一类舌状绦虫传染病模型及其性态分析

Performance Analysis of a Ligulaosis Model

以舌状绦虫病的传播为背景,建立并分析了一类含有S,I传染病仓室的食饵—捕食者系统模型.首先,证明了系统解的正性和有界性;其次,计算出了模型的基本再生数和分析了平衡点存在的条件;然后,证明了种群灭绝平衡点是不稳定的,并给出了仅易感食饵种群存在平衡点局部渐近稳定的条件和易感食饵和捕食者种群共存平衡点局部渐近稳定的条件;最后,通过构造Lyapunov函数,得出了仅易感食饵种群存在平衡点和易感食饵与捕食者种群共存平衡点的全局渐近稳定性.

In this paper,based on the background of ligulaosis trasmission,we establish and analyze a prey-predator model which includes S,I infectious diseases compartments.First,we show the positivity and boundedness of the solutions of the system.Next,we calculate the basic reproduction number of the model and analyze the conditions of the existence of equlibria.Then,we prove that the population extinction equilibrium point is unstable,and give the local asymptotic stability conditions of the susceptible prey only equilibrium and the susceptible prey and predator coexistence equilibrium.Finally,by constructing Lyapunov functions,we obtain the global asymptotic stability of the susceptible prey only equilibrium and the susceptible prey and predator coexistence equilibrium.