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

Show full item record

Title: Deterministic and stochastic discrete-time epidemic models with applications to amphibians
Author: Emmert, Keith Eric
Abstract: 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 .
URI: http : / /hdl .handle .net /2346 /10637
Date: 2004-08

Citation

Emmert, Keith Eric Deterministic and stochastic discrete-time epidemic models with applications to amphibians. Doctoral dissertation, Texas Tech University. Available electronically from http : / /hdl .handle .net /2346 /10637 .

Files in this item

Files Size Format View

There are no files associated with this item.

This item appears in the following Collection(s)

Show full item record

Search DSpace

Advanced Search

Browse