v[n] := (v[o]*h[o] + v[o]*cv*(1-h[o])) /
(v[o]*h[o] + v[o]*cv*(1-h[o]) + (1-v[o])*cv*h[o] + (1-v[o])*(1-h[o]));
Hokay.
Let's say for convenience that
x = (v[o]*h[o] + v[o]*cv*(1-h[o]))
and
y = (1-v[o])*cv*h[o] + (1-v[o])*(1-h[o])
Then we can write the formula as v[n] :=
x / (
x +
y)
v is the proportion of A type viruses,
h is the proportion of A type hosts. We assume that the virus does not select its host type but ends up in either A or B at random.
So the proportion of A type viruses that that wind up in an A type host is
h, and the proportion that wind up in a B type host is 1 -
h.
cv represents the fitness of an A virus in a B host relative to the fitness of an A virus in an A host.
y is just the same calculation but for the B virus, the proportion of which is given by 1 -
v.
The reason we divde by
x +
y is that we want
v to express a
proportion of the population.
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Does that make sense?