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Description:
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A discrete -time model is formulated for spread of disease in a structured host population . The host population is sub -divided into three developmental stages , larval , 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 disease . The analysis assumes parameters of the model are constants . Several different submodels 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 . 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 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 submodels 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 . |