An SEIRS epidemic model with stochastic transmission
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Date
2017
Authors
Journal Title
Journal ISSN
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Publisher
Springer
Abstract
For an SEIRS epidemic model with stochastic perturbations on transmission from the susceptible class to the latent and infectious classes, we prove the existence of global positive solutions. For sufficiently small values of the perturbation parameter, we prove the almost surely exponential stability of the disease-free equilibrium whenever a certain invariant R? is below unity. Here R?<R, the latter being the basic reproduction number of the underlying deterministic model. Biologically, the main result has the following significance for a disease model that has an incubation phase of the pathogen: A small stochastic perturbation on the transmission rate from susceptible to infectious via the latent phase will enhance the stability of the disease-free state if both components of the perturbation are non-trivial; otherwise the stability will not be disturbed. Simulations illustrate the main stability theorem.
Description
Keywords
Ordinary differential equations (ode), Stochastic differential equation (sde)
Citation
Witbooi, P.J. (2017). An SEIRS epidemic model with stochastic transmission. Advances in Difference Equations, 2017: 109. http://dx.doi.org/10.1186/s13662-017-1166-6