The Basic Birth-Death Model for Microbial Infections

Abstract
On the assumption that parasite populations in vivo are governed by a linear, homogeneous birth‐death process with undistributed parameters and that they generate only marginally faster than the host can destroy them, the distribution of their number at any time is obtained in terms of a Bessel function of imaginary argument. From this is derived the distribution of incubation period, defined as the first‐passage time to a high response threshold. Various properties of the model are noted and compared with known characteristics of the infectious process.