Population extinction in deterministic and stochastic discrete-time epidemic models with periodic coefficients with applications to amphibian populations. (English) Zbl 1157.92323
Summary: 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.
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.
MSC:
| 92D30 | Epidemiology |
| 60J85 | Applications of branching processes |
| 65C20 | Probabilistic models, generic numerical methods in probability and statistics |
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