Nonlinear stochastic analysis for a stochastic SIS epidemic model

Abstract

This paper considers a stochastic Susceptible-Infected-Susceptible (SIS) epidemic model with nonlinear saturated incidence. The threshold conditions for disease extinction and stochastic permanence are obtained by using nonlinear stochastic analysis for Feller's test and the canonical probability method. Consequently, this improves and extends some previous results obtained by using Lyapunov method. A series of numerical simulations are carried out to illustrate our theoretical findings.

A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps

“…Epidemic models are inevitably subject to environmental noise. Most epidemic models are driven by white noise, and many results have been achieved in this area [11][12][13][14][15][16][17][18][19]. However, under severe environmental perturbations, such as avian influenza, severe acute respiratory syndrome, volcanic eruptions, earthquakes, and hurricanes, the continuity of solutions may be broken; accordingly, a jump process should be introduced to prevent and control diseases [20][21][22][23].…”

Analysis of a Fractional-order “SVEIR” Epidemic Mo del with a General Nonlinear Saturated Incidence Rate in a Continuous Reactor

“…The qualitative study of epidemiological models such as the "SIS", "SIR", "SEIR" and "SVEIR" models has been a field of intense and varied research [6,7,8,9,10,11,12,13,14,15,16,17]. An excellent review of the literature, but not very recent, was made by Hethcote [18].…”

Mathematical Analysis of a Fractional-order "SIR" Epidemic Model with a General Nonlinear Saturated Incidence Rate in a Chemostat

“…The qualitative study of epidemiological models such as the "SIR" model is and has been a field of intense and varied research [3,1,4,5,6,7,8,9,10,11,12]. An excellent review of the literature, but not very recent, was made by Hethcote [2].…”