连续和脉冲接种的SVIS传染病模型的动力学研究
首发时间:2019-07-30
摘要:假设总人口不变,建立了连续及脉冲接种的SVIS传染病动力学模型. 对于连续型模型,利用常微分方程的稳定性理论和Lasalle不变原理,得到了决定疾病消亡与否的基本再生数,证明了当基本再生数小于零时,存在一个无病平衡点,且无病平衡点全局吸引;当基本再生数大于零时,存在一个无病平衡点和一个地方病平衡点,且无病平衡点不稳定,地方病平衡点全局渐近稳定. 对于接种脉冲模型,利用不动点定理、分支理论证明了脉冲作用下无病周期解和地方病周期解的存在性,利用floquet定理得到了无病周期解渐近稳定的条件. 最后,利用数值模拟验证了所得结果的正确性.
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Dynamics of a SVIS epidemic model with continuous and impulsive vaccination
Abstract:Assuming that the total population remains unchanged, an SVIS epidemic model with continuous and impulsive vaccination of infectious diseases is established. For the continuous model, the basic reproduction number which determines whether the disease will die out or not is obtained by the stability theory of ordinary differential equation and Lasalle invariance principle. When the basic reproduction number was greater than 1, there was a disease-free equilibrium point and disease-free equilibrium is globally attractively. When the basic reproduction number was less than 1, there are a disease-free equilibrium point and an endemic equilibrium point, and the disease-free equilibrium point is unstable. At the same time, the endemic equilibrium point is globally asymptotically stable. For the continuous model, The existence of disease-free periodic solution and endemic periodic solution under impulsive vaccination are proved by using fixed point theorem and bifurcation theory, and disease-free periodic solution is proved by Floquet theorem. The conditions for asymptotic stability of periodic solutions are given. Finally, the correctness of the results is verified by numerical simulation.
Keywords: Dynamic system Continuous vaccination impulsive vaccination Basic reproduction number Stability
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