Mathematical analysis of epidemic model to assess the impact of lockdown on COVID-19

Abstract

Covid-19 and its variants, have been a worst pandemic, the entire world has witnessed. Tens of millions of cases have been recorded in over 210 countries and territories as part of the ongoing global pandemic that is still going on today. In this paper, we propose a SEI mathematical model to investigate the