一类盘尾丝虫病模型的稳定性分析

Stability analysis of a class of onchocerciasis model

为了研究盘尾丝虫病的防控模式,建立了一类SEIHUV传染病模型,考虑了对感染者的药物治疗和人们的个人保护行为。利用微分方程基本理论证明了模型解的非负性和有界性,计算了模型的基本再生数,给出了平衡点存在的条件;利用线性化方法和比较原理讨论了平衡点的稳定性,并研究了疾病的持久性。数值模拟了正平衡点的局部稳定性及参数对基本再生数与疾病流行的影响。研究结果表明:患者接受治疗和采取防护措施都对疾病的传播有一定的防控作用。

In order to study the model for prevention and control of onchocerciasis,a SEIHUV epidemic model is established,considering the drug treatment of infected persons and people′ s personal protection behavior.The basic theory of differential equations is used to prove the nonnegative and bounded solution of the model.The basic reproduction number of the model is calculated,and the conditions for the existence of the equilibrium point are given.The stability of the equilibrium point is discussed by linearization method and comparison principle,and the persistence of the disease is studied.The local stability of the positive equilibrium point and the influence of parameters on the basic reproduction number and disease epidemic are numerically simulated.The results show that protective measures and the patients who received treatment have certain prevention and control effects.