%% Figure 1(a)
function DT_divorce
close all
clear all

global beta gamma mu I_b

opts=odeset('Events',@RCI);


mu=1/21900;
beta=1;
gamma=1/5;
I_b=1e-6;

cont=.5;

cont_end=365;
tend=80*365;

Zsq=mu*beta;
Z=-I_b*beta*(mu+gamma)-mu*(mu+gamma+beta);
noZ=mu*(mu+gamma);
S_star=(-Z-sqrt(Z^2-4*Zsq*noZ))/(2*Zsq);
% otherS_star=(-Z+sqrt(Z^2-4*Zsq*noZ))/Zsq;
I_star=-(beta*S_star*I_b-mu+mu*S_star)/(beta*S_star);

initials=[S_star I_star S_star I_star 0 0];

tspan1=0:1:365;
tspan2=365:1:cont_end+365;
tspan3=cont_end+365:1:tend+365;

[T1,Y1]=ode45(@SIR,tspan1,initials,[],0);
[T2,Y2,te1,ye1,ie1]=ode45(@SIR,tspan2,[Y1(end,1:4) 0 0],opts,cont);
[T3,Y3,te2,ye2,ie2]=ode45(@SIR,tspan3,Y2(length(Y2),:),opts,0);
T=[T1(1:length(T1)-1);T2(1:length(T2)-1);T3]-365;
Y=[Y1(1:length(Y1)-1,:);Y2(1:length(Y2)-1,:);Y3];


figure(1)
hold on
fill([0,0,1,1],[0,1.75,1.75,0],[.95,.95,.95],'EdgeColor','None')
[hAx,hLine1,hLine2]=plotyy(T(365:end)/365,Y(365:end,5)./Y(365:end,6),T/365,Y(:,2));
leg=legend('Control Period','Relative Cumulative Incidence','Proportion Infective','Location','Northeast');
set(leg,'FontSize',15)
plot(T(1:10:end),ones(length(T(1:10:end)),1),'r:','linewidth',2)
set(hLine2,'Color','k','LineWidth',2)
set(hLine1,'Color','r','LineWidth',2)
set(hAx(2),'YColor','k','FontSize',25,'XLim',[-1 tend/365],'YLim',[-1e-8 10e-3],'YTick',linspace(0,10e-3,6))
set(hAx(1),'YColor','r','FontSize',25,'XLim',[-1 tend/365],'YLim',[0 1.75],'YTick',linspace(0,1.75,8))
xticks(0:10:tend/365-1)
ylabel(hAx(2),'Proportion of Population Infective')
ylabel(hAx(1),'Relative Cumulative Incidence')
xlabel(hAx(1),'Time (yrs)')
hold off

%Create Beta matrix for R_t
b_mat=ones(1,length(T));
b_mat(T>0)=1-cont;
b_mat(T>365)=1;

figure(2)
subplot(3,1,1)
hold on
fill([0,0,1,1],[0,1.75,1.75,0],[.95,.95,.95],'EdgeColor','None')
[hAx,hLine1,hLine2]=plotyy(T(365:end)/365,Y(365:end,5)./Y(365:end,6),T/365,Y(:,2));
leg=legend('Control Period','Location','Northeast');
set(leg,'FontSize',15)
plot(T(1:10:end),ones(length(T(1:10:end)),1),'r:','linewidth',2)
set(hLine2,'Color','k','LineWidth',2)
set(hLine1,'Color','r','LineWidth',2)
set(hAx(2),'YColor','k','FontSize',25,'YLim',[-1e-8 10e-3],'YTick',linspace(0,10e-3,6))
set(hAx(1),'YColor','r','FontSize',25,'YLim',[0 1.75],'YTick',linspace(0,1.5,4))
xticks(0:tend/365-1)
ylabel(hAx(2),'Infectives')
ylabel(hAx(1),'RCI')
hold off
subplot(3,1,2)
hold on
fill([0,0,1,1],[.151,1.75,1.75,.151],[.95,.95,.95],'EdgeColor','None')
plot(T/365,Y(:,1),'k','linewidth',2)
plot(T/365,Y(1,1)*ones(length(T),1),'k--')
xlabel('Time (yrs)')
ylabel('Susceptibles')
xticks(0:tend/365-1)
set(gca,'fontsize',25)
axis([-1 50 .15 .25])
hold off
subplot(3,1,3)
hold on
fill([0,0,1,1],[.505,1.75,1.75,.505],[.95,.95,.95],'EdgeColor','None')
plot(T/365,Y(:,1).*b_mat'*beta/gamma,'k','linewidth',2)
plot(T/365,ones(length(T),1),'k--')
xlabel('Time (yrs)')
ylabel('R_t')
xticks(0:tend/365)
axis([-1 50 0.5 1.2])
set(gca,'fontsize',25)
hold off

hold off

end

function [value,isterminal,direction]=RCI(t,y,mod)

value=[y(5)-y(6),y(5)-y(6)];
isterminal=[0,0];
direction=[1,-1];

end

function y=SIR(t,y,mod)
global beta gamma mu I_b
S1=y(1);
S2=y(3);
I1=y(2);
I2=y(4);

c=1-mod;

y(1)=mu*(1-S1)-c*beta*S1*(I1+I_b);
y(2)=c*beta*S1*(I1+I_b)-(gamma+mu)*I1;
y(3)=mu*(1-S2)-beta*S2*(I2+I_b);
y(4)=beta*S2*(I2+I_b)-(gamma+mu)*I2;
y(5)=c*beta*S1*(I1+I_b);
y(6)=beta*S2*(I2+I_b);



end

%% Figure 1(b)
function DT_Divorce_NewHeat
close all
clear all

global gamma mu I_b

num=50;

mu=1/21900;
gamma=1/5;
I_b=1e-6;


cont=1;

R0=linspace(1,100,num);

beta=R0*(gamma+mu);
controlLength=365*linspace(1/12,80,num);


