Vectorial Capacity with Forcing
When mosquito bionomic parameters are forced by weather or vector control, vectorial capacity (VC) is different every day, \(V(t)\). Here, we describe vectorial capacity and its temporal dispersaion.
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Vectorial capacity (VC) is defined as the number of infective bites arising from all the mosquitoes blood feeding on a single human on a single day.
If the bionomic parameters are constant, then VC is the same every day. If bionomic paramters vary over time, forced by weather or vector control, then VC the expected number of infective bites arising changes day by day. We can also describe the temporal dispersion of those bites at a point in time, \(\ell\), after mosquitoes become infected. Let \(G_\tau(\ell)\) denote the probability a mosquito that has survived to become infectious, survives to day \(\ell\)
\[V_\ell(t, \ell) = \begin{cases} 0 & \text{if } \ell < t + \tau(t) \\ B\left(t\right) \Upsilon\left(t, \tau\left(t\right)\right) f(\ell) q(\ell) G_\tau(\ell) & \text{if } \ell > t+\tau(t) \end{cases}\] So \[V(t) = B\left(t\right) \Upsilon\left(t, \tau\left(t\right)\right) \int_{t+\tau(t)}^\infty f(\ell) g_\ell e^{-g \ell} d\ell\] The annual average VC is:
\[V_A = \int_0^{365} V(t) \; dt\]