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part_III.m
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part_III.m
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close all;
load COVID_STL.mat;
%%
%================Delta Wave Interactions================
%Initialize population for two regions
POP_1 = 2876487;
POP_2 = 1263619;
%Travel matrix 1
S2to1 = 0.21; %travel rate of Susceptible pop2 to region 1
I2to1 = 0.15;
R2to1 = 0.23;
T_1 = [S2to1,0 ,0 ,0;
0 ,I2to1 ,0 ,0;
0 ,0 ,R2to1,0;
0 ,0 ,0 ,0];
%Travel matrix 2
S1to2 = 0.22; %travel rate of Susceptible pop1 to region 2
I1to2 = 0.14;
R1to2 = 0.31;
T_2 = [S1to2, 0 ,0 ,0;
0 ,I1to2 ,0 ,0;
0 ,0 ,R1to2,0;
0 ,0 ,0 ,0];
%Transition Matrix 1
r_infec1 = unknowns_opt_D(1);
r_recover1 = unknowns_opt_D(3);
r_reinfec1 = unknowns_opt_D(2);
r_death1 = unknowns_opt_D(4);
A_1 = [1-r_infec1 - S1to2, r_recover1 ,r_reinfec1 ,0;
r_infec1, 1-r_recover1-r_death1 - I1to2,0 ,0;
0 ,0 ,1-r_reinfec1 - R1to2 ,0;
0 ,r_death1, 0 ,1];
%Transition Matrix 2
r_infec2 = 0.15;
r_recover2 = 0.02;
r_reinfec2 = 0.04;
r_death2 = 0.03;
A_2 = [1-r_infec2 - S2to1, r_recover2 ,r_reinfec2 ,0;
r_infec2, 1-r_recover2-r_death2 - I2to1,0 ,0;
0 ,0 ,1-r_reinfec2 - R2to1,0;
0 ,r_death2, 0 ,1];
%concatenating 4 matrices
A_travel = [A_1,T_1;T_2,A_2];
%Initial SIRD conditions of region 1 and 2
sir_ini = [POP_1,0,0,0,POP_2,0,0,0]';
%days of interactions
t = 1000;
sir_tot = zeros(8,t);
sir_tot(:,1) = sir_ini;
for i = 2:t
sir_ini = A_travel * sir_ini;
sir_tot(:,i) = sir_ini;
end
%extract data from interactions model
I_1 = sir_tot(2,:);
I_2 = sir_tot(6,:);
D_1 = sir_tot(4,:);
D_2 = sir_tot(8,:);
cum_cases_1 = cumsum(I_1)*POP_1;
cum_cases_2 = cumsum(I_2)*POP_2;
%plotting the data
figure;
hold on;
plot(cum_cases_1);
plot(cum_cases_2);
title('Delta Wave Regions Interactions')
legend('Region 1 Cases','Region 2 Cases');
xlabel('Days')
ylabel('Cases')
hold off;
%----------------------Higher Travel Rate Delta Wave-------------------
%Travel matrix 1
S2to1 = 0.5; %travel rate of Susceptible pop2 to region 1
I2to1 = 0.4;
R2to1 = 0.36;
T_1 = [S2to1,0 ,0 ,0;
0 ,I2to1 ,0 ,0;
0 ,0 ,R2to1,0;
0 ,0 ,0 ,0];
%Travel matrix 2
S1to2 = 0.45; %travel rate of Susceptible pop1 to region 2
I1to2 = 0.39;
R1to2 = 0.47;
T_2 = [S1to2, 0 ,0 ,0;
0 ,I1to2 ,0 ,0;
0 ,0 ,R1to2,0;
0 ,0 ,0 ,0];
%Transition Matrix 1
r_infec1 = unknowns_opt_D(1);
r_recover1 = unknowns_opt_D(3);
r_reinfec1 = unknowns_opt_D(2);
r_death1 = unknowns_opt_D(4);
A_1 = [1-r_infec1 - S1to2, r_recover1 ,r_reinfec1 ,0;
r_infec1, 1-r_recover1-r_death1 - I1to2,0 ,0;
0 ,0 ,1-r_reinfec1 - R1to2 ,0;
0 ,r_death1, 0 ,1];
%Transition Matrix 2
r_infec2 = 0.15;
r_recover2 = 0.02;
r_reinfec2 = 0.04;
r_death2 = 0.03;
A_2 = [1-r_infec2 - S2to1, r_recover2 ,r_reinfec2 ,0;
r_infec2, 1-r_recover2-r_death2 - I2to1,0 ,0;
0 ,0 ,1-r_reinfec2 - R2to1,0;
0 ,r_death2, 0 ,1];
%concatenating 4 matrices
