In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average ...In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average of the stochastic solution in the case of small population size. The choice of this model takes into account the random fluctuations inherent to the epidemiological characteristics of rural populations of Niger, notably a high prevalence of measles in children under 5, coupled with a very low immunization coverage.展开更多
In this paper, the SVIR epidemic models with continuous vaccination strategies investi- gated by Liu, Takeuchi and Iwamo, [SVIR epidemic models with vaccination strategies, J. Theor. Biol. 253 （2008） 1 11], allowing...In this paper, the SVIR epidemic models with continuous vaccination strategies investi- gated by Liu, Takeuchi and Iwamo, [SVIR epidemic models with vaccination strategies, J. Theor. Biol. 253 （2008） 1 11], allowing random fluctuation around the endemic equi- librium and the transmission rate t3 are analyzed. The equilibrium state of the model with random perturbation is locally asymptotically stable as shown by a Lyapunov stability analysis.展开更多
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
In this paper, a multi-group SVIR epidemic model with age of vaccination is considered. The model allows the vaccinated individuals to become susceptible after the vaccine loses its protective properties, and the vacc...In this paper, a multi-group SVIR epidemic model with age of vaccination is considered. The model allows the vaccinated individuals to become susceptible after the vaccine loses its protective properties, and the vaccination classes satisfy first-order the partial differential equations structured by vaccination age. Combining the Lyapunov functional method with a graph-theoretic approach, we show that the global stability of endemic equilibrium for the strongly connected system is determined by the basic reproduction number. In addition, the dynamics for non-strongly connected model are also investi- gated, depending on the basic reproduction numbers corresponding to each strongly connected component. Numerical simulations are carried out to support the theoretical conclusions.展开更多
文摘In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average of the stochastic solution in the case of small population size. The choice of this model takes into account the random fluctuations inherent to the epidemiological characteristics of rural populations of Niger, notably a high prevalence of measles in children under 5, coupled with a very low immunization coverage.
文摘In this paper, the SVIR epidemic models with continuous vaccination strategies investi- gated by Liu, Takeuchi and Iwamo, [SVIR epidemic models with vaccination strategies, J. Theor. Biol. 253 （2008） 1 11], allowing random fluctuation around the endemic equi- librium and the transmission rate t3 are analyzed. The equilibrium state of the model with random perturbation is locally asymptotically stable as shown by a Lyapunov stability analysis.
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.
基金This research was supported by grants from the Shandong Provincial Natural Science Foundation of China （No. ZR2015AM018）, and Chinese NSF Grants （Nos. 11671110 and 11201097）.
文摘In this paper, a multi-group SVIR epidemic model with age of vaccination is considered. The model allows the vaccinated individuals to become susceptible after the vaccine loses its protective properties, and the vaccination classes satisfy first-order the partial differential equations structured by vaccination age. Combining the Lyapunov functional method with a graph-theoretic approach, we show that the global stability of endemic equilibrium for the strongly connected system is determined by the basic reproduction number. In addition, the dynamics for non-strongly connected model are also investi- gated, depending on the basic reproduction numbers corresponding to each strongly connected component. Numerical simulations are carried out to support the theoretical conclusions.
