using Matlab Modify the model derived in class to assess the following situation. Suppose an epidemic $($which shall remain nameless$)$ raises all group death rates for given period of time $($i$.$e$.$ it works much like the pulse script from last week & problem $2).$ This epidemic also lowers b$2$ birthrate. Assume migration is constant for group P$2.$

SETUP:

parameters$=[$ b$2,$d$1,$d$2,$d$3,$d$4,$t$12,$t$23,$t$34]$ where

b$2,$ birth rate in group $2$

di$,$ death rates in group Pi

tij, transition from group Pi to group Pj due to ageing

Epidemic effects $=[$b$2$Epifactor,drateEpifactor,tStartEpi,tEndEpi$],$ where

b$2$Epifactor, b$2$Epi$=$ b$2*$b$2$Epifactor

drateEpifactor, d$1$Epi$=$ d$1*$drateEpifactor$,$ etc.

M$2$ann, constant migration rate for P$2$

initial conditions $=[$ Pinit$1,$Pinit$2,$Pinit$3,$Pinit$4]$

time data $=[$tinit$,$tfinal,delt$]$

RESULTS:

P$1,$P$2,$P$3,$P$4,$ group time histories as row vectors. If these conventions are not followed an incorrect answer will result. $\%$ Parameters

b$2=\mathrm{.}025$;

d$1=\mathrm{.}004$;

d$2=\mathrm{.}0075$;

d$3=\mathrm{.}012$;

d$4=\mathrm{.}019$;

t$12=\mathrm{.}067$;

t$23=\mathrm{.}04$;

t$34=\mathrm{.}04$;

b$2$Epifactor$=0\mathrm{.}5$; $\%$ decreases b$2$

drateEpifactor$=2\mathrm{.}0$; $\%$ increases di

tStartEpi$=25$;

tEndEpi$=40$;

$\%$ Migration effect M$2$

M$2$ann$=80$;

$\%$ Initial conditions $($in $1000\text{'}$s for convenience$)$

Pinit$1=1200$;

Pinit$2=1000$;

Pinit$3=800$;

Pinit$4=600$;

$\%$ Solution control data

tinit$=0.$;

tfinal$=100.$;

delt$=0\mathrm{.}5$;

$\%\%$ Your code goes here $\%\%$

$\%$ DISPLAY RESULTS SECTION $-----$ THIS SECTION WILL HELP YOU VISUALIZE YOUR RESULTS

figure

subplot$(2,1,1)$

plot$($t$,$P$1($:$),\text{'}-\text{'},$t$,$P$2($:$),\text{'}--\text{'},$'LineWidth',$2)$;

title$(\text{'}$Case $3$: Epidemic. P$1,$ P$2$ histories'$)$;

$\%$xlabel$(\text{'}$t$,$ years'$)$;

ylabel$(\text{'}$P$1,$ P$2\text{'})$;

legend$(\text{'}$P$1\text{'},\text{'}$P$2\text{'})$;

grid on

subplot$(2,1,2)$

plot$($t$,$P$1($:$),\text{'}-\text{'},$t$,$P$2($:$),\text{'}--\text{'},$t$,$P$3($:$),\text{'}-.\text{'},$t$,$P$4($:$),...$

$\text{'}$:$\text{'},$'LineWidth',$2)$;

title$(\text{'}$P$1,$ P$2,$ P$3,$ P$4$ histories'$)$;

xlabel$(\text{'}$t$,$ years'$)$

ylabel$(\text{'}$P$1,$ P$2,$ P$3,$ P$4\text{'})$;

legend$(\text{'}$P$1\text{'},\text{'}$P$2\text{'},\text{'}$P$3\text{'},\text{'}$P$4\text{'})$

grid on

$\%------------------------------------------------------------------------$