A SEIAR epidemic model for Covid-19 with migration and stochastic transmission

In the case of a highly infectious disease like covid-19, understanding the role of population migration is important and challenging. In this research, we study the global dynamics of a covid-19 epidemic model, which incorporates population migration and stochastic rate of transmission. It is shown that in both deterministic and stochastic environments, the models are globally Lyapunov stable near the disease-free equilibrium point, which is determined by a threshold parameter. More ever, the effect of migration on Covid-19 is analyzed, and it has been found that the number of infections as well as the peak value of the infection curve, is more when there is more population migrating, and the results are supported by numerical illustrations with their epidemiological relevance. The disease-free equilibrium of the associated time delay model is linearly asymptotically stable, and the endemic equilibrium has more bifurcation for higher values of the time delay parameter. 2000 MSC: 92B10