Zsq=mu*beta;
Z=-I_b*beta*(mu+gamma)-mu*(mu+gamma+beta);
noZ=mu*(mu+gamma);
S_star=(-Z-sqrt(Z.^2-4*Zsq.*noZ))./(2*Zsq);

I_star=-(beta.*S_star*I_b-mu+mu*S_star)./(beta.*S_star);

initials=[S_star; I_star; S_star; I_star; zeros(1,length(R0)); zeros(1,length(R0))];

RCI=zeros(length(R0),length(controlLength));

for i=1:length(beta)
    for j=1:length(controlLength)
        tspan1=0:1:controlLength(j);
        tspan2=controlLength(j):1:controlLength(j)+365*25;
        [T1,Y1]=ode45(@SIR,tspan1,initials(:,i),[],[cont beta(i)]);
        [T2,Y2]=ode45(@SIR,tspan2,Y1(length(Y1),:),[],[0 beta(i)]);
        RCI(i,j)=max(Y2(:,5)./Y2(:,6));
        CA(i,j)=min(Y2(:,6)-Y2(:,5));
        times=T2(Y2(:,2)>initials(2,i));
        time(i,j)=times(1);
        [i j]
    end
end

RCI2=RCI;
RCI2(RCI2<=1)=NaN;

FS1=30;

figure(1)
colormap(jet);
b=image(round(controlLength/365),R0,RCI2,'CDataMapping','scaled');
set(b,'AlphaData',~isnan(RCI2))
set(gca,'YDir','normal')
xlabel('Duration of Control (yrs)','FontSize',FS1)
ylabel('\it{R}_0','FontSize',FS1)
c=colorbar;
caxis([1 1.7])
ylabel(c,'Maximum Observed RCI','FontSize',FS1)
xt=get(gca,'XTick');
set(gca,'fontsize',FS1)


figure(2)
colormap(flipud(jet));
image(round(controlLength/365),R0,CA*2e6,'CDataMapping','scaled')
set(gca,'YDir','normal')
xlabel('Length of Control Period (yrs)','FontSize',FS1)
ylabel('\it{R}_0','FontSize',FS1)
c=colorbar;
ylabel(c,'Lowest Number of Cases Averted','FontSize',FS1)


end

function y=SIR(t,y,params)
global gamma mu I_b
S1=y(1);
S2=y(3);
I1=y(2);
I2=y(4);

c=1-params(1);
beta=params(2);

y(1)=mu*(1-S1)-c*beta*S1*(I1+I_b);
y(2)=c*beta*S1*(I1+I_b)-(gamma+mu)*I1;
y(3)=mu*(1-S2)-beta*S2*(I2+I_b);
y(4)=beta*S2*(I2+I_b)-(gamma+mu)*I2;
y(5)=c*beta*S1*(I1+I_b);
y(6)=beta*S2*(I2+I_b);



end

%% Figure 1(c)
function DT_Divorce_lengthxstrength
close all
clear all


global gamma mu I_b

num=150;

mu=1/21900;
gamma=1/5;
I_b=1e-6;

R0=5;
beta=R0*gamma;
controlLength=365*linspace(1/12,20,num);
strength=linspace(0,1,num);


Zsq=mu*beta;
Z=-I_b*beta*(mu+gamma)-mu*(mu+gamma+beta);
noZ=mu*(mu+gamma);
S_star=(-Z-sqrt(Z.^2-4*Zsq.*noZ))./(2*Zsq);
I_star=-(beta.*S_star*I_b-mu+mu*S_star)./(beta.*S_star);

initials=[S_star; I_star; S_star; I_star; zeros(1,length(R0)); zeros(1,length(R0))];

RCI=zeros(num,num);

for i=1:length(controlLength)
    for j=1:length(strength)
        tspan1=0:1:controlLength(i);
        tspan2=controlLength(i):1:controlLength(i)+365*25;
        [T1,Y1]=ode45(@SIR,tspan1,initials(:),[],[strength(j) beta]);
        [T2,Y2]=ode45(@SIR,tspan2,Y1(length(Y1),:),[],[0 beta]);
        RCI(i,j)=max(Y2(:,5)./Y2(:,6));
        CA(i,j)=-max(Y2(:,6)-Y2(:,5));
        [i j]
    end
end

RCI2=RCI;
RCI2(RCI2<=1)=NaN;

FS1=30;
FS2=40;

figure(1)
colormap(jet);
b=image(strength,round(controlLength/365),RCI2,'CDataMapping','scaled');
set(b,'AlphaData',~isnan(RCI2))
set(gca,'YDir','normal')
set(gca,'FontSize',FS1)
xlabel('Effectiveness of Control','FontSize',FS1)
ylabel('Duration of Control (yrs)','FontSize',FS1)
c=colorbar;
caxis([1 1.7])
ylabel(c,'Maximum Observed RCI','FontSize',FS1)

figure(2)
colormap(flipud(jet));
image(strength,round(controlLength/365),CA*2e6,'CDataMapping','scaled')
set(gca,'YDir','normal')
xlabel('Effectiveness of Control','FontSize',FS1)
ylabel('Length of Control Period (yrs)','FontSize',FS1)
c=colorbar;
ylabel(c,'Lowest Number of Cases Averted','FontSize',FS1)

end

function y=SIR(t,y,params)
global gamma mu I_b
S1=y(1);
S2=y(3);
I1=y(2);
I2=y(4);

c=1-params(1);
beta=params(2);

y(1)=mu*(1-S1)-c*beta*S1*(I1+I_b);
y(2)=c*beta*S1*(I1+I_b)-(gamma+mu)*I1;
y(3)=mu*(1-S2)-beta*S2*(I2+I_b);
y(4)=beta*S2*(I2+I_b)-(gamma+mu)*I2;
y(5)=c*beta*S1*(I1+I_b);
y(6)=beta*S2*(I2+I_b);



end

%% Figure 2(a)
function Seasonal_divorce
close all
clear all

global beta0 beta1 gamma mu I_b

opts=odeset('Events',@RCI);

mu=1/21900;
beta0=1;
beta1=.01;
gamma=1/5;
I_b=1e-6;

cont=.9;


cont_end=365*1;
shift=1-mod(cont_end,1);
tend=5*365;

