mscolli

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11 years, 21 days

MaplePrimes Activity


These are answers submitted by mscolli

restart:
with(PDEtools):
with(DEtools):
with(plots):

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;   #This is a function of t because it will be used as an infectiousness function. Currently it is considered constant, again for ease of making the worksheet run however this is supposed to be either a negative exponential or a decreasing step function.
beta :=  (R0 * d * (d + mu + gam) * (d + alpha))/(lambda*alpha);
v := 0.8;


#Below are integral definition. The ODE for S(t) is an IDE but with these definitions we have an ODE to make it simpler to solve.
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);

pdesys:[ diff(S(t),t) - lambda + d*S(t) + beta*S(t)*int( Y(a,t), a=0..infinity) + v*p*S(t) - omega*int(V(a,t),a=0..infinity)-f*int(R(a,t),a=0..infinity) = 0,
diff(E(a,t),t) + diff(E(a,t),a) + d*E(a,t) + alpha*E(a,t)=0,
diff(Y(a,t),t) + diff(Y(a,t),a) + d*Y(a,t) + gam*Y(a,t) + mu*Y(a,t)=0,
diff(R(a,t),t) + diff(R(a,t),a) + f*R(a,t) + d*R(a,t)=0,
diff(V(a,t),t) + diff(V(a,t),a) + omega*V(a,t) + d*V(a,t)=0];

#Here we see that in the boundary conditions there is a dependence on the solution of each of the pdes. This is how it is supposed to read.
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*S(t)];

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

PDEplot(pdesys,IBCs);
#I realize it is redundant to solve the PDE system and plot the pde system and not the solution that I take time to calculate but I was checking to see if a solution would be calcuated. I also tried to plot only the solution to the system but was unsuccessful in that.

Thanks

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