Spatiotemporal Dynamics Analysis Of A Degenerate Reaction-diffusion Model With Different Infection Period

Nowadays,the spread of infectious diseases causes a huge burden on human health,society and economy.In some infectious diseases,such as cholera,hepatitis A and AIDS,the infected hosts carry different levels of pathogens during the disease period,which leads to different clinical symptoms.It is worth to be aware that recessive hosts does not present any clinical symptoms.This leads to great difficulties in disease prevention and control.Therefore,this paper establishes two models in which the spatially heterogeneous environment with multiple infectious stages of degenerative reaction diffusion.We apply the relevant mathematical theories to explore the transmission mechanism of such infectious diseases and provide effective measures for disease control and prevention.Mathematically,the well-posedness of two models and the existence of global attractors are proved.The basic reproduction number of the models are defined and use it as a threshold to characterize the persistence and extinction of the disease.In addition,the asymptotic behavior of the positive steady state when the diffusion rate of the susceptible host is infinite or infinitesimal is investigated.In particular,in the spatially homogeneous case,by constructing two Lyapunov functions to prove that the positive equilibrium points are globally attractive.Finally,threshold dynamic results validated by numerical simulations,the effect of spatially heterogeneous parameters on the basic regeneration number is simulated,and the degree of influence of multiple transmission rates on disease transmission is compared.Biologically,the results of this paper suggest that control of disease transmission requires a multifaceted approach,although the transmission from person to person leads the transmission of disease,the transmission of human and pathogens in the environment cannot be ignored.If any of these factors are ignored,the risk of disease transmission will be underestimated.In addition,the analytical approach of our model can be used in other similar epidemiological degenerative reactive diffusion models.