Zsq=mu*beta0;
Z=-I_b*beta0*(mu+gamma)-mu*(mu+gamma+beta0);
noZ=mu*(mu+gamma);
S_star=(-Z-sqrt(Z^2-4*Zsq*noZ))/(2*Zsq);
I_star=-(beta0*S_star*I_b-mu+mu*S_star)/(beta0*S_star);

inits=[S_star I_star S_star I_star 0 0];

tspan0=0:1:36500+365*shift;

[T,Y]=ode45(@SIR_seasonal,tspan0,inits,[],0);

initials=[Y(end,1:4) 0 0];

tspan1=365*shift:1:(365*shift)+365;
tspan2=tspan1(end):1:tspan1(end)+cont_end;
tspan3=tspan2(end):1:tend+tspan2(end);

[T1,Y1]=ode45(@SIR_seasonal,tspan1,initials,[],0);
[T2,Y2,te1,ye1,ie1]=ode45(@SIR_seasonal,tspan2,[Y1(end,1:4) 0 0],opts,cont);
[T3,Y3,te2,ye2,ie2]=ode45(@SIR_seasonal,tspan3,Y2(end,:),opts,0);
T=([T1(1:length(T1)-1);T2(1:length(T2)-1);T3]-365*shift)-365;
Y=[Y1(1:length(Y1)-1,:);Y2(1:length(Y2)-1,:);Y3];
te2=te2+1;

figure(4)
hold on
fill(([tspan2(1),tspan2(1),tspan2(end),tspan2(end)]-365)/365-shift,[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
[hAx,hLine1,hLine2]=plotyy(T(365:end)/365,Y(365:end,5)./Y(365:end,6),T/365,Y(:,2));
leg=legend('Control Period','Relative Cumulative Incidence','Proportion Infective','Location','Northwest');
set(leg,'FontSize',15)
plot(T(1:10:end),ones(length(T(1:10:end)),1),'r:','linewidth',2)
set(hLine2,'Color','k','LineWidth',2)
set(hLine1,'Color','r','LineWidth',2)
set(hAx(2),'YColor','k','FontSize',25,'YLim',[-1e-8 1e-2],'YTick',linspace(0,1e-2,6))
set(hAx(1),'YColor','r','FontSize',25,'YLim',[0 1.75],'YTick',linspace(0,1.75,8))
xticks([0 1 2 3 4 5 6])
ylabel(hAx(2),'Proportion of Population Infective')
ylabel(hAx(1),'Relative Cumulative Incidence')
xlabel(hAx(1),'Time (yrs)','FontSize',25)
hold off

end

function [value,isterminal,direction]=RCI(t,y,mod)

value=[y(5)-y(6),y(5)-y(6)];
isterminal=[0,0];
direction=[1,-1];

end

function y=SIR_seasonal(t,y,mod)
global beta0 beta1 gamma mu I_b
S1=y(1);
S2=y(3);
I1=y(2);
I2=y(4);

c=1-mod;

y(1)=mu*(1-S1)-c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b);
y(2)=c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b)-(gamma+mu)*I1;
y(3)=mu*(1-S2)-beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b);
y(4)=beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b)-(gamma+mu)*I2;
y(5)=c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b);
y(6)=beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b);



end

%% Figure 2(b)
function Seasonal_Divorce_NewHeat
close all
clear all

global gamma mu I_b beta1

num=150;

mu=1/21900;
beta1=.01;
gamma=1/5;
I_b=1e-6;


R0=linspace(2,20,num);
beta0=R0*gamma;
controlLength=365*linspace(1/10,10,num);


Zsq=mu*beta0;
Z=-I_b*beta0*(mu+gamma)-mu*(mu+gamma+beta0);
noZ=mu*(mu+gamma);
S_star=(-Z-sqrt(Z.^2-4*Zsq.*noZ))./(2*Zsq);
I_star=-(beta0.*S_star*I_b-mu+mu*S_star)./(beta0.*S_star);

inits=[S_star; I_star; S_star; I_star; zeros(1,length(R0)); zeros(1,length(R0))];

RCI=zeros(length(R0),length(controlLength));

for i=1:length(beta0)
    [Tb,Yb]=ode15s(@SIR_seasonal,0:10:36500,inits(:,i),[],[beta0(i) 0]);
    initials=[Yb(end,1:4) 0 0];
    for j=1:length(controlLength)
        tspan1=0:5:controlLength(j);
        tspan2=controlLength(j):5:controlLength(j)+365*25;
        [T1,Y1]=ode45(@SIR_seasonal,tspan1,initials,[],[beta0(i) 1]);
        [T2,Y2]=ode45(@SIR_seasonal,tspan2,Y1(length(Y1),:),[],[beta0(i) 0]);
        RCI(i,j)=max(Y2(:,5)./Y2(:,6));
        [i j]
    end
end

RCI2=RCI;
RCI2(RCI2<=1)=NaN;

