alphas, 100, 100)\n",
"plot = Plots.plot(predictions, label = taus', xlabel = \"Time\", ylabel = \"% of infected\")\n",
"png(\"img/q6_2.png\")\n",
"display(plot)"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Same as before but applied on toulouse_neigh. May be a bit long to run.\n",
"betas = [0.05, 0.1, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95]\n",
"alphas = [0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2]\n",
"\n",
"predictions, taus = Simulation_SIS(toulouse_neigh, 100, betas, alphas, 100, 100)\n",
"plot = Plots.plot(predictions, label = taus', xlabel = \"Time\", ylabel = \"% of infected\")\n",
"png(\"img/q6_3.png\")\n",
"display(plot)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 7 (written): Change the initial number of infected in the scripts above, is it in accordance with your answer in Question 2 ?\n",
"\n",
"> On remarque que plus l'on augmente le nombre initial d'infecté, plus le pourcentage d'infectés dans la population converge rapidement. On peut le voir notament avec la tangente à l'origine qui est de pente plus importante pour un nombre d'infecté initial élevé."
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Change the initial number of infected\n",
"betas = [0.5]\n",
"alphas = [0.2]\n",
"\n",
"plot = Plots.plot()\n",
"for i in [5 10 50 100]\n",
" predictions, _ = Simulation_SIS(toulouse_neigh, i, betas, alphas, 50, 100)\n",
" Plots.plot!(predictions, label = i, xlabel = \"Time\", ylabel = \"% of infected\")\n",
"end\n",
"\n",
"png(\"img/q7.png\")\n",
"display(plot)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 9 (written): Describe the figure and draw conclusions on the epidemic behavior for different degrees $d$ on regular graphs. Thus, in addition of the inner properties of the disease ($\\alpha$, $\\beta$, $\\tau$) what other parameter is essential in the spreading ? Finally, what analogy can be done with real life from this experiment ?\n",
" \n",
"> Le degré $d$ du graphe représente le nombre de connections par individus. Ainsi plus $d$ est elevé plus individus se connaissent entre eux et plus l'infection est rapide. On l'observe sur le graphique, le taux d'infectés est directement proportionnel à $d$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"## Part 2 - SIR and SAIR model\n",
" \n",
"Unfortunately SIS model is valuable for diseases we can catch back since a cured person can get ill again. This is true for the flu, the cold, etc. However COVID-19 might create immunity for whom already got it and SIS can not take into account immune or dead persons. That is why we propose in this part to consider another model more adapted to COVID-19 called SIR. It stands for Susceptible $\\rightarrow$ Infected $\\rightarrow$ Recovered where the susceptible group contains those who remain susceptible to the infection, the infected group consists of those who not only have the disease but are also in the contagious period of the disease, and the recovered group contains those who were ill, got cured, are not contagious and can not get ill anymore.\n",
"\n",
"###### M. Youssef and C. Scoglio, _\"An individual-based approach to SIR epidemics in contact networks\"_, Journal of Theoretical Biology 283 (2011)\n",
" \n",
"One limitation of SIR is that it does not model the reaction of humans when they feel the presence of the epidemic. Indeed, if feeling threaten or surrounded by infected, an individual may change its behaviors: wear mask, wash its hands, etc. This result in a smaller infection rate. That is why in this part we will also consider a variant of SIR called SAIR which stands for Susceptible $\\rightarrow$ Alert $\\rightarrow$ Infected $\\rightarrow$ Recovered. A susceptible individual becomes infected by the infection rate $\\beta_0$, an infected individual recovers and gets immune by the curing rate $\\alpha$, an individual can observe the states of its neighbors, then a susceptible individual might go to the alert state if surrounded by infected individuals with an alert rate $\\kappa$ on each contact with an infected, an alert inividual becomes infected by the infection rate $\\beta_1$ where $0<\\beta_1<\\beta_0$. In our simple SAIR model, an individual can not go back to a susceptible state when he got into the alert state.\n",
"\n",
"###### F. Darabi Sahneh and C. Scoglio, _\"Epidemic Spread in Human Networks\"_, 50th IEEE Conf. Decision and Contol, Orlando, Florida (2011)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"### 2.1 SIR\n",
" \n",
"The vector containing the disease status `state` has to change a bit since we added a new state. Hence it will be an `Array{Int32,1}` where Susceptible=0, Infected=1, and Recovered=2."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Question 11 (code): Implement the function `Simulation_SIR` (respect the header and the specifications).\n",
" \n",
"###### The corrector should be able to write `predictions, taus = Simulation_SIR(net,nbinf,betas,alphas,t,nbsimu)` with your code."
