Branching model with state dependent offspring distribution for Chlamydia spread

Chlamydiae are bacteria with an interesting unusual developmental cycle. A single bacterium in its infectious form (elementary body, EB) enters the host cell, where it converts into its dividing form (reticulate body, RB), and divides by binary fission. Since only the EB form is infectious, before the host cell dies, RBs start to convert into EBs. After the host cell dies RBs do not survive. We model the population growth by a 2-type discrete-time branching process, where the probability of duplication depends on the state. Maximizing the EB production leads to a stochastic optimization problem. Simulation study shows that our novel model is able to reproduce the main features of the development of the population.