Study On The Transmission Dynamics Of Infectious Diseases With Migration In Patch Environment

It has been thousands of years since the spread of infectious diseases.The control and extinction of infectious diseases is still a major problem in the world.With the passage of time and social progress,although transportation is convenient,this factor has a great impact on the spread of infectious diseases.Therefore,migration is also considered in the epidemic model in this paper,which makes the model more practical and the results more effective.In the first chapter,the research basis and significance of infectious disease transmission with migration in patch environment are expounded.In the second chapter,we consider an SIS epidemic model with migration and residence time in a patch environment.If₀R?1,the disease-free equilibrium is globally asymptotically stable and the disease dies out.With the same migration rate of susceptible and infectious individuals and without disease-induced death,whenR₀(29)1,the endemic equilibrium is unique and globally asymptotically stable.Finally,the above conclusions were validated by numerical simulations,and the effects of mobility and residence time on the disease were observed.In the third chapter,according to the spread of COVID-19,we established SEAIHR patch model,and considered the model with population migration based on this model.According to the closure of Wuhan and a large number of domestic ribose tests,we divided the outbreak time into two sections,and then estimated the parameters(MCMC parameter estimation method)by using the data of the World Health Organization and the National Health and Construction Committee,and simulated the model.Through the simulation,we can see that the plaque model with migration is more realistic for the spread of COVID-19 in a wide range of countries,and the estimated parameters also show that it is very effective to seal the city and carry out a lot of nucleic acid detection.Because there were local cases in Beijing on June 11,and the number continued to rise,we finally predicted the epidemic situation in Beijing by using the patch model established preliminarily,and the simulation showed that the epidemic situation can basically end until October 7.In this paper,epidemic models with migration in patch environment are mainly considered.In the first part,residence time and migration are combined,and a series of results are obtained by analyzing the stability of the model.In the second part,migration is considered in the model according to the spread of COVID-19,and the number of cases in each provinces is fitted by numerical simulation.The results show that the city closure strategy and a large number of nucleic acid detection are effective.