Deterministic and stochastic epidemic models with multiple pathogens

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Title: Deterministic and stochastic epidemic models with multiple pathogens
Author: Kirupaharan, Nadarajah
Abstract: 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 .
URI: http : / /hdl .handle .net /2346 /15936
Date: 2003-08

Citation

Deterministic and stochastic epidemic models with multiple pathogens. Doctoral dissertation, Texas Tech University. Available electronically from http : / /hdl .handle .net /2346 /15936 .

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