FS1=30;

figure(1)
colormap(jet);
b=image(round(controlLength/365),R0,RCI2,'CDataMapping','scaled');
set(b,'AlphaData',~isnan(RCI2))
set(gca,'YDir','normal')
set(gca,'FontSize',FS1)
xlabel('Duration of Control (yrs)','FontSize',FS1)
ylabel('\it{R}_0','FontSize',FS1)
c=colorbar;
caxis([1 1.7])
ylabel(c,'Maximum Observed RCI','FontSize',FS1)

end

function y=SIR_seasonal(t,y,params)
global beta1 gamma mu I_b
S1=y(1);
S2=y(3);
I1=y(2);
I2=y(4);

c=1-params(2);
beta0=params(1);

y(1)=mu*(1-S1)-c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b);
y(2)=c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b)-(gamma+mu)*I1;
y(3)=mu*(1-S2)-beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b);
y(4)=beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b)-(gamma+mu)*I2;
y(5)=c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b);
y(6)=beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b);



end

%% Figure 2(c)
function Seasonal_Divorce_Heat_startxend
close all
clear all


global gamma mu I_b beta1

num=75;

mu=1/21900;
beta1=.01;
gamma=1/5;
I_b=1e-6;


R0=10;
beta0=R0*gamma;
endTime=365*linspace(13/12,20,num);
startTime=365*linspace(0,5,num);


Zsq=mu*beta0;
Z=-I_b*beta0*(mu+gamma)-mu*(mu+gamma+beta0);
noZ=mu*(mu+gamma);
S_star=(-Z-sqrt(Z.^2-4*Zsq.*noZ))./(2*Zsq);
I_star=-(beta0.*S_star*I_b-mu+mu*S_star)./(beta0.*S_star);

inits=[S_star; I_star; S_star; I_star; zeros(1,length(R0)); zeros(1,length(R0))];

RCI=zeros(length(startTime),length(endTime));

for i=1:length(startTime)
    [Tb,Yb]=ode15s(@SIR_seasonal,0:10:36500+startTime(i),inits,[],[beta0 0]);
    initials=[Yb(end,1:4) 0 0];
    for j=1:length(endTime)
        if(endTime(j)-startTime(i)<6)
           RCI(i,j)=NaN;
           [i j]
        else
            tspan1=startTime(i):5:endTime(j);
            tspan2=tspan1(end):5:tspan1(end)+365*25;
            [T1,Y1]=ode45(@SIR_seasonal,tspan1,initials,[],[beta0 1]);
            [T2,Y2]=ode45(@SIR_seasonal,tspan2,Y1(size(Y1,1),:),[],[beta0 0]);
            RCI(i,j)=max(Y2(:,5)./Y2(:,6));
            [i j] 
        end
    end
end


FS1=30;

figure(1)
colormap(jet);
b=image(startTime,endTime,RCI','CDataMapping','scaled');
set(b,'AlphaData',~isnan(RCI'))
set(gca,'YDir','normal')
set(gca,'FontSize',FS1)
ylabel('Day Control is Ended','FontSize',FS1)
xlabel('Day Control is Started','FontSize',FS1)
c=colorbar;
caxis([1 1.7])
ylabel(c,'Peak RCI','FontSize',FS1)

hold on
for k=1:3
t=linspace(0,365,25);
plot(t,365*k+t,'k:','LineWidth',2)
end
hold off
end

function y=SIR_seasonal(t,y,params)
global beta1 gamma mu I_b
S1=y(1);
S2=y(3);
I1=y(2);
I2=y(4);

c=1-params(2);
beta0=params(1);

y(1)=mu*(1-S1)-c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b);
y(2)=c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b)-(gamma+mu)*I1;
y(3)=mu*(1-S2)-beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b);
y(4)=beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b)-(gamma+mu)*I2;
y(5)=c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b);
y(6)=beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b);

end

%% Figure 3
function Seasonal_VB_divorce
close all
clear all

global b d phi psi g r k mu I_b My_S My_I My_R My_V r_s

%influx of susceptible hosts
b=45.7;
%Host background per-capita mortality rate
d=1/21900;
%Vector to host transmission rate
psi=.3;
%Host to vector transmission rate
phi=.3;
%Natural infectious host recovery rate
g=1/6;
%Intrinsic per-capita vector growth rate
r=0.835;
%density-dependent effects on recruitment
k=3.675e-7;
%Vector per-capita mortality rate
mu=1/10;
%Seasonality term
r_s=.01;

I_b=1e-6;

cont=1;

Z=((r-mu)*psi+k*b)*phi*I_b*d^2+((((r-mu)*psi+k*b)*g*I_b-b*psi*(r-mu))*phi+b^2*k*mu)*d+b^2*g*k*mu;
noZ=I_b*b*d*phi*psi*(mu-r);
Zsq=d*(d+g)*((r-mu)*psi+k*b)*phi;

My_I=-(Z-sqrt(Z^2-4*noZ*Zsq))/(2*Zsq);
My_S=-(1/d)*(My_I*(d+g)-b);
My_R=(g/d)*My_I;
My_U=(mu*My_I*((r-mu)*psi+k*b)*(d+g))/((((mu+phi)*d+g*mu)*My_I+I_b*d*phi)*k*psi);
My_V=My_I*b*(d+g)/(psi*((-d-g)*My_I+b));

initials=[My_S(1) My_I(1) My_R(1) My_U(1) My_V(1) 0];

[T,Y]=ode45(@SIR_spray,0:1:36500,initials,[],0);
initials=Y(end,:);

tspan1=0:1:365;
tspan2=365:1:365*2;
tspan3=2*365:1:365*7;

[T1,Y1]=ode45(@SIR_spray,tspan1,initials,[],0);

[T2,Y2]=ode45(@SIR_spray,tspan2,[Y1(end,1:5) 0],[],cont);
[T3,Y3]=ode45(@SIR_spray,tspan3,Y2(length(Y2),:),[],0);

T=[T1(1:length(T1)-1);T2(1:length(T2)-1);T3]-365;
Y=[Y1(1:length(Y1)-1,:);Y2(1:length(Y2)-1,:);Y3];

[TB1,YB1]=ode45(@SIR_spray,0:1:365,initials,[],0);
[TB2,YB2]=ode45(@SIR_spray,365:1:365*7,[YB1(end,1:5) 0],[],0);

