修改后的 SIR 模型

Question

我正在制作一个修改后的 SIR 模型，其中添加了疫苗接种参数 V。最初，图中的所有节点都是易感的，并且有一些最初被感染的人。最初感染的人邻居首先接种了概率 w（这意味着他们不会被感染），然后他们感染了概率 b。接种疫苗的人的总数受 VI 控制，VI 是总人口的一小部分。

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()

我的代码的问题是S + V+ I+R的总数应该等于N，并且接种疫苗的人数也最多达到5。应该比这更高。

Answer 1

您的问题是 V 仅衡量在该时间步内接种疫苗的总人数，而不是累计接种疫苗的人数。

所以S+I+V+R 不是恒定的。如果您希望V 为累计接种次数，请执行V.append(V[-1]+len(vaccinated))

我不确定这个测试if len(vaccinated)< (Vl*N) 是否也符合您的想法。它正在检查在给定时间步长内接种疫苗的人数是否少于总人口的一部分。我怀疑你想使用累计接种次数。