Human Transmitting Capacity
The human transmitting capacity (HTC) is a measure of how many days a host spends fully infectious.
Related | HTC Matrix | Parasite Generation
If we start with a basic formula for \(R_0,\) we can rewrite it with three components:
Vectorial capacity (VC or \(V\)) is the number of infective bites arising from all the mosquitoes blood feeding on a single fully infectious human on a single day.
Transmission efficiency \((b)\) is the number of infections per infectious bite
Human transmitting capacity (HTC or \(D\)) is the number of fully infectious days.
The general formula is:
\[R_0 = b V D\]
Definition
Let \(c(\alpha)\) denote the expected infectiousness at infection age \(\alpha,\) and let \(r(\alpha)\) denote the fraction of infections that have persisted to age \(\alpha.\) A formula for the HTC on day \(\ell > t\) for an infection that started on day \(t\) is: \[D_\ell(t, \ell) = c(\ell) r(\ell)\] and \[D = \int_t^\infty c(\ell) r(\ell) d\ell.\]
Example
In Ross’s model, infections clear at a constant rate, \(r,\) so \[D = \int_0^\infty c e^{-r\alpha} d\alpha = \frac{c}{r}.\]