The deterministic limit of a stochastic logistic model with individual variation.
We consider a Markov chain model similar to the stochastic logistic model except that it allows for variation amongst individuals in the population. We prove that as the population size grows, the process can be approximated by a deterministic process. The equilibrium points of the limiting process and their stability are determined. Applications to modelling epidemics and metapopulations are discussed.
School of Mathematics and Physics, University of Queensland, St Lucia, Brisbane, 4072, Australia. r.mcvinish@uq.edu.au
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McVinish
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Pollett
D003141:Communicable Diseases / Q000453:epidemiology; D058872:Epidemics; D006801:Humans; D016015:Logistic Models; D008390:Markov Chains; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics; D013269:Stochastic Processes