A_travel = [A_1,T_1;T_2,A_2];
%Initial SIRD conditions of region 1 and 2
sir_ini = [POP_1,0,0,0,POP_2,0,0,0]';
%days of interactions
t = 1000;
sir_tot = zeros(8,t);
sir_tot(:,1) = sir_ini;
for i = 2:t
sir_ini = A_travel * sir_ini;
sir_tot(:,i) = sir_ini;
end
%extract data from interactions model
I_1 = sir_tot(2,:);
I_2 = sir_tot(6,:);
D_1 = sir_tot(4,:);
D_2 = sir_tot(8,:);
cum_cases_1 = cumsum(I_1)*POP_1;
cum_cases_2 = cumsum(I_2)*POP_2;
%plotting the data
figure;
hold on;
plot(cum_cases_1);
plot(cum_cases_2);
title('Higher Travel Rate Delta Wave Regions Interactions')
legend('Region 1 Cases','Region 2 Cases');
xlabel('Days')
ylabel('Cases')
hold off;
%-----------------------Restricted travel Policy Delta ------------------
%policy - infected population in two regions cannot travel, others are
%encouraged to not travel
%Travel matrix 1
S2to1 = 0.02; %travel rate of Susceptible pop2 to region 1
I2to1 = 0;
R2to1 = 0.02;
T_1 = [S2to1,0 ,0 ,0;
0 ,I2to1 ,0 ,0;
0 ,0 ,R2to1,0;
0 ,0 ,0 ,0];
%Travel matrix 2
S1to2 = 0.03; %travel rate of Susceptible pop1 to region 2
I1to2 = 0;
R1to2 = 0.2;
T_2 = [S1to2, 0 ,0 ,0;
0 ,I1to2 ,0 ,0;
0 ,0 ,R1to2,0;
0 ,0 ,0 ,0];
%Transition Matrix 1
r_infec1 = unknowns_opt_D(1);
r_recover1 = unknowns_opt_D(3);
r_reinfec1 = unknowns_opt_D(2);
r_death1 = unknowns_opt_D(4);
A_1 = [1-r_infec1 - S1to2, r_recover1 ,r_reinfec1 ,0;
r_infec1, 1-r_recover1-r_death1 - I1to2,0 ,0;
0 ,0 ,1-r_reinfec1 - R1to2 ,0;
0 ,r_death1, 0 ,1];
%Transition Matrix 2
r_infec2 = 0.15;
r_recover2 = 0.02;
r_reinfec2 = 0.04;
r_death2 = 0.03;
A_2 = [1-r_infec2 - S2to1, r_recover2 ,r_reinfec2 ,0;
r_infec2, 1-r_recover2-r_death2 - I2to1,0 ,0;
0 ,0 ,1-r_reinfec2 - R2to1,0;
0 ,r_death2, 0 ,1];
%concatenating 4 matrices
A_travel = [A_1,T_1;T_2,A_2];
%Initial SIRD conditions of region 1 and 2
sir_ini = [POP_1,0,0,0,POP_2,0,0,0]';
%days of interactions
t = 1000;
sir_tot = zeros(8,t);
sir_tot(:,1) = sir_ini;
for i = 2:t
sir_ini = A_travel * sir_ini;
sir_tot(:,i) = sir_ini;
end
%extract data from interactions model
I_1 = sir_tot(2,:);
I_2 = sir_tot(6,:);
D_1 = sir_tot(4,:);
D_2 = sir_tot(8,:);
cum_cases_1 = cumsum(I_1)*POP_1;
cum_cases_2 = cumsum(I_2)*POP_2;
%plotting the data
figure;
hold on;
plot(cum_cases_1);
plot(cum_cases_2);
title('Policied Delta Wave Regions Interactions')
legend('Region 1 Cases','Region 2 Cases');
xlabel('Days')
ylabel('Cases')
hold off;
%%
%=======================Omicron Wave Interactions========================
%Initialize population for two regions
POP_1 = 2876487;
POP_2 = 1263619;
%Travel matrix 1
S2to1 = 0.09; %travel rate of Susceptible pop2 to region 1
I2to1 = 0.11;
R2to1 = 0.08;
T_1 = [S2to1,0 ,0 ,0;
0 ,I2to1 ,0 ,0;
0 ,0 ,R2to1,0;
0 ,0 ,0 ,0];
%Travel matrix 2
S1to2 = 0.15; %travel rate of Susceptible pop1 to region 2
I1to2 = 0.11;
R1to2 = 0.13;
T_2 = [S1to2, 0 ,0 ,0;
0 ,I1to2 ,0 ,0;
0 ,0 ,R1to2,0;
0 ,0 ,0 ,0];
