具有饱和发生率的血吸虫病动力学分析

Dynamic Analysis of Schistosomiasis with Saturating Incidence

血吸虫病是我国一种严重的寄生虫病,并且在湖北、安徽、湖南、江苏、四川和云南成地方病.结合中国血吸虫病的现状及特点,考虑人群、牛群以及水环境中的钉螺、尾蚴和毛蚴之间的相互传染,建立了具有饱和发生率的血吸虫病动力学模型,给出了模型的基本再生数.通过构造Lyapunov函数证明了当基本再生数小于1时,模型的无病平衡点全局渐近稳定;当基本再生数大于1时,模型的地方病平衡点也是全局渐近稳定的.最后,利用数值模拟验证了理论结果.

Schistosomiasis is still one of the most serious parasitic diseases in China and remains endemic in seven provinces,including Hubei,Anhui,Hunan,Jiangsu,Jiangxi,Sichuan,and Yunnan.Combining the current situation and characteristics of schistosomiasis in China,and considering the transmission with human,beef and snail,cercariae and miracidium in the aquatic environment,the schistosomiasis dynamical model with saturating incidence is formulated.We obtain the basic reproduction number of this model.By using Lyapunov functions,we conclude that if the basic reproduction number is less than 1,then the diseasefree equilibrium is globally asymptotically stable,if the basic reproduction number is more than 1,then the unique endemic equilibrium is also globally asymptotically stable.Finally,numerical simulation is used to verify the theoretical results.