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Simulation_SIR"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\"Take a contact network, different diseases (defined by different parameters alpha and beta), a number of initial infected people and process nbsimu simulations of SIR over t time steps. You will provide the prediction of the percentage of infected at each time t as well as the spreading rate of each disease.\n",
"\n",
"* PARAMS\n",
" - net (LightGraph): graph representing the contact network\n",
" - nbinf (Int32): number of infected at the start of each simulation\n",
" - betas (Array{Float64,1}): array of infection rate on edges\n",
" - alphas (Array{Float64,1}): array of curing rate on vertices\n",
" - t (Int32): number of time step\n",
" - nbsimu (Int32): number of simulations\n",
"\n",
"* RETURNS\n",
" - (Array{Float64,3}): the prediction of the percentage of infected, the percentage of susceptible and the percentage of recovered at each time step and for each disease. The first dimension contains the time steps,the second contains the diseases, and the third the status(Infected: [:,:,1], Recovered: [:,:,2], Susceptible: [:,:,3])\n",
" - (Array{Float64,1}): effective spreading rate for each disease\n",
"\"\"\"\n",
"function Simulation_SIR(net, nbinf, betas, alphas, t, nbsimu)\n",
" taus = zeros(length(alphas))\n",
" prediction = zeros(t+1, length(taus), 3)\n",
"\n",
" for (i, (beta, alpha)) in enumerate(zip(betas, alphas))\n",
" taus[i] = round(beta / alpha, digits = 2)\n",
" for _ in 1:nbsimu\n",
" state = new_state(net, nbinf)\n",
" _, X = SIR2(net, state, beta, alpha, t)\n",
" prediction[:, i, :] += X ./ nbsimu ./ length(state)\n",
" end\n",
" end\n",
"\n",
" return prediction, taus\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 12 (written): Run the script below and describe what you see. Why the infected curve does not behave the same as for SIS ? \n",
"\n",
"> On observe la présence de la nouvelle coube \"Recovered\" qui vient retirer progressivement des indidividus de la population infectable. Ainsi, on observe que le graph converge vers un état final, et non vers un état stable comme dans le cas du modèle SIS."
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [
{
"data": {
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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Script launching prediction on one disease on n7_2A and plotting the percentage\n",
"# of infected, susceptible and recovered at each time step.\n",
"predictions, taus = Simulation_SIR(n7_2A, 2, [0.3], [0.2], 50, 1000)\n",
"\n",
"plot = Plots.plot(\n",
" [predictions[:, :, 1] predictions[:, :, 2] predictions[:, :, 3]],\n",
" label = [\"Susceptible\" \"Infected\" \"Recovered\"],\n",
" xlabel = \"t\",\n",
" ylabel = \"%\",\n",
" palette=node_colors\n",
")\n",
"png(\"img/q12.png\")\n",
"display(plot)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 13 (written): As for Question 6 script 2 plot the evolution of the percentage of infected for many $\\tau$. Describe what you see.\n",
"\n",
"> Globalement $\\tau$ semble déterminer la hauteur du pic maximal de l'infection, plus $\\tau$ est élevé, plus l'infection est importante. De même, les valeurs de $\\beta$ et $\\alpha$ semblent déterminer la longueur du pic, plus celles-ci sont élevées, plus le pic d'infection sera court dans le temps."
