project007.ipynb 47.8 KB
Newer Older
Litwin Bartosz's avatar
Litwin Bartosz committed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters \n",
    "N = 1000\n",
    "I0, R0 = 20, 0\n",
    "S0 = N - I0 - R0\n",
    "beta = 0.5  # contacts per person per time/infection rate\n",
    "gamma = 0.2# recovery rate\n",
    "T = 200    \n",
    "dt = 0.01  \n",
    "num_steps = int(T / dt)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_values = np.linspace(0, T, num_steps + 1)\n",
    "S_values = np.zeros(num_steps + 1)\n",
    "I_values = np.zeros(num_steps + 1)\n",
    "R_values = np.zeros(num_steps + 1)\n",
    "S_values[0] = S0\n",
    "I_values[0] = I0\n",
    "R_values[0] = R0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(num_steps):\n",
    "    dS = -beta * S_values[i] * I_values[i] * dt/N\n",
    "    dI = (beta * S_values[i] * I_values[i]/N - gamma * I_values[i]) * dt\n",
    "    dR = gamma * I_values[i] * dt\n",
    "    S_values[i+1] = S_values[i] + dS\n",
    "    I_values[i+1] = I_values[i] + dI\n",
    "    R_values[i+1] = R_values[i] + dR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.plot(t_values, S_values, label='Susceptible')\n",
    "plt.plot(t_values, I_values, label='Infected')\n",
    "plt.plot(t_values, R_values, label='Removed')\n",
    "plt.title('SIR Model')\n",
    "plt.xlabel('days')\n",
    "plt.ylabel('Number of Individuals')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pisa-uDfVh2Mu-py3.10",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}