The authors discuss the existence of pseudo almost periodic solutions of differential equations with piecewise constant argument by means of introducing new concept, pseudo almost periodic sequence.
In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by t...In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If R0 〉 1, there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail.展开更多
文摘The authors discuss the existence of pseudo almost periodic solutions of differential equations with piecewise constant argument by means of introducing new concept, pseudo almost periodic sequence.
文摘In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If R0 〉 1, there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail.
