Analysis Of Dynamic Behavior For Epidemic Model With Age-structure And Schistosomiasis

It has become an important research method to explore and analyze the law and control strategy of infectious diseases by differential equation model.In recent years,the epidemic model with age structure,Schistosomiasis and impulsive differential equations have been favored by researchers and been fruitful.The specific research work of this paper is as follows:In second chapter we firstly introduce the epidemic model with age structure and model with periodic of their historical background and research significance.Then re-search situation and progress of dynamic behavior for the two kinds of models recently are also listed and briefly summarized,we also simply introduced the main research con-tent of this article in this section.The vaccination,latent and relapse period are three important factors affecting the whole disease development.In this chapter,we propose an SVEIR epidemic model with continuous age-dependent vaccination,latency and relapse,at the same time,the non-linear incidence rate is also considered.Uniform persistence of the model is proved by reformulating it as the so called Volterra integral equations.The basic reproduction num-ber R0,which completely determines the global dynamics of the model,is derived.By using Lyapunov functionals,the global stability of the equilibria is obtained.Namely,the disease-free equilibrium is globally asymptotically stable if R0<1,while if R0>1 the endemic equilibrium is globally asymptotically stable.Finally,two numerical examples support our main analytical results.In the forth chapter,Schistosomiasis,a parasitic disease caused by Schistosoma Japonicum,is still one of the most serious parasitic diseases in China and remains en-demic in seven provinces,including Hubei,Anhui,Hunan,Jiangsu,Jiangxi,Sichuan,and Yunnan.The monthly data of human schistosomiasis cases in Hubei,Hunan,and Anhui provinces(lake and marshland regions)released by the Chinese Center for Disease Control and Prevention(China CDC)display a periodic pattern with more cases in late summer and early autumn.Based on this observation,we construct a deterministic model with periodic transmission rates to study the seasonal transmission dynamics of schistosomiasis in these lake and marshland regions in China.We calculate the basic reproduction num-ber R0,discuss the dynamical behavior of solutions,and use the model to fit the monthly data of human schistosomiasis cases in Hubei.We also perform some sensitivity analysis of the basic reproduction number R0 in terms of model parameters.Our results indicate that treatment of at-risk population groups,improving sanitation,hygiene education,and snail control are effective measures in controlling human schistosomiasis in these lakes and marshland regions.In the fifth chapter,a general predator-prey model with disease in the prey and double impulsive control is proposed and investigated for the purpose of integrated pest man-agement.By using the Floquet theory,the comparison theorem of impulsive differential equations and the persistence theory of dynamical systems,we obtain that if threshold value R0<1,then the susceptible pest eradication periodic solution is globally asymp-totically stable,and if R0>1,then the model is permanent.The numerical examples not only illustrate the theoretical results,but also show that when the model is permanent,then it may possess an unique globally attractive T-periodic solution.