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Equivalent experiment as for Question 6 script 2\n",
"# Script launching predictions on different diseases on karat7 and printing the precentage of infected at each time step.\n",
"betas = [0.05, 0.1, 0.01, 0.4, 0.04, 0.05, 0.005]\n",
"alphas = [0.05, 0.1, 0.01, 0.1, 0.01, 0.1, 0.01]\n",
"\n",
"predictions, taus = Simulation_SIR(karat7, 2, betas, alphas, 100, 1000)\n",
"plot = Plots.plot(predictions[:, :, 2], label = taus', xlabel = \"Time\", ylabel = \"% of infected\")\n",
"png(\"img/q13_1.png\")\n",
"display(plot)"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"betas = [0.05, 0.1, 0.01, 0.4, 0.04, 0.05, 0.005]\n",
"alphas = [0.05, 0.1, 0.01, 0.1, 0.01, 0.1, 0.01]\n",
"\n",
"predictions, taus = Simulation_SIR(n7_2A, 10, betas, alphas, 100, 1000)\n",
"plot = Plots.plot(predictions[:, :, 2], label = taus', xlabel = \"Time\", ylabel = \"% of infected\")\n",
"png(\"img/q13_2.png\")\n",
"display(plot)"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Same as before but applied on toulouse_neigh. May be a bit long to run.\n",
"betas = [0.05, 0.1, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95]\n",
"alphas = [0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2]\n",
"\n",
"predictions, taus = Simulation_SIR(toulouse_neigh, 100, betas, alphas, 100, 1000)\n",
"plot = Plots.plot(predictions[:, :, 2], label = taus', xlabel = \"Time\", ylabel = \"% of infected\")\n",
"png(\"img/q13_3.png\")\n",
"display(plot)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 14 (code): Implement a script plotting the number of infected over 75 time steps for $\\beta=0.3$ and $\\alpha=0.2$ fixed and on 3 contact networks:\n",
" \n",
"* A regular graph of 200 vertices with degree 2.\n",
"* A regular graph of 200 vertices with degree 5.\n",
"* A regular graph of 200 vertices with degree 10."
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plots of the number of infected people according to tau over 75 time steps for 3 contact networks.\n",
"n = 200\n",
"Plots.plot()\n",
"betas = [0.3]\n",
"alphas = [0.2]\n",
"\n",
"plot = Plots.plot()\n",
"for d in [2 5 10]\n",
" net = random_regular_graph(n, d)\n",
" predictions, taus = Simulation_SIR(net, 1, betas, alphas, 75, 1000)\n",
" Plots.plot!(predictions[:, :, 2], label = d, xlabel = \"Time\", ylabel = \"% of infected\")\n",
"end\n",
"Plots.plot!()\n",
"\n",
"png(\"img/q14.png\")\n",
"display(plot)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 15 (written): From the previous figure, explain why lockdown can be interesting when hospital places are lacking ?\n",
"\n",
"> On observe qu'en diminuant le nombre de contacts potentiels entre les personnes d'un réseau, le nombre maximal d'infecté à un temps donné diminue. Ainsi par la mise en place d'un confinement les hopitaux peuvent être capable de supporter plus facilement la charge d'infectés."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"### 2.2 SAIR\n",
" \n",
"The vector containing the disease status `state` has to change a bit since we added a new state. Hence it will be an `Array{Int32,1}` where Susceptible=0, Infected=1, Recovered=2, and Alert=3."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Question 17 (code): Implement the function `Simulation_SAIR` (respect the header and the specifications).\n",
" \n",
"###### The corrector should be able to write `predictions, taus = Simulation_SAIR(net,nbinf,betas0,betas1,alphas,kappas,t,nbsimu)` with your code."