YB=[YB1(1:length(YB1)-1,:);YB2(1:length(YB2),:)];
max(Y((365+1):end,6)./YB((365+1):end,6))

figure(4)
hold on
fill([0,0,1,1],[-1,2,2,-1],[.95,.95,.95],'EdgeColor','None')
[hAx,hLine1,hLine2]=plotyy(T((365+1):end)/365,Y((365+1):end,6)./YB((365+1):end,6),T/365,Y(:,2)/(1000830));
leg=legend('Control Period','Relative Cumulative Incidence','Proportion Infective','Location','Northwest');
set(leg,'FontSize',15)
plot(T(1:10:end),ones(length(T(1:10:end)),1),'r:','linewidth',2)
set(hLine2,'Color','k','LineWidth',2)
set(hLine1,'Color','r','LineWidth',2)
set(hAx(2),'YColor','k','FontSize',25,'YLim',[-1e-8 10e-3],'YTick',linspace(0,10e-3,6))
set(hAx(1),'YColor','r','FontSize',25,'YLim',[0 2],'YTick',linspace(0,2,9))
xticks([0 1 2 3 4 5 6])
ylabel(hAx(2),'Proportion of Host Population Infective')
ylabel(hAx(1),'Relative Cumulative Incidence')
xlabel(hAx(1),'Time (yrs)')
hold off

end

function [value,isterminal,direction]=RCI(t,y,mod)
global My_S My_I My_R My_V phi

value=[y(6)-phi*My_S*My_V*t./(My_S+My_I+My_R),y(6)-phi*My_S*My_V*t./(My_S+My_I+My_R)];
isterminal=[0,0];
direction=[1,-1];

end

function y=SIR_spray(t,y,params)
global b d psi phi g r k mu I_b r_s


sigma=1+params;

%%State Variables
S=y(1);
I=y(2);
R=y(3);
U=y(4);
V=y(5);

%Susceptibles
y(1)=b-psi*(V*S)/(S+I+R)-d*S;
%Infectives
y(2)=psi*(V*S)/(S+I+R)-(d+g)*I;
%Removed
y(3)=g*I-d*R;
%Susceptible vectors (U)
y(4)=(U+V)*(r*(1+r_s*cos(2*pi*t/365))-k*(U+V))-phi*U*(I+I_b)/(S+I+R)-sigma*mu*U;
%Infected Vectors(V)
y(5)=phi*U*(I+I_b)/(S+I+R)-sigma*mu*V;
%New infectives
y(6)=phi*S*V/(S+I+R);

end

%%  Figure 4(a)
function Seasonal_divorce_pulsing
close all
clear all

global beta0 beta1 gamma mu I_b

opts=odeset('Events',@RCI);
name='Seasonal(10)_pulse';

mu=1/21900;
% gamma=2.5;
beta0=1;
beta1=.01;
gamma=1/5;
I_b=1e-6;

cont=.9;


cont_end=365*1;
shift=1-mod(cont_end,1);
tend=5*365;

Zsq=mu*beta0;
Z=-I_b*beta0*(mu+gamma)-mu*(mu+gamma+beta0);
noZ=mu*(mu+gamma);
S_star=(-Z-sqrt(Z^2-4*Zsq*noZ))/(2*Zsq);
I_star=-(beta0*S_star*I_b-mu+mu*S_star)/(beta0*S_star);

inits=[S_star I_star S_star I_star 0 0];

tspan0=0:1:36500+365*shift;

[T,Y]=ode45(@SIR_seasonal,tspan0,inits,[],0);

initials=[Y(end,1:4) 0 0];

tspan1=365*shift:1:(365*shift)+365*3;
ton=365*1/12;
toff=365*11/12;

[T1,Y1]=ode45(@SIR_seasonal,tspan1,initials,[],0);
Y1(5:6)=[0,0];
for i=1:12
[T2,Y2,te1,ye1,ie1]=ode45(@SIR_seasonal,T1(end):1:T1(end)+ton,Y1(end,:),opts,cont);
[T3,Y3,te2,ye2,ie2]=ode45(@SIR_seasonal,T2(end):1:T2(end)+toff,Y2(end,:),opts,0);
T1=[T1(1:length(T1)-1);T2(1:length(T2)-1);T3];
Y1=[Y1(1:length(Y1)-1,:);Y2(1:length(Y2)-1,:);Y3];
end
[T3,Y3,te2,ye2,ie2]=ode45(@SIR_seasonal,T1(end):1:T1(end)+365*10,Y1(end,:),opts,0);
Y=[Y1(1:length(Y1)-1,:);Y3];
T=[T1(1:length(T1)-1);T3]-(365*4);

te2=te2+1;

figure(4)
hold on
fill([0,0,1/12,1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
[hAx,hLine1,hLine2]=plotyy(T(365*3:end)/365,Y(365*3:end,5)./Y(365*3:end,6),T/365,Y(:,2));
leg=legend('Control Period','Relative Cumulative Incidence','Proportion Infective','Location','Northeast');
set(leg,'FontSize',15)
plot(linspace(0,T(end),length(T(1:10:end))),ones(length(T(1:10:end)),1),'r:','linewidth',2)
for i=1:11
    fill([i,i,i+1/12,i+1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
end
set(hLine2,'Color','k','LineWidth',2)
set(hLine1,'Color','r','LineWidth',2)
set(hAx(2),'YColor','k','FontSize',25,'YLim',[-1e-8 8e-3],'YTick',linspace(0,8e-3,5))
set(hAx(1),'YColor','r','FontSize',25,'YLim',[0 1.75],'YTick',linspace(0,1.75,8))
xticks(0:2:T(end)/365)
ylabel(hAx(2),'Proportion of Population Infective')
ylabel(hAx(1),'Relative Cumulative Incidence')
xlabel(hAx(1),'Time (yrs)','FontSize',25)
xlim(hAx(1),[-3 T(end)/365])
xlim(hAx(2),[-3 T(end)/365])
hold off

