A stochastic model of the dynamics of host-pathogen systems with mutation

In this paper a stochastic model of the dynamics of host-pathogen systems with mutation is constructed. In previous works deterministic models of host-pathogen systems with no mutation were considered. The evolution of the pathogen population in any generation of the host is formulated as a multidimensional birth and death process, while the evolution of genotypic frequencies in successive generations of the host is described by a solution of a nonlinear vector difference equation. A general solution of the differential equations of the multidimensional birth and death process is presented and expressions for the stationary distribution, whenever it exists, and the mean time to extinction, when absorbing states are present, are derived. Some answers to questions raised in the discussion of a previous paper (Mode, 1962) are also contained in this paper. The research reported in this paper was supported by the United States Atomic Energy Comission, Division of Biology and Medicine Project AT(45-1)-1729.