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Simulation_SAIR"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\"\n",
"Take a contact network, different diseases (defined by different parameters alpha and beta), a number of initial infected people and process nbsimu simulations of SAIR over t time steps. You will provide the prediction of the percentage of infected at each time t as well as the spreading rate of each disease.\n",
"\n",
"* PARAMS\n",
" - net (LightGraph): graph representing the contact network\n",
" - nbinf (Int32): number of infected at the start of each simulation\n",
" - betas0 (Array{Float64,1}): array of infection rate when not alert on edges\n",
" - betas1 (Array{Float64,1}): array of infection rate when alert on edges\n",
" - alphas (Array{Float64,1}): array of curing rate on vertices\n",
" - kappas (Array{Float64,1}): array of alerting rate on edges\n",
" - t (Int32): number of time step\n",
" - nbsimu (Int32): number of simulations\n",
"\n",
"* RETURNS\n",
" - (Array{Float64,3}): the prediction of the percentage of infected, the percentage of susceptible and the percentage of recovered at each time step and for each disease. The first dimension contains the time steps, the second contains the diseases, and the third the status (Infected: [:,:,1], Recovered: [:,:,2], Susceptible: [:,:,3])\n",
" - (Array{Float64,1}): effective spreading rate for each disease\n",
"\"\"\"\n",
"function Simulation_SAIR(net, nbinf, betas0, betas1, alphas, kappas, t, nbsimu)\n",
" taus = zeros(length(alphas))\n",
" prediction = zeros(t+1, length(taus), 4)\n",
"\n",
" for (i, (beta0, beta1, alpha, kappa)) in enumerate(zip(betas0, betas1, alphas, kappas))\n",
" taus[i] = round(beta0 / alpha, digits = 2)\n",
" for _ in 1:nbsimu\n",
" state = new_state(net, nbinf)\n",
" _, X = SAIR2(net, state, beta0, beta1, alpha, kappa, t)\n",
" prediction[:, i, :] += X ./ nbsimu ./ length(state)\n",
" end\n",
" end\n",
"\n",
" return prediction, taus\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 18 (written): Run the script below comparing the number of infected of SAIR and SIR and comment what you see.\n",
"\n",
"> On observe que le pic d'infection maximal de l'épidemie est moins important."
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {},
"outputs": [
{
"data": {
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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Script launching prediction on one disease on toulouse_neigh and plotting the percentage\n",
"# of infected at each time step for SIR and SAIR.\n",
"predictions1, _ = Simulation_SAIR(toulouse_neigh, 2, [0.2], [0.1], [0.1], [0.5], 100, 1000)\n",
"predictions2, _ = Simulation_SIR( toulouse_neigh, 2, [0.2], [0.1], 100, 1000)\n",
"\n",
"plot = Plots.plot(\n",
" [predictions1[:, :, 2] predictions2[:, :, 2]],\n",
" label = [\"SAIR\" \"SIR\"],\n",
" xlabel = \"t\",\n",
" ylabel = \"%\"\n",
")\n",
"png(\"img/q18.png\")\n",
"display(plot)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 19 (written): Of course the presented SIS, SIR, and SAIR models are limitated in their modelization of the reality. Formulate few of these limitations (at least 2). Propose few algorithm addons/ideas (at least 2) which would make the models more complex and more accurate in regards to the reality.\n",
"\n",
"> Pour rendre la simulation plus précise, nous pourrions faire en sorte que les personnes dans l'état \"recovered\" puissent repasser dans un état \"suceptible\" après un certain moment. Il serait aussi possible de rajouter une dynamique dans les relations du graphe (i.e. quand les individus vont au travail, chez eux, au cinéma...)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"## Part 3 - Discover patient zero\n",
" \n",
"In the two previous parts you may have realised that understanding and controlling the spread of epidemics on contact networks is an important task. However, information about the origin of the epidemic could be also extremely useful to reduce or prevent future outbreaks. Thus, in this part we will focus on algorithm solutions to answer this issue.\n",
" \n",
"The stochastic nature of infection propagation makes the estimation of the epidemic origin intrinsically hard: indeed, different initial conditions can lead to the same configuration at the observation time. Methods such as the distance centrality or the Jordan center try to approximate it. They both rely on spatial information by stating that the first infected is probably at the center of the cluster of infection. Mathematically:\n",
" \n",
"* The jordan center is expressed as $\\min_{v\\in \\mathcal{I}}\\max_{n\\in \\mathcal{I}}d(v,n)$ where $\\mathcal{I}$ is a connected component of the original contact network containing all infected and recovered vertices, and where $d(\\cdot,\\cdot)$ is the distance (= the shortest path) between 2 vertices (if not weighted graph each edge accounts for 1 unit). \n",
"* The distance centrality is expressed as $\\min_{v\\in \\mathcal{I}}\\sum_{n\\in \\mathcal{I}}d(v,n)(\\delta_{n,I} + \\delta_{n,R}/\\alpha)$, where $\\delta_{n,I}=1$ if the vertex n is infected ($=0$ otherwise), and where $\\delta_{n,R}=1$ if the vertex n is recovered ($=0$ otherwise). You may note that in distance centrality we increase the weight of the recovered vertices by a factor $1/\\alpha$, it translates the fact that recovered vertices tend to be closer to the origin of the epidemic since they probably got ill before.\n",
" \n",
" \n",
"We formulate the problem as follow: given a contact network and a snapshot of epidemic spread at a certain time, determine the infection source. A snapshot is a given `state` array for a contact network.\n",
"\n",
"###### A. Y. Lokhov, M. Mézard, H. Ohta, and L. Zdeborová, _\"Inferring the origin of an epidemic with a dynamic message-passing algorithm\"_, Physical Review (2014)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Question 20 (code): Implement the function `jordan` (respect the header and the specifications). You will need to use the function `dijkstra_shortest_paths` of the LighGraphs library, refer to the doc for more information. If there are multiple minimal vertices, then return the first one.\n",
" \n",
"###### The corrector should be able to write `zero = jordan(g,state,alpha)` with your code."
