Human Transmitting Capacity
The human transmitting capacity (HTC) is a measure of how many days a host spends fully infectious.
See Related for links to closely related vignettes.
We start by looking at a simple infection in a single population stratum. For the \(i^{th}\) population stratum, if we let \(c_i(\alpha)\) denote the probability that a mosquito would get infected on day \(\alpha\) of the infection, and \(r_i(\alpha)\) the probability a human remains infected, then the HTC for that stratum is defined as:
\[D_i = \int_0^\infty c_i(\alpha) r_i(\alpha) d\alpha.\] In Ross’s model, infections clear at a constant rate, \(r,\) so \[D = \int_0^\infty c e^{-r\alpha} d\alpha = \frac{c}{r}.\]