食饵染病的非自治生态-流行病模型的分析

Analysis of a Nonautonomous Eco-epidemic Model with Disease in the Prey

研究了一类疾病仅在食饵中传播的非自治捕食者-食饵模型.文中假定捕食者受密度制约影响,在捕食时具有甄别能力而只捕食健康的食饵,且具有HollingⅢ类功效函数;对于食饵,将其分为食饵易感者和食饵染病者两类,模型假定疾病发生率为非线性的,且考虑到了环境对食饵种群的容纳量.文中运用Barbalat引理、比较原理等稳定性理论的相关方法,找到了系统的正向不变集,证明了模型解的最终有界性;通过理论分析,分别得到了两种群持续生存、周期解的存在性以及周期解全局渐进稳定的相关条件;最后,通过MATLAB数值模拟,验证了有关结论.

In this paper, a nonautonomous eco-epidemic model with disease in the prey is studied. It is assumed that the predator is affected by the density restriction and only eats the healthy prey, as well as the predator response function is of HollingⅢ type; For prey, which is divided into the susceptible and infectives, the model assumes that the disease occurrence rate is nonlinear, with taking into account the environment on the prey population carrying capacity.Using the Barbalat lemma, the comparison principle and other relevant methods of stability theory, the positive invariant set of the system is found, the ultimate boundedness of the solution about this system is proved; By theoretical analysis, the conditions of persistence of these two species、existence of periodic solutions、the global asymptotic stability of the periodic solutions are got; Finally, the relevant conclusions are verified by MATLAB numerical simulation.