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{
\bf Homework for Lecture 16 of Dr. Z.'s Dynamical Models in Biology class
}
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Email the answers (as a .pdf file) to

ShaloshBEkhad@gmail.com

by 8:00pm Monday, Nov. 3, 2025.

Subject: hw16

with an attachment hw16FirstLast.pdf 




{\bf 1.} For the generalized Hardy-Weinberg model given by HWg(u,v,M) where M is a 3 by 3 preferance matrix

Type

{\tt M:=RandMat(3,30); T:=HWg(u,v,M); SSSgN(T,[u,v]);}

40 times and record in how many cases only one of the alleles AA, Aa, aa will survive (i.e. the output is cloase to [0,1], [1,0], or [0,0])
and in how many of them they wull also survive.



{\bf 2.} for each of b=c=0.1, 0.15,  0.2, 0.25, 0.3, 0.35, 0.4

Using

{\tt SSSgN(AllenSIR(a,b,c,x,y),[x,y]);}

for a=(b+c)/2 , a=(b+c), a=1.5*(b+c), a=2*(b+c), a=10*(b+c), a=100*(b+c)

Confirm, in each case,  that in the Linda Allen model, for $a=(b+c)/2$ in the long run there are no infected individuals, but after $a=(b+c)$,  they will start showing up.
Also confirm that even for large a, they will not all be infected but $x_n$ and $y_n$ tend to some number.




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