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"jordan"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\"\n",
"Find patient zero by mean of the jordan center method.\n",
"\n",
"* PARAMS\n",
" - g (LightGraph): graph representing the contact network\n",
" - state (Array{Int32,1}): disease status of each vertex\n",
"\n",
"* RETURNS\n",
" - (Int32): the patient zero vertex number \n",
"\"\"\"\n",
"function jordan(g, state)\n",
" n = nv(g)\n",
" d = zeros(n, n)\n",
" for i in 1:n \n",
" d[i,:] = dijkstra_shortest_paths(g, i).dists\n",
" end\n",
"\n",
" _, min_index = findmin(maximum(d, dims = 1))\n",
" _, jordan_center = min_index.I\n",
"\n",
" return jordan_center\n",
"end\n",
"\n",
"# karat7_state = new_state(karat7, 1)\n",
"# println(jordan(karat7, karat7_state))\n",
"\n",
"# nodefillc = node_colors[karat7_state.+1]\n",
"# gplot(karat7, nodefillc = nodefillc, nodelabel=1:nv(karat7))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Question 21 (code): Implement the function `distance` (respect the header and the specifications). You will need to use the function `dijkstra_shortest_paths` of the LighGraphs library, refer to the doc for more information. If there are multiple minimal vertices, then return the first one.\n",
" \n",
"###### The corrector should be able to write `zero = distance(g,state,alpha)` with your code."
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"distance"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\"Find patient zero by mean of the distance centrality method.\n",
"\n",
"* PARAMS\n",
" - g (LightGraph): graph representing the contact network\n",
" - state (Array{Int32,1}): disease status of each vertex\n",
" - alpha (Float64): curing rate\n",
"\n",
"* RETURNS\n",
" - (Int32): the patient zero vertex number \n",
"\"\"\"\n",
"function distance(g, state, alpha = 1.0)\n",
"\n",
" n = nv(g)\n",
" \n",
" d = zeros(n, n)\n",
" for i in 1:n \n",
" d[i,:] = dijkstra_shortest_paths(g, i).dists\n",
" end\n",
"\n",
" delta_infected = (state .== 1)\n",
" delta_recovered = (state .== 2)\n",
"\n",
" _, distance_centrality = findmin(\n",
" sum(\n",
" d[:,i] .* (delta_infected + delta_recovered / alpha)\n",
" )\n",
" for i in 1:n\n",
" )\n",
"\n",
" return distance_centrality\n",
"end\n",
"\n",
"# karat7_state = new_state(karat7, 0)\n",
"# karat7_state[1] = 1\n",
"# karat7_state[3] = 1\n",
"# karat7_state[8] = 2\n",
"# distance(karat7, karat7_state, 0.1)\n",
"\n",
"# nodefillc = node_colors[karat7_state.+1]\n",
"# display(gplot(karat7, nodefillc = nodefillc, nodelabel=1:nv(karat7)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"