# Question:Initial/boundary condition problems!!!!

## Question:Initial/boundary condition problems!!!!

Maple

So Maple and I are not the greatest friends and I need help. I have searched google, this forum and other forums for help to no avail. If somebody would be so kind as to help me with the problems that I am having that would be greatly appreciated.

I think the problems are in the initial and boundary conditions because there are so many recursive statements but I am unsure how to enter these so that I get a favourable result. Without the boundary and initial conditions I do get a general solution.

Hopefully I can gain some insight into this problem and maybe have some results.

I also apologize for the sloppy input but I have never posted anything here so I do not know how to post worksheets in a easily readable format. If anyone can tell me how to do this, I will repost my worksheet.

Shannon

>                             restart

>                   with(PDEtools); with(plots);

>                          with(DEtools)

> #Ideally I would like a system solved analytically and the results plotted. I would like the results for S,E,I,R,D plotted on the same graph.I have no idea what I have done wrong but I believe my issue lies in the fact that the system I am trying to solve is recursive.

>

>                             f := 0.5

> alpha := 0.3257;

> d := 0.00761;

> mu := 0.0015;

> omega := 1;

> lambda := 0.01028;

> gam := 0.49089;

> R0 := 1.42;

> p(t) := 0.1;

> beta :=  (R0 * d * (d + mu + gam) * (d + alpha))/(lambda*alpha);

>                             v := 0.8

>          int(Y(a, t), a = 0 .. infinity) := Y(a, t);

>            int(V(a, t), a = 0 .. infinity) := V(a, t);

>            int(R(a, t), a = 0 .. infinity) := R(a, t);

>            int(S(t), a = 0 .. infinity) := S(t);

>

>           [/ d      \

> pdesys := [|--- S(t)| - lambda + d S(t)

>           [\ dt     /

>

>    + S(t) beta int(Y(a, t), a = 0 .. infinity) + v p(t) S(t)

>

>    - omega int(V(a, t), a = 0 .. infinity) - f int(R(a, t), a = 0 .. infinity) =

>

>      / d         \   / d         \

>   0, |--- E(a, t)| + |--- E(a, t)| + d E(a, t) + alpha E(a, t) = 0,

>      \ dt        /   \ da        /

>

>   / d         \   / d         \

>   |--- Y(a, t)| + |--- Y(a, t)| + d Y(a, t) + gam Y(a, t) + mu Y(a, t) = 0,

>   \ dt        /   \ da        /

>

>   / d         \   / d         \

>   |--- R(a, t)| + |--- R(a, t)| + f R(a, t) + d R(a, t) = 0,

>   \ dt        /   \ da        /

>

>   / d         \   / d         \                ]

>   |--- V(a, t)| + |--- V(a, t)| + d V(a, t) = 0]

>   \ dt        /   \ da        /                ]

> print();

> IBCs := [E(a, 0) = 0, Y(a, 0) = 0.05, R(a, 0) = 0, V(a, 0) = 0, S(0) = 0.95], [

>

>   E(0, t) = beta S(t) Y(a, t), Y(0, t) = alpha E(a, t), R(0, t) = gam Y(a, t),

>

>   V(0, t) = v p(t) S(t)]

> print();

> pdesol := pdsolve(pdesys, IBCs, numeric, time = t, range = 0 .. 60)

>                      PDEplot(pdesys, IBCs)

> ﻿