改进型SIR mod

Question

我正在做一个修改的SIR模型，添加了一个疫苗接种参数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。最初受感染的人首先接种prob-w（这意味着他们不能被感染），然后再感染prob-b。接种疫苗的总人数由Vl控制，Vl是总人口的一部分。你知道吗

这是我的密码-

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，接种疫苗的人数也最多达到5人。应该比这个高。你知道吗

Answer 1

你的问题是，V只是衡量在该时间段内接种疫苗的总人数，而不是累计接种人数。你知道吗

所以S+I+V+R不是常数。如果你希望V是疫苗接种的累计次数，那么就做V.append(V[-1]+len(vaccinated))

我不确定这个测试if len(vaccinated)< (Vl*N)是否也符合你的想法。它正在检查在给定的时间段内接种疫苗的人数是否少于整个人口的一部分。我怀疑你想用累计接种次数。你知道吗