  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.