%Set up control matrix for R_t
b_mat=ones(length(T),1);
for i=1:12
    b_mat(T>i*365)=1-cont;
    b_mat(T>i*365+(365/12))=1;
end

figure(1)
subplot(3,1,1)
hold on
fill([0,0,1/12,1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
[hAx,hLine1,hLine2]=plotyy(T(365*3:end)/365,Y(365*3:end,5)./Y(365*3:end,6),T/365,Y(:,2));
leg=legend('Control Period','Location','Northeast');t');
set(leg,'FontSize',15)
plot(linspace(0,T(end),length(T(1:10:end))),ones(length(T(1:10:end)),1),'r:','linewidth',2)
for i=1:11
    fill([i,i,i+1/12,i+1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
end
set(hLine2,'Color','k','LineWidth',2)
set(hLine1,'Color','r','LineWidth',2)
set(hAx(2),'YColor','k','FontSize',25,'YLim',[-1e-8 8e-3],'YTick',linspace(0,8e-3,5))
set(hAx(1),'YColor','r','FontSize',25,'YLim',[0 1.75],'YTick',linspace(0,1.5,4))
xticks(0:2:T(end)/365)
ylabel(hAx(2),'Infectives')
ylabel(hAx(1),'RCI')
xlim(hAx(1),[-3 T(end)/365])
xlim(hAx(2),[-3 T(end)/365])
hold off
subplot(3,1,2)
hold on
plot(T(7:end)/365,Y(7:end,1),'k','linewidth',2)
plot(T(7:end)/365,Y(1,1)*ones(length(T(7:end)),1),'k--')
fill([0,0,1/12,1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
for i=1:11
    fill([i,i,i+1/12,i+1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
end
hold off
xlim([-3 T(end)/365])
ylim([.15 .25])
xticks(0:2:T(end)/365)
xlabel('Time (yrs)')
ylabel('Susceptibles')
set(gca,'fontsize',25)
subplot(3,1,3)
hold on
fill([0,0,1/12,1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
for i=1:11
    fill([i,i,i+1/12,i+1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
end
plot(T(7:end)/365,Y(7:end,1).*b_mat(7:end).*beta0.*(1+beta1.*cos(2*pi*T(7:end)/365))/gamma,'k','linewidth',2)
plot(T(7:end)/365,ones(length(T(7:end)),1),'k--')
xlabel('Time (yrs)')
ylabel('R_t')
axis([-3 T(end)/365 0 1.5])
xticks(0:2:T(end)/365)
set(gca,'fontsize',25)
hold off


end

function [value,isterminal,direction]=RCI(t,y,mod)

value=[y(5)-y(6),y(5)-y(6)];
isterminal=[0,0];
direction=[1,-1];

end

function y=SIR_seasonal(t,y,mod)
global beta0 beta1 gamma mu I_b
S1=y(1);
S2=y(3);
I1=y(2);
I2=y(4);

c=1-mod;

y(1)=mu*(1-S1)-c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b);
y(2)=c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b)-(gamma+mu)*I1;
y(3)=mu*(1-S2)-beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b);
y(4)=beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b)-(gamma+mu)*I2;
y(5)=c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b);
y(6)=beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b);



end

%% Figure 4(b)
function Seasonal_divorce_reactive
close all
clear all

global beta0 beta1 gamma mu I_b

opts=odeset('Events',@outbreak);

mu=1/21900;
beta0=1;
beta1=.02;
gamma=1/5;
I_b=1e-6;

cont=.9;


cont_end=365*1;
shift=1-mod(cont_end,1);
tend=5*365;

Zsq=mu*beta0;
Z=-I_b*beta0*(mu+gamma)-mu*(mu+gamma+beta0);
noZ=mu*(mu+gamma);
S_star=(-Z-sqrt(Z^2-4*Zsq*noZ))/(2*Zsq);
I_star=-(beta0*S_star*I_b-mu+mu*S_star)/(beta0*S_star);

inits=[S_star I_star S_star I_star 0 0];

tspan0=0:1:36500+365*shift;

[T,Y]=ode45(@SIR_seasonal,tspan0,inits,[],0);

initials=[Y(end,1:4) 0 0];

tspan1=365*shift:1:(365*shift)+365*3;
ton=365*1/12;
toff=365*11/12;

[T1,Y1]=ode45(@SIR_seasonal,tspan1,initials,[],0);
Y1(5:6)=[0,0];
cont_times=0;
for i=1:12
[T2,Y2]=ode45(@SIR_seasonal,T1(end):1:T1(end)+ton,Y1(end,:),[],cont);
[T3,Y3,te,ye,ie]=ode45(@SIR_seasonal,T2(end):1:T2(end)+toff,Y2(end,:),opts,0);
T1=[T1(1:length(T1)-1);T2(1:length(T2)-1);T3];
Y1=[Y1(1:length(Y1)-1,:);Y2(1:length(Y2)-1,:);Y3];
cont_times=[cont_times te-365*4];
end
[T3,Y3]=ode45(@SIR_seasonal,T1(end):1:T1(end)+365*10,Y1(end,:),[],0);
Y=[Y1(1:length(Y1)-1,:);Y3];
T=[T1(1:length(T1)-1);T3]-(365*4);


figure(4)
hold on
fill([0,0,1/12,1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
[hAx,hLine1,hLine2]=plotyy(T(365:end)/365,Y(365:end,5)./Y(365:end,6),T/365,Y(:,2));
leg=legend('Control Period','Relative Cumulative Incidence','Proportion Infective','Location','Northeast');
set(leg,'FontSize',15)
plot(T(1:10:end),ones(length(T(1:10:end)),1),'r:','linewidth',2)
for i=1:11
    fill([cont_times(i+1)/365,cont_times(i+1)/365,cont_times(i+1)/365+1/12,cont_times(i+1)/365+1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
end
set(hLine2,'Color','k','LineWidth',2)
set(hLine1,'Color','r','LineWidth',2)
set(hAx(2),'YColor','k','FontSize',25,'YLim',[-1e-8 16e-3],'YTick',linspace(0,16e-3,5))
set(hAx(1),'YColor','r','FontSize',25,'YLim',[0 2],'YTick',linspace(0,2,9))
xticks(0:2:T(end)/365)
ylabel(hAx(2),'Proportion of Population Infective')
ylabel(hAx(1),'Relative Cumulative Incidence')
xlabel(hAx(1),'Time (yrs)','FontSize',25)
xlim(hAx(1),[-3 T(end)/365])
xlim(hAx(2),[-3 T(end)/365])
hold off

