修改后的SIR模型

本文介绍了修改后的SIR模型的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！

问题描述

我正在制作带有增加的疫苗接种参数V的修改后的SIR模型.最初，图中的所有节点都是易受感染的，并且有一些最初感染的人.最初感染邻居的人首先被接种了概率w(这意味着他们不能被感染)，然后又被感染了概率b.接种疫苗的总人数由V1控制，而V1是总人口的一小部分.

I am making a modified SIR model with an added vaccination parameter V. InitIALLY all the nodes in the graph are susceptible and there are a few initially infected people. The initial infected people neighbours are first vaccinated with prob w (which means they cant be infected) and then they are infected with prob b. The total number of vaccinated people is controlled by Vl which is a fraction of the total population.

这是我的代码-

import networkx as nx
import random
import scipy
from collections import defaultdict
from collections import Counter
import matplotlib.pyplot as plt
import numpy as np
from statistics import mean
from random import choice
from random import sample

def test_transmission(u, v, p):

    return random.random()<p


def discrete_SIR(G,
                initial_infecteds=None, initial_recovereds = None,beta=0.8,
                rho = None, w=0.5,Vl=1,tmin = 0, tmax = 100000,
                return_full_data = False):


    if G.has_node(initial_infecteds):
        initial_infecteds=[initial_infecteds]

    N=  G.order()
    t = [tmin]
    S = [N-len(initial_infecteds)]
    I = [len(initial_infecteds)]
    R = [0]
    V = [0]

    susceptible = defaultdict(lambda: True)
    #above line is equivalent to u.susceptible=True for all nodes.

    for u in initial_infecteds:
        susceptible[u] = False
    if initial_recovereds is not None:
        for u in initial_recovereds:
            susceptible[u] = False

    infecteds = set(initial_infecteds)
    print('len of infected initially',len(infecteds))

    while infecteds and t[-1]<tmax :
        print('len of infected on each iter',len(infecteds))
        new_infecteds = set()
        vaccinated = set()
        #infector = {}  #used for returning full data.  a waste of time otherwise
        for u in infecteds:
            print('u-->' +str(u))
            for v in G.neighbors(u):
                print('v --> '+ str(v))
            ##vaccination
                if len(vaccinated)+V[-1]< (Vl*N)  : #check if vaccination over or not
                #V.append(V[-1]+len(vaccinated))< (Vl*N)
                    #print(len(vaccinated),Vl*N)
                    print("HI")
                    print(V[-1])

                    if susceptible[v] and test_transmission(u, v, w):

                        vaccinated.add(v)
                        susceptible[v] = False
                        print('transmitting vaccination')

                    elif susceptible[v] and test_transmission(u,v,beta):
                        new_infecteds.add(v)
                        susceptible[v]=False
                        print('transmitting infection')
                else:

                    print("BYE")
                    if susceptible[v] and test_transmission(u, v,beta):
                        new_infecteds.add(v)
                        susceptible[v] = False
                        #infector[v] = [u]



        infecteds = new_infecteds

        R.append(R[-1]+I[-1])
        V.append(len(vaccinated)+V[-1])
        I.append(len(infecteds))
        S.append(N-V[-1]-I[-1]-R[-1])
        #S.append(S[-1]-V[-1]-I[-1])
        t.append(t[-1]+1)

        print('\n')
        print('time is',str(t) +' --> ')
        print('infected is',I)
        print('sum is',R[-1]+V[-1]+I[-1]+S[-1])
        print('R V I S',str(R[-1])+','+str(V[-1])+','+str(I[-1])+','+str(S[-1]))
        print('time t[-1]',t[-1])


    if not return_full_data:
        return scipy.array(t), scipy.array(S),scipy.array(V), scipy.array(I), \
               scipy.array(R)





m=100
G=nx.grid_2d_graph(m,m,periodic=True)

def avg_deg(self,num_nodes):
        return self.number_of_edges() * 2 / num_nodes


def avg_degree(num_nodes,target_deg):

    G=nx.Graph()

    G.add_nodes_from(range(num_nodes))
    while avg_deg(G,num_nodes) < target_deg:
        n1, n2 = sample(G.nodes(), 2)
        G.add_edge(n1, n2, weight=1)

    nx.draw(G)
    plt.show()
    return G


initial_infections = [(u,v) for (u,v) in G if u==int(m/2) and v==int(m/2)]

t, S, V, I, R = discrete_SIR(G,initial_infecteds= initial_infections,beta=0.8,w=0.05,Vl=0.1)

plt.figure()
plt.plot(t,I,ls='-',color='red')
plt.plot(t,R,ls='--',color='orange')
plt.plot(t,S,ls='--',color='green')
plt.plot(t,V,ls='-',color='black')
plt.show()

我的代码存在问题，即S + V + I + R的总数应等于N，并且接种人数最多也要达到5.该数量应该更高.

The problem with my code is the total number of S + V+ I+R should be equal to N and the number of vaccinated people is also at max coming to be 5. It should be higher than that.

vaccinations

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