SEIR model

Suppose there is a vampire apocalypse in $2050.$ There are five populations: $S,E,$I,$R($recovered$),$ and $V($vampire$).$ There are two possible disease trajectories:

$SEIV$

or

$SER$

In trajectory $1,$ those who are exposed will get infected and become a zombie. This portion of the population does not have garlic to prevent infection.

In trajectory $2,$ those who are exposed, but eat garlic immediately after exposure, recover in $2$ days $(\frac{1}{}).$ There is no infectious phase for this population.

Assume that $20\%$ of the total population $()$ has prepared for the apocalypse and keeps garlic in a place that is immediately accessible.

Given: $=0\mathrm{.}5d^{-1}$;$=10d^{-1}$;$=0\mathrm{.}2d^{-1}$;$=0\mathrm{.}5d^{-1}.$

Write a differential equation for each population $(S,E,$I,$R,V.$ It can be helpful to draw a picture$/$flow diagram.

Plot each population fraction as a function of time for $30$ days. Set the initial conditions for $S$ and $E$ to $0\mathrm{.}999$ and $0\mathrm{.}001,$ respectively. Show your code from MATLAB $($or another program$).$