Spatiotemporal Dynamics Of Infectious Diseases Transmission Systems With Nonlocal Incidence

Since ancient times,the large-scale epidemics of infectious diseases have seriously threatened human life and property.The research on the propagation laws and the prevention and control measures of infectious diseases has always been the focus of scientists' attention.Dynamic models are very important tools to study infectious diseases.The incidences in these models depend on the transmission route of the diseases,human behavior,environmental temperature and humidity,transportation,economy and politics,etc.,therefore it is of great significance to select or construct an appropriate incidence according to the actual situation for the study of infectious diseases.In reality,for many infectious diseases such as influenza,COVID-19 and Brucellosis,infection can occur between susceptible individuals and infected individuals without direct contact,such as through aerosols in the air,public facilities and feces.Such infection is called nonlocal infection.In this paper,for nonlocal infection,we proposed an SIR infectious disease diffusive model with periodic nonlocal incidence and periodic parameters,an SIS nonlocal pair approximation model with birth and death on the space network and an SI infectious disease diffusive model with infection rate dependent on aggregation,respectively.The main research contents and innovation points are as follows:(1)Analysis of a local diffusive SIR model with seasonality and nonlocal incidence of infection.We established an SIR diffusive model with periodic nonlocal incidence and periodic parameters for influenza,Brucellosis and other infectious diseases which can be infected nonlocally and have seasonality.We obtained theoretically the global well-posedness and the dissipativity of the solutions of the model,the basic reproduction number and threshold theory.It is proved that the basic reproduction number of the model with nonlocal infection is smaller than that of the local model without considering periodicity.We numerically discussed the effects of periodicity and nonlocal incidence on the basic reproduction number,endemic size,the transient peak value and the peak arrival time of I(t).It is found that compared with local infection,nonlocal infection will lead to collectiveinfection in a short time due to its faster spread.When the effective infection area of disease is relatively small,seasonal factors can cause some regions to avoid a major outbreak in the early stages of the disease.(2)Analysis of an SIS nonlocal pair approximation model with birth and death on the space network.In view of the heterogeneity of contact between individuals in space,we extended the pair approximation model on the complex network to the space network,and established an SIS nonlocal pair approximation model with birth and death on the space network under the assumption of certain individual diffusion behavior.We obtained theoretically the global well-posedness and the dissipativity of the solutions and the basic reproduction number of the model.We numerically discussed the asymptotic behavior of the solution of the model.(3)Turing pattern analysis of an SI diffusive model with infection rate dependent on aggregation of the infected individuals.For the situation that the infection rate at each location is approximated by the infection rate of the whole space,we modified the infection rate at each location by the spatiotemporal heterogeneity of the local absolute density and the global absolute density of infected individuals for the first time.And then we established an SI diffusive model with infection rate dependent on aggregation.We obtained theoretically the global well-posedness and the dissipativity of the solutions of the model,the basic reproduction number.It is found that when the basic reproduction number is less than 1,the disease-free equilibrium point is locally asymptotically stable,but not necessarily globally asymptotically stable.For the modified model,we derived the Turing region.In addition to the common spots pattern,spots and striped coexistence pattern,striped pattern,we found rectangles pattern which is not common in the epidemic model.