%Set up control matrix for R_t
b_mat=ones(length(T),1);
for i=1:12
    b_mat(T>cont_times(i))=1-cont;
    b_mat(T>cont_times(i)+(365/12))=1;
end

figure(1)
subplot(3,1,1)
hold on
fill([0,0,1/12,1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
[hAx,hLine1,hLine2]=plotyy(T(365:end)/365,Y(365:end,5)./Y(365:end,6),T/365,Y(:,2));
leg=legend('Control Period','Location','Northeast');
set(leg,'FontSize',15)
plot(T(1:10:end),ones(length(T(1:10:end)),1),'r:','linewidth',2)
for i=1:11
    fill([cont_times(i+1)/365,cont_times(i+1)/365,cont_times(i+1)/365+1/12,cont_times(i+1)/365+1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
end
set(hLine2,'Color','k','LineWidth',2)
set(hLine1,'Color','r','LineWidth',2)
set(hAx(2),'YColor','k','FontSize',25,'YLim',[-1e-8 16e-3],'YTick',linspace(0,16e-3,5))
set(hAx(1),'YColor','r','FontSize',25,'YLim',[0 2],'YTick',linspace(0,2,5))
xticks(0:2:T(end)/365)
ylabel(hAx(2),'Proportion Infective')
ylabel(hAx(1),'RCI')
xlabel(hAx(1),'Time (yrs)','FontSize',25)
xlim(hAx(1),[-3 T(end)/365])
xlim(hAx(2),[-3 T(end)/365])
hold off

subplot(3,1,2)
hold on
plot(T(7:end)/365,Y(7:end,1),'k','linewidth',2)
plot(T(7:end)/365,Y(7,1)*ones(length(T(7:end)),1),'k--')
fill([0,0,1/12,1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
for i=1:11
    fill([cont_times(i+1)/365,cont_times(i+1)/365,cont_times(i+1)/365+1/12,cont_times(i+1)/365+1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
end
hold off
xlim([-3 T(end)/365])
ylim([.05 .25])
xticks(0:2:T(end)/365)
xlabel('Time (yrs)')
ylabel('Susceptibles')
set(gca,'fontsize',25)

subplot(3,1,3)
hold on
fill([0,0,1/12,1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
for i=1:11
    fill([cont_times(i+1)/365,cont_times(i+1)/365,cont_times(i+1)/365+1/12,cont_times(i+1)/365+1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
end
plot(T(7:end)/365,Y(7:end,1).*b_mat(7:end).*beta0.*(1+beta1.*cos(2*pi*T(7:end)/365))/gamma,'k','linewidth',2)
plot(T(7:end)/365,ones(length(T(7:end)),1),'k--')
xlabel('Time (yrs)')
ylabel('R_t')
axis([-3 T(end)/365 0 2])
xticks(0:2:T(end)/365)
set(gca,'fontsize',25)
hold off

end

function [value,isterminal,direction]=outbreak(t,y,mod)

value=y(2)-1e-4;
isterminal=1;
direction=1;

end

function y=SIR_seasonal(t,y,mod)
global beta0 beta1 gamma mu I_b
S1=y(1);
S2=y(3);
I1=y(2);
I2=y(4);

c=1-mod;

y(1)=mu*(1-S1)-c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b);
y(2)=c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b)-(gamma+mu)*I1;
y(3)=mu*(1-S2)-beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b);
y(4)=beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b)-(gamma+mu)*I2;
y(5)=c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b);
y(6)=beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b);

end
%% Figure 4(c)
function Seasonal_divorce_predictive
close all
clear all

global beta0 beta1 gamma mu I_b

mu=1/21900;
beta0=1;
beta1=.02;
gamma=1/5;
I_b=1e-6;

cont=.9;


cont_end=365*1;
shift=1-mod(cont_end,1);
tend=5*365;
ndays=365;

Zsq=mu*beta0;
Z=-I_b*beta0*(mu+gamma)-mu*(mu+gamma+beta0);
noZ=mu*(mu+gamma);
S_star=(-Z-sqrt(Z^2-4*Zsq*noZ))/(2*Zsq);
I_star=-(beta0*S_star*I_b-mu+mu*S_star)/(beta0*S_star);

inits=[S_star I_star S_star I_star 0 0];

tspan0=0:1:36500+365*shift;

[T,Y]=ode45(@SIR_seasonal,tspan0,inits,[],0);

initials=[Y(end,1:4) 0 0];

tspan1=365*shift:1:(365*shift)+365*3;
ton=365*1/12;
toff=365*11/12;

