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This paper considers a three species eco-epidemiological model perturbed by white noise. Stochastic stability and long time behavior around the equilibrium of deterministic eco-epidemiological model are analyzed by Lyapunov methods. Numerical simulations for a set of parameter values are presented to illustrate the analytical findings. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we include stochastic perturbations into SIR and SEIR epidemic models with saturated incidence and investigate their dynamics according to the basic reproduction number . The long time behavior of the two stochastic systems is studied. Mainly, we utilize stochastic Lyapunov functions to show under some conditions, the solution has the ergodic property as , while exponential stability as . At last, we make simulations to conform our analytical results. [Copyright &y& Elsevier]

Abstract: In this paper, we present a DI SIR epidemic model with two categories stochastic perturbations. The long time behavior of the two stochastic systems is studied. Mainly, we show how the solution goes around the infection-free equilibrium and the endemic equilibrium of deterministic system under different conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the two-group SIR model introduced by Guo, Li and Shuai [H.B. Guo, M.Y. Li, Z. Shuai, Global stability of the endemic equilibrium of multigroup SIR epidemic models, Can. Appl. Math. Q. 14 (2006) 259–284], allowing random fluctuation around the endemic equilibrium. We prove the endemic equilibrium of the model with random perturbation is stochastic asymptotically stable in the large. In addition, the stability condition is obtained by the construction of Lyapunov function. Finally, numerical simulations are presented to illustrate our mathematical findings. [Copyright &y& Elsevier]