A model for strep throat infection: dynamics of contingency gene selection in an infected host
An ordinary differential equations model for strep throat infection is constructed to compute the bacterial population densities of genotype combinations with binary switches in contingency genes. Theoretical analysis for the existence of solutions and the stability of the steady states is first preformed. Numerical simulations are then performed to investigate how the bacterial population evolves from the initial state with all turned-off genes to a state with all turned-on genes. More simulations show how the mutation frequency, the selection rates, the number of contingency genes, and the carrying capacity of the population affect the domination of the class with all turned-on genes. To improve the efficiency of the computation, a modified model is developed. The asymptotic behavior of the first model and the modified model is proved to be the same under certain conditions on the mutation frequency and selection rates. The results from the simulations demonstrate the ability of the bacterial population to adapt to the host within a realistically observed time frame of 3 to 6 days. The models can be used to understand the important role of contingency genes in the capacity of the bacterial pathogen to adapt to a host.