Dynamic Modeling And Research For The Spread Of Infectious Diseases In Environmental Pollution

With the development of the industrialized society,the environmental pollution has become more common,which includes air sewage pollution,agricultural pollution,water pollution and so on.Environmental pollution is widely distributed,which is related to viruses,bacteria,dust,pesticide,fertilizer and so on,and it endangers health of human and animal by the atmosphere,soil,water,food and so on.Specially,its effect on the spread of infectious diseases is worthy to study,which is a practical and hot topic.This paper builds dynamics model for the analysis the impact of pollutants in environmental on the spread of infectious diseases.Chapter 1,firstly,gives the general situation of infectious diseases and environmental pollutants,and introduces the influence of pollutants on the spread of infectious diseases,especially,the impact of fog and haze on the spread of influenza.Then,it introduces the development process of the disease transmission dynamics model.Finally,the research on the influence of pollutants on the disease transmission is described.In chapter 2,according to the general mechanism of the spread of infectious diseases,the formation and diffusion mechanism of pollutants,the paper sets up the transmission of infectious disease dynamics model with the infection-induced death.In theory,we discuss the existence and stability of the equilibria,and analyze the Hopf bifurcation,and give the critical value of pollutants concentration in environment between extinction and persistent of the population.The numerical simulation verifies above theoretical results.In chapter 3,the paper sets up the transmission of infectious disease dynamics model without the infection-induced death.In theory,we calculate the basic reproductive number of the SIS model in environmental pollution,discuss the existence and stability of the equilibria,and give the critical value of pollutants concentration in environment between extinction and persistent of the population.The numerical simulation verifies above theoretical results.By the sensitivity analysis,we assess the impact of pollutants on infectious diseases and provide the measures.In chapter 4,the above model is extended to study the impact of pollutants on the spread of specific infectious diseases,specifically the effect of fine particles in fog and haze on the spread of the infectious diseases.By considering the periodic outbreaks of influenza and the revolving of haze weather,we build the non-autonomous dynamics model that discuss the influence of fog and haze on the transmission of the disease.By using the number of the infected of influenza monthly and PM2.5 concentration data in Zhejiang province,we verify the rationality of the model and estimate the parameter values of the model,and calculate the basic reproductive number of influenza transmission in Zhejiang province.In addition,the numerical method is the best way to predicate the development trend of total population and fine particles concentration in Zhejiang province.And by the sensitivity analysis of parameters,we evaluate the preventive and controlling measures.Chapter 5,gives the conclusions and the prospects.