SPATIAL DYNAMIC ANALYSIS FOR COVID-19 EPIDEMIC MODEL WITH DIFFUSION AND BEDDINGTON-DEANGELIS TYPE INCIDENCE

Abstract

A diffusion SEIAR model with Beddington-DeAngelis type incidence is proposed to characterize the spread of COVID-19 with spatial transmission. First, the well-posedness of solution is studied. Second, the basic reproduction number R0 is derived and served as a threshold value to determine whether COVID-19 will spread. Meanwhile, we consider the effect of diffusion on the spread of COVID-19 in spatial homogenous environment, by which we can obtain that if R0 < 1, then the infection-free steady state is globally asymptotically stable, while if R0 > 1, then the endemic steady state is globally asymptotically stable. Furthermore, according to the official reporting data about COVID-19 in Wuhan, China, the actual value of R0 is estimated, and comparing with other types of incidence, we find that the estimated peak with Beddington-DeAngelis type incidence is more close to the cases in reality. Finally, by numerical simulations, we can see that the diffusion behavior has evident impact on the spread of COVID-19 in spatial heterogeneity than homogeneity of environment.