[T1,Y1]=ode45(@SIR_seasonal,tspan1,initials,[],0);
Y1(5:6)=[0,0];
cont_times=zeros(12,1);
for i=1:12
    [T2,Y2]=ode45(@SIR_seasonal,T1(end):1:T1(end)+ton,Y1(end,:),[],cont);
    cont_times(i)=T1(end);
    checks=zeros(365,1);
    for j=1:ndays
        [T3,Y3]=ode45(@SIR_seasonal,T2(end):1:T2(end)+j,Y2(end,:),[],0);
        [T4,Y4]=ode45(@SIR_seasonal,T3(end):1:T3(end)+ton,Y3(end,:),[],cont);
        [T5,Y5]=ode45(@SIR_seasonal,T4(end):1:T4(end)+365*10,Y4(end,:),[],0);
        checks(j)=max(Y5(:,5)./Y5(:,6));
    end
    [~,ind]=min(checks);
    [T3,Y3]=ode45(@SIR_seasonal,T2(end):1:T2(end)+ind,Y2(end,:),[],0);
    T1=[T1(1:length(T1)-1);T2(1:length(T2)-1);T3];
    Y1=[Y1(1:length(Y1)-1,:);Y2(1:length(Y2)-1,:);Y3];
end
[T3,Y3]=ode45(@SIR_seasonal,T1(end):1:T1(end)+365*10,Y1(end,:),[],0);
Y=[Y1(1:length(Y1)-1,:);Y3];
T=[T1(1:length(T1)-1);T3]-(365*4);
cont_times=cont_times-(365*4);

figure(4)
hold on
fill([0,0,1/12,1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
[hAx,hLine1,hLine2]=plotyy(T(365*3:end)/365,Y(365*3:end,5)./Y(365*3:end,6),T/365,Y(:,2));
leg=legend('Control Period','Relative Cumulative Incidence','Proportion Infective','Location','Northeast');
set(leg,'FontSize',15)
plot(linspace(0,T(end),length(T(1:10:end))),ones(length(T(1:10:end)),1),'r:','linewidth',2)
for i=2:12
    fill([cont_times(i)/365,cont_times(i)/365,cont_times(i)/365+1/12,cont_times(i)/365+1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
end
set(hLine2,'Color','k','LineWidth',2)
set(hLine1,'Color','r','LineWidth',2)
set(hAx(2),'YColor','k','FontSize',25,'YLim',[-1e-8 8e-3],'YTick',linspace(0,8e-3,5))
set(hAx(1),'YColor','r','FontSize',25,'YLim',[0 1.75],'YTick',linspace(0,1.75,8))
xticks(0:2:T(end)/365)
ylabel(hAx(2),'Proportion of Population Infective')
ylabel(hAx(1),'Relative Cumulative Incidence')
xlabel(hAx(1),'Time (yrs)','FontSize',25)
xlim(hAx(1),[-3 T(end)/365])
xlim(hAx(2),[-3 T(end)/365])
hold off

%Set up control matrix for R_t
b_mat=ones(length(T),1);
for i=1:12
    b_mat(T>i*365)=1-cont;
    b_mat(T>i*365+(365/12))=1;
end

figure(1)
subplot(3,1,1)
hold on
fill([0,0,1/12,1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
[hAx,hLine1,hLine2]=plotyy(T(365*3:end)/365,Y(365*3:end,5)./Y(365*3:end,6),T/365,Y(:,2));
leg=legend('Control Period','Location','Northeast');
set(leg,'FontSize',15)
plot(linspace(0,T(end),length(T(1:10:end))),ones(length(T(1:10:end)),1),'r:','linewidth',2)
for i=2:12
    fill([cont_times(i)/365,cont_times(i)/365,cont_times(i)/365+1/12,cont_times(i)/365+1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
end
set(hLine2,'Color','k','LineWidth',2)
set(hLine1,'Color','r','LineWidth',2)
set(hAx(2),'YColor','k','FontSize',25,'YLim',[-1e-8 8e-3],'YTick',linspace(0,8e-3,5))
set(hAx(1),'YColor','r','FontSize',25,'YLim',[0 1.75],'YTick',linspace(0,1.5,4))
xticks(0:2:T(end)/365)
ylabel(hAx(2),'Infectives')
ylabel(hAx(1),'RCI')
xlim(hAx(1),[-3 T(end)/365])
xlim(hAx(2),[-3 T(end)/365])
hold off
subplot(3,1,2)
hold on
plot(T(7:end)/365,Y(7:end,1),'k','linewidth',2)
plot(T(7:end)/365,Y(1,1)*ones(length(T(7:end)),1),'k--')
fill([0,0,1/12,1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
for i=2:12
    fill([cont_times(i)/365,cont_times(i)/365,cont_times(i)/365+1/12,cont_times(i)/365+1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
end
hold off
xlim([-3 T(end)/365])
ylim([.15 .25])
xticks(0:2:T(end)/365)
xlabel('Time (yrs)')
ylabel('Susceptibles')
set(gca,'fontsize',25)
subplot(3,1,3)
hold on
fill([0,0,1/12,1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
for i=2:12
    fill([cont_times(i)/365,cont_times(i)/365,cont_times(i)/365+1/12,cont_times(i)/365+1/12],[-.1,2,2,-.1],[.95,.95,.95],'EdgeColor','None')
end
plot(T(7:end)/365,Y(7:end,1).*b_mat(7:end).*beta0.*(1+beta1.*cos(2*pi*T(7:end)/365))/gamma,'k','linewidth',2)
plot(T(7:end)/365,ones(length(T(7:end)),1),'k--')
xlabel('Time (yrs)')
ylabel('R_t')
axis([-3 T(end)/365 0 1.5])
xticks(0:2:T(end)/365)
set(gca,'fontsize',25)
hold off

end

function [value,isterminal,direction]=RCI(t,y,mod)

value=[y(5)-y(6),y(5)-y(6)];
isterminal=[0,0];
direction=[1,-1];

end

function y=SIR_seasonal(t,y,mod)
global beta0 beta1 gamma mu I_b
S1=y(1);
S2=y(3);
I1=y(2);
I2=y(4);

c=1-mod;

y(1)=mu*(1-S1)-c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b);
y(2)=c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b)-(gamma+mu)*I1;
y(3)=mu*(1-S2)-beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b);
y(4)=beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b)-(gamma+mu)*I2;
y(5)=c*beta0*(1+beta1*cos(2*pi*t/365))*S1*(I1+I_b);
y(6)=beta0*(1+beta1*cos(2*pi*t/365))*S2*(I2+I_b);



end