Open AccessPOPULATION EXTINCTION IN DETERMINISTICAND STOCHASTIC DISCRETE‐TIME EPIDEMIC MODELS WITH PERIODIC COEFFICIENTS WITH APPLICATIONS TO AMPHIBIAN POPULATIONS
Author(s) -
EMMERT KEITH E.,
ALLEN LINDA J.S.
Publication year - 2006
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/j.1939-7445.2006.tb00178.x
Subject(s) - extinction (optical mineralogy) , population , biology , amphibian , discrete time and continuous time , population model , stage (stratigraphy) , extinction probability , stochastic modelling , transmission (telecommunications) , epidemic model , basic reproduction number , ecology , demography , mathematics , statistics , population size , computer science , paleontology , telecommunications , sociology
. Discrete‐time deterministic and stochastic epidemic models are formulated for the spread of disease in a structured host population. The models have applications to a fungal pathogen affecting amphibian populations. The host population is structured according to two developmental stages, juveniles and adults. The juvenile stage is a post‐metamorphic, nonreproductive stage, whereas the adult stage is reproductive. Each developmental stage is further subdivided according to disease status, either susceptible or infected. There is no recovery from disease. Each year is divided into a fixed number of periods, the first period represents a time of births and the remaining time periods there are no births, only survival within a stage, transition to another stage or transmission of infection. Conditions are derived for population extinction and for local stability of the disease‐free equilibrium and the endemic equilibrium. It is shown that high transmission rates can destabilize the disease‐free equilibrium and low survival probabilities can lead to population extinction. Numerical simulations illustrate the dynamics of the deterministic and stochastic models.