Temporospatial Complexity In A Reaction-Diffusion Epidemic Model With Nonlinear Incidence Rate

Spatial epidemiology mainly studies the spatial vary regulation of disease risk or incidence.Epidemic models using reaction-diffusion to predict how disease dis-tribute and how they transit in the space,it can be used to estimate the formation of spatial patterns on a large scale and the transmission velocity of disease.In this paper,temporospatial complexity in a reaction-diffusion I-R model with a nonlinear incidence rate of saturated mass action under zero-flux boundary conditions,which includes the behavioral changes and crowding effect of the infective individuals,is investigated.Firstly,we give an analysis of the boundedness,dissipation,and lo-cal stability of the positive equilibrium.In addition,we discuss the non-existence and existence of positive nonconstant solutions.On the basis of these results,Tur-ing instability caused by diffusion is investigated.The analysis results show that the evolutionary processes that involve organism distribution and the interaction of spatially distributed infection with local diffusion.Finally through numerical sim-ulation.We find that:choosing the appropriate parameters,the model presents a complex pattern dynamic structure,such as the spot,stripe,hole pattern controlled by diffusion.