A Generation: In the Mosquitoes
The Vectorial Capacity Matrix Function
In 1964, Garrett-Jones extracted the parameters from Macdonald’s formula for \(R_0\) and called the formula vectorial capacity:
\[V = m \frac{a^2}{-\ln p} p^n\] We rewrite it in an updated form:
The model was formulated in continuous time, where \(g\) was the daily survival rate, such that \(p = e^{-g}\) or equivalently \(g = -ln p\) and \(p^n = e^{-gn}.\)
The human blood feeding rate is split into an overall blood feeding rate \(f\) and the human fraction \(q\) such that \(a=fq.\)
\(m\) is the ratio of humans to mosquitoes, \(m=M/H\)
We turn \(M\) into a variable, then the simplest model is:
\[\frac{dM}{dt} = \Lambda - g M\]
The formula we use is:
\[\frac{\Lambda}{H} \frac{f^2 q^2}{g^2} e^{-gn}.\]