Study On Mathematical Models Of COVID-19 And Waterborne Infectious Diseases

In order to better study the COVID-19 outbreak,the role of asymptomatic infections and asymptomatic infections in water-borne transmission,and mathematical models have been established for theoretical analysis and numerical analysis.The main research contents are as follows:In chapter 1,introduce the development history of infectious diseases,the outbreak of the COVID-19 and asymptomatic infections,the status quo of domestic and foreign research and related definitions,theorems and other theoretical knowledge.In chapter 2,for the COVID-19,we established the SEIAR model,in which the number of contacts and the existing confirmed cases were closely combined,and the data of Wuhan and Guangzhou were collected.The least two were used in the software.Multiplication for parameter fitting,predictive analysis of the situation of new cases in Guangzhou and Wuhan,peak time and other measurement indicators of the model.In chapter 3,we consider that the presence of asymptomatic infections in water-borne infectious diseases can change the transmission situation,and establish a infectious disease model.By using the Lyapunov second method and constructing a suitable Lyapunov function,it is proved that when the basic reproduction number is less than or equal to 1,the system is globally asymptotically stable at the disease-free equilibrium point,and when the basic reproduction number is greater than 1,the system is in endemic equilibrium,and the point is globally asymptotically stable.When ignoring birth and death rate,we calculate the final size of the model.The proportion of asymptomatic infections p takes any value,and the basic reproduction number increases monotonically with the asymptomatic infection adjustment factor k;there is a critical ₀^k,when 0?k?k₀,the basic reproduction number decreases monotonously with the proportion of asymptomatic infections,when k₀?k?1,the basic reproduction number increases monotonously with the proportion of asymptomatic infections p,and finally,a numerical simulation is performed.In chapter 4,based on the previous research,we consider that pathogens in water can reproduce by themselves,but the growth is limited by the environment.Therefore,we assume that the growth of pathogens in water is in line with Logistic growth,and establish a water with growth and satisfying Logistic growth.Dynamics model of water-borne infectious disease.Calculate the basic reproduction number and final size of the model.Use data to verify that the growth and extinction of basic waterborne bacteria can change the dynamics of basic infectious diseases.