Deterministic and stochastic epidemic models with multiple pathogens
Competitive exclusion and coexistence of multiple pathogens in deterministic and stochastic epidemic models are investigated in this dissertation which consists of three parts. In the first part, the persistence and extinction dynamics of multiple pathogen strains for discrete-time SIS epidemic model in a single patch and in two patches are studied. It is shown for the single patch model that the basic reproduction number determines which strain dominates and persists. 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 starin will co-exist.
In the second part, the stochastic spatial epidemic models with multiple pathogen strains for the above deterministic models are formulated as discrete-time Markov chain models and analyzed for coexistence and comptetitive exclusion. When infected individuals disperse between two patches, coexistence may occur in the stochastic model. However, in the stochastic model, eventually disease extinction occurs but it will take a long time. An estimate for the probability of disease extinction is obtained for the stochastic model. The distribution conditioned on non-extiction is compared to the solution of the deterministic model.
In the third part, the dynamics of continuous- time stochastic SIS and SIR epidemic models with multiple pathogen strains and density-dependent mortality are studied using stochastic differential equation models. The dynamics of these stochastic models are then compared to the analogous deterministic models. In the deterministic model, there can be competitive exclusion, where only one strain, the dominant one, persists or there can be coexistence, persistence of more than one strain. In the stochastic model, all strains will eventually be eliminated because the disease-free state is an absorbing state. Generally, it will take a long time until all strains are eliminated. Numerical examples show that coexistence cases predicted in the deterministic models may not occur in the stochastic models.