Dynamic Models Of Infectious Diseases Based On Information Dissemination And Internet Search Data

Infectious diseases have been harmful to human health for a long time.In recent years,avian influenza A(H7N9)virus,as a novel avian-origin influenza virus,has been spreading rapidly and has a great impact on human health and the national economy.In order to reduce the losses caused by infectious diseases,early prevention and surveillance of infectious diseases are particularly important.With the globalization of the economy and the rapid development of science and technology,the spread of information gradually increases the number of susceptible people who get information,which can prompt them to take preventive measures as early as possible to avoid infection.In addition,the high utilization rate of internet search engines and the timeliness of data make the internet search data widely used in epidemic monitoring of infectious diseases.Therefore,in this thesis,we establish two types of infectious disease models with information dissemination,then analyze the model respectively,and analyze the epidemic trend of avian influenza A(H7N9)combining the internet search data.Chapter 1,firstly,we introduce the research significance of infectious disease model,information dissemination and internet search data,then we give a brief introduction of H7N9 avian influenza,finally we introduce the development of infectious disease model containing information transmission and the application of internet search data in infectious diseases.Chapter 2,first of all,we introduce the selection of the search engines,then according to the propagation mechanism of avian influenza A(H7N9)virus,we establish H7N9 transmission dynamical model based on the Baidu index.Next,we apply the next generation matrix method of periodic system to give the basic reproductive number of the system and demonstrate the existence and stability of disease-free equilibrium and positive periodic solution.Moreover,the relevant keywords of H7N9 are selected,and the correlation between the actual cases and composite Baidu index is given,following,the actual cases and Baidu index are fitted by the least square method,we verify the rationality of the model.Lastly,the effect of avian mortality on the transmission threshold and epidemic trend of avian influenza A(H7N9)virus is analyzed,which provides support for disease prevention and control.Chapter 3,considering the limitation of the impact of information on susceptible persons and the fact that information is not only provided by the infected,but also depends on public activities and susceptible persons with information,we establish a class of nonlinear infectious disease models with saturation of information impact,then we analyze existence conditions of the equilibrium point of the system,and analyze the stability of the equilibrium point by using the Hurwitz criterion and the Lyapunov asymptotic stability theorem and the LaSalle invariant set principle.