diff --git a/part_III.m b/part_III.m
index 7a9d36b..1f8dd99 100644
--- a/part_III.m
+++ b/part_III.m
@@ -92,6 +92,89 @@
 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 ------------------
@@ -118,6 +201,28 @@
       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 
@@ -259,8 +364,6 @@
 hold off;
 
 
-%plotting the combined cum cases and deaths
-
 
 %-----------------------Restricted travel Policy Omicron ------------------
 %policy infected population in two 
@@ -284,7 +387,27 @@
       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