Deterministic and stochastic epidemic models with multiple pathogens

In the first part of the dissertation, the dynamics of discrete-time SIS epidemic models with multiple pathogen strains are studied. The population infected with these strains may be confined to one geographic region or patch or may disperse between two patches. The models are systems of difference equations. It is the purpose of this investigation to study the persistence and extinction dynamics of multiple pathogen strains in a single patch and in two patches. It is shown for the single patch model that the basic reproduction number determines which strain dominates and persists. The strain with the largest basic reproduction number is the one that persists and outcompetes all other strains provided its magnitude is greater than one. However, in the two-patch epidemic model, both the dispersal probabilities and the basic reproduction numbers for each strain determine whether a strain persists. With two patches, there is a greater chance that more than one strain will coexist. Analytical results are complemented with numerical simulations to help illustrate both competitive exclusion and coexistence of pathogens strains within the host population.; In the second part of the dissertation, the dynamics of continuous-time stochastic SIS and SIR epidemic models with multiple pathogen strains in a population are studied using stochastic differential equation models. Stochastic differential equations are derived from the corresponding system of ordinary differential equations assuming there is demographic stochasticity. The dynamics of these stochastic models are then compared to the analogue deterministic models. Generally in the deterministic model, the strain with the largest basic reproduction number is the one that persists and outcompetes all other strains if its magnitude is greater than one. In the stochastic model, all strains will eventually be eliminated. However, if the population size is sufficiently large, it may take a long time until all strains are eliminated. Examples are discussed where there is coexistence of both strains in the deterministic SIR model with two strains but we show that coexistence does not occur in the stochastic model. Numerical examples are presented for the stochastic epidemic models.