Modeling a SI epidemic with stochastic transmission: hyperbolic incidence rate

Alejandra Christen, M. Angélica Maulén-Yañez, Eduardo González-Olivares, Michel Curé

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

2 Citas (Scopus)


In this paper a stochastic susceptible-infectious (SI) epidemic model is analysed, which is based on the model proposed by Roberts and Saha (Appl Math Lett 12: 37–41, 1999), considering a hyperbolic type nonlinear incidence rate. Assuming the proportion of infected population varies with time, our new model is described by an ordinary differential equation, which is analogous to the equation that describes the double Allee effect. The limit of the solution of this equation (deterministic model) is found when time tends to infinity. Then, the asymptotic behaviour of a stochastic fluctuation due to the environmental variation in the coefficient of disease transmission is studied. Thus a stochastic differential equation (SDE) is obtained and the existence of a unique solution is proved. Moreover, the SDE is analysed through the associated Fokker–Planck equation to obtain the invariant measure when the proportion of the infected population reaches steady state. An explicit expression for invariant measure is found and we study some of its properties. The long time behaviour of deterministic and stochastic models are compared by simulations. According to our knowledge this incidence rate has not been previously used for this type of epidemic models.

Idioma originalInglés
Páginas (desde-hasta)1005-1026
Número de páginas22
PublicaciónJournal of Mathematical Biology
EstadoPublicada - 1 mar. 2018
Publicado de forma externa


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