包虫病多宿主传播的数学建模及动力学分析

Mathematical Modeling and Dynamic Analyzing of Multi-homing Echinococcosis Transmit

建立了一类具有标准发生率的包虫病动力学模型,证明了相关稳定性结论,并进行了包虫病控制策略的数值仿真。利用李雅普诺夫函数法证明得到模型在基本再生数R0<1时,无病平衡点全局渐进稳定,R0>1且(σ+c)I1^*≤μ1S1^*时,地方病平衡点全局渐近稳定。利用文献中的数据对模型进行敏感性分析,结果表明,羊染病率对包虫病的传播影响较大。最后对控制策略进行评价,结果表明综合控制是最经济有效的方法。

In this paper,a class of Echinococcosis dynamics model with standard incidence was established;relative stability conclusion was verified;and mathematical simulation of Echinococcosis controlling strategy was carried on.It was proved by using the Lyapunov function method that when the basic reproductive number R0<1,disease-free equilibrium globally asymptotically stable;and when the basic reproductive number R0>1 and(σ+c)I1^*≤μ1S1^*,the endemic equilibrium global asymptotic stability.Sensitivity analysis of models was carried out by using data from the literature,the results showed that the transmission rate from dog to livestock had great influence on the transmission of Echinococcosis.Finally,the control strategy was evaluated,the results showed that complex control was most economical and feasible.