%Transition Matrix 1
r_infec1 = unknowns_opt_O(1);
r_recover1 = unknowns_opt_O(3);
r_reinfec1 = unknowns_opt_O(2);
r_death1 = unknowns_opt_O(4);
A_1 = [1-r_infec1 - S1to2, r_recover1 ,r_reinfec1 ,0;
r_infec1, 1-r_recover1-r_death1 - I1to2,0 ,0;
0 ,0 ,1-r_reinfec1 - R1to2 ,0;
0 ,r_death1, 0 ,1];
%Transition Matrix 2
r_infec2 = 0.3;
r_recover2 = 0.08;
r_reinfec2 = 0.04;
r_death2 = 0.03;
A_2 = [1-r_infec2 - S2to1, r_recover2 ,r_reinfec2 ,0;
r_infec2, 1-r_recover2-r_death2 - I2to1,0 ,0;
0 ,0 ,1-r_reinfec2 - R2to1,0;
0 ,r_death2, 0 ,1];
%concatenating 4 matrices
A_travel = [A_1,T_1;T_2,A_2];
%Initial SIRD conditions of region 1 and 2
sir_ini = [POP_1,0,0,0,POP_2,0,0,0]';
%days of interactions
t = 500;
sir_tot = zeros(8,t);
sir_tot(:,1) = sir_ini;
for i = 2:t
sir_ini = A_travel * sir_ini;
sir_tot(:,i) = sir_ini;
end
%extract data from interactions model
I_1 = sir_tot(2,:);
I_2 = sir_tot(6,:);
D_1 = sir_tot(4,:);
D_2 = sir_tot(8,:);
cum_cases_1 = cumsum(I_1)*POP_1;
cum_cases_2 = cumsum(I_2)*POP_2;
%plotting the data
figure;
hold on;
plot(cum_cases_1);
plot(cum_cases_2);
title('Omicron Wave Regions Interactions')
legend('Region 1 Cases','Region 2 Cases');
xlabel('Days')
ylabel('Cases')
hold off;
%-----------------------Restricted travel Policy Omicron ------------------
%policy infected population in two
%Travel matrix 1
S2to1 = 0.03; %travel rate of Susceptible pop2 to region 1
I2to1 = 0;
R2to1 = 0.04;
T_1 = [S2to1,0 ,0 ,0;
0 ,I2to1 ,0 ,0;
0 ,0 ,R2to1,0;
0 ,0 ,0 ,0];
%Travel matrix 2
S1to2 = 0.07; %travel rate of Susceptible pop1 to region 2
I1to2 = 0;
R1to2 = 0.05;
T_2 = [S1to2, 0 ,0 ,0;
0 ,I1to2 ,0 ,0;
0 ,0 ,R1to2,0;
0 ,0 ,0 ,0];
%Transition Matrix 1
r_infec1 = unknowns_opt_O(1);
r_recover1 = unknowns_opt_O(3);
r_reinfec1 = unknowns_opt_O(2);
r_death1 = unknowns_opt_O(4);
A_1 = [1-r_infec1 - S1to2, r_recover1 ,r_reinfec1 ,0;
r_infec1, 1-r_recover1-r_death1 - I1to2,0 ,0;
0 ,0 ,1-r_reinfec1 - R1to2 ,0;
0 ,r_death1, 0 ,1];
%Transition Matrix 2
r_infec2 = 0.3;
r_recover2 = 0.08;
r_reinfec2 = 0.04;
r_death2 = 0.03;
A_2 = [1-r_infec2 - S2to1, r_recover2 ,r_reinfec2 ,0;
r_infec2, 1-r_recover2-r_death2 - I2to1,0 ,0;
0 ,0 ,1-r_reinfec2 - R2to1,0;
0 ,r_death2, 0 ,1];
%concatenating 4 matrices
A_travel = [A_1,T_1;T_2,A_2];
%Initial SIRD conditions of region 1 and 2
sir_ini = [POP_1,0,0,0,POP_2,0,0,0]';
%days of interactions
t = 500;
sir_tot = zeros(8,t);
sir_tot(:,1) = sir_ini;
for i = 2:t
sir_ini = A_travel * sir_ini;
sir_tot(:,i) = sir_ini;
end
%extract data from interactions model
I_1 = sir_tot(2,:);
I_2 = sir_tot(6,:);
D_1 = sir_tot(4,:);
D_2 = sir_tot(8,:);
cum_cases_1 = cumsum(I_1)*POP_1;
cum_cases_2 = cumsum(I_2)*POP_2;
%plotting the data
figure;
hold on;
plot(cum_cases_1);
plot(cum_cases_2);
title('Policied Omicron Wave Regions Interactions')
legend('Region 1 Cases','Region 2 Cases');
xlabel('Days')
ylabel('Cases')
hold off;
%%