Deterministic and stochastic discrete-time epidemic models with applications to amphibians.

摘要

First, a discrete-time model is formulated for the spread of disease in a structured host population. The host population is sub divided into three developmental stages, larva, juvenile, and adult, and each stage can be infected by the pathogen. Recovery from the disease is possible with this model. We investigate conditions on the parameters where either the host population does not survive or the host population survives and is free from the disease. The analysis assumes that the parameters of the model are constants. Several different sub models of the full structured epidemic model are studied and conditions are derived for global stability of the extinction equilibrium and local stability of the disease-free equilibrium. Some numerical examples are presented to illustrate the dynamics of the model when the disease-free equilibrium is not stable. The motivation for this model is the spread of a fungal pathogen in an amphibian population.; A second discrete-time deterministic and stochastic epidemic model is formulated for the spread of disease in a structured host population. This model differs from the previous model because the parameters of this model are periodic. The host population is again subdivided, but this time into two developmental stages, juvenile and adult. Each stage can be infected by the pathogen, but there is no recovery from the disease. Several sub models of the full model are studied and conditions for global extinction as well as local stability of the disease-free solutions are given. Stochastic and deterministic examples illustrating the dynamics of the model are presented. The motivation for this model is the spread of a fungal pathogen in amphibian populations which are explosive breeders.