In view of the outbreak of the new coronavirus in February 2020, the spread of the virus in the population has attracted people's attention. Here, the cellular automata is used to simply simulate the spread of the virus in the population.
Initialization of data
The following code sets the GUI buttons and initializes the population distribution. Here I take the population distribution as a two-dimensional normal distribution.
To calculate the normal distribution of two-dimensional scatter points, you can use matlabmvnrnd函数
The specific usage is (taking double variables as an example) : first construct the mean vector of the two variables, then construct the covariance matrix, the input is mvnrnd (mean vector, covariance matrix, the number of points you want), the output of this function It is a matrix with n rows and 2 columns. The two elements in each row represent the row subscripts and column subscripts of the obtained normal distribution points (assuming a two-dimensional positive matrix in an infinite matrix with the mean point as the center). State distribution of cast points).
% 设置GUI按键
plotbutton=uicontrol('style','pushbutton','string','运行', 'fontsize',12, 'position',[150,400,50,20], 'callback', 'run=1;');
erasebutton=uicontrol('style','pushbutton','string','停止','fontsize',12,'position',[250,400,50,20],'callback','freeze=1;');
quitbutton=uicontrol('style','pushbutton','string','退出','fontsize',12,'position',[350,400,50,20],'callback','stop=1;close;');
number = uicontrol('style','text','string','1','fontsize',12, 'position',[20,400,50,20]);
total_num=100;
n=100;
mu=[50,50];% 均值向量
Sigma=[200 0;0 200];% 协方差矩阵
r=mvnrnd(mu,Sigma,total_num);
r=fix(r);
z = zeros(n,n);
k=sub2ind(size(z),r(:,1),r(:,2));%得到人的坐标的序列索引
healthy = z;inf=z;carrier=z;cardate=z;%初始化三种类型的人群的矩阵以及携带日期的矩阵
first=randi([10,90]);
healthy(k)=200;healthy(k(first))=0;%一开始没有感染者
carrier(k(first))=200;cardate(k(first))=1;%初始化携带者天数矩阵
% 建立图像句柄
Main loop
% 主事件循环
stop= 0; run = 1;freeze = 0;
while stop==0
if run==1
%先进行感染判断
[x11,y11]=find(inf~=0);
m=[];n=[];
for i=1:length(x11)
m=[m;x11(i)-2:x11(i)+2];
n=[n;y11(i)-2:y11(i)+2];
m(m<1)=1;m(m>100)=100;
n(n<1)=1;n(n>100)=100;
end
%m的每一行为距离感染者为2以内的行坐标
%n的每一行为距离感染者为2以内的列坐标
%接下来判断这个以感染者为中心5*5的矩阵中是否有健康人
x22=[];y22=[];fm=0;
if ~isempty(m)
fm=length(m(:,1));
end
for i=1:fm
mat=healthy(m(i,:),n(i,:));%某个感染者附近的坐标
[x21,y21]=find(healthy(m(i,:),n(i,:))~=0);%healthy(m(i,:),n(i,:)是5*5的矩阵，其第几行就代表m那一行的第几个元素，n同理对应列下标
x22=[x22,m(i,x21)];y22=[y22,n(i,y21)];
end
for i=1:length(x22)
pro=rand;a=pro>0.6;b=pro<0.6;
healthy(x22(i),y22(i))=200*a;
carrier(x22(i),y22(i))=200*b;
cardate(x22(i),y22(i))=b;
end
%得到感染者附近的健康人坐标，并以一定的概率使其成为携带者
%接下来进行携带者变为感染者,以及携带天数增加
date=find(cardate==4);
carrier(date)=0;cardate(date)=0;inf(date)=200;
cardate(cardate~=0)=cardate(cardate~=0)+1;
% 现在来进行人群的移动
[x1_,y1_]=find(inf~=0);infnum=length(x1_);
inf=z;
for i=1: infnum
x1_(i)=randi([x1_(i)-7,x1_(i)+7]);y1_(i)=randi([y1_(i)-7,y1_(i)+7]);
while x1_(i)<3||x1_(i)>97||y1_(i)<3||y1_(i)>97 %若碰壁则重新取点
x1_(i)=randi([x1_(i)-7,x1_(i)+7]);y1_(i)=randi([y1_(i)-7,y1_(i)+7]);
if x1_(i)<0%因为重新取点可能导致不停的往一个方向加或减从而永远也无法跳出while所以对于过分的点直接让其等于一个正常值
x1_(i)=3;
elseif y1_(i)<0
y1_(i)=3;
elseif x1_(i)>100
x1_(i)=97;
elseif y1_(i)>100
y1_(i)=97;
end
end
end%感染者的移动
idx1=sub2ind(size(z),x1_,y1_);%得出感染者移动后的坐标索引
inf(idx1)=200;%将感染者的位置标注在矩阵上
[x2,y2]=find(healthy~=0);healnum=length(x2);%得到健康人的矩阵行列索引，以及健康人的数量
healthy = z;
for i=1: healnum
x2(i)=randi([x2(i)-7,x2(i)+7]);y2(i)=randi([y2(i)-7,y2(i)+7]);%健康人随机运动
while x2(i)<3||x2(i)>97||y2(i)<3||y2(i)>97||~isempty(find(idx1==sub2ind(size(z),x2(i),y2(i)), 1))%检测健康人是否与感染者的位置重叠若重叠则换位置
x2(i)=randi([x2(i)-7,x2(i)+7]);y2(i)=randi([y2(i)-7,y2(i)+7]);
if x2(i)<0
x2(i)=3;
elseif y2(i)<0
y2(i)=3;
elseif x2(i)>100
x2(i)=97;
elseif y2(i)>100
y2(i)=97;
end
end
end
idx2=sub2ind(size(z),x2,y2);%得到健康人移动后的下标
healthy(idx2)=200;
[x3,y3]=find(carrier~=0);carnum=length(x3);
dateidx=sub2ind(size(z),x3,y3);
cardate_=cardate;
cardate=z;
carrier=z;
for i=1: carnum
x3(i)=randi([x3(i)-7,x3(i)+7]);y3(i)=randi([y3(i)-7,y3(i)+7]);%携带者随机运动
while x3(i)<3||x3(i)>97||y3(i)<3||y3(i)>97||~isempty(find(idx1==sub2ind(size(z),x3(i),y3(i)), 1))||~isempty(find(idx2==sub2ind(size(z),x3(i),y3(i)), 1))%检测携带者是否与感染者和健康人的位置重叠若重叠则重新取点
x3(i)=randi([x3(i)-7,x3(i)+7]);y3(i)=randi([y3(i)-7,y3(i)+7]);
if x3(i)<0
x3(i)=3;
elseif y3(i)<0
y3(i)=3;
elseif x3(i)>100
x3(i)=97;
elseif y1(i)>100
y3(i)=97;
end
end
end
idx3=sub2ind(size(z),x3,y3);%得到携带者移动后的下标索引
cardate(idx3)=cardate_(dateidx);
carrier(idx3)=200;
image(cat(3,inf,healthy,carrier));
stepnumber = 1 + str2double(get(number,'string'));%更新迭代步数，每迭代一次就加一
set(number,'string',num2str(stepnumber))%将加一后的迭代代数更新
pause(0.7)
end
if freeze==1
run = 0;
freeze = 0;
end
end
It can be seen that if no measures are taken, the spread of new coronary pneumonia is getting faster and faster in the early stage, but when the number of infected people approaches the total number of people, the growth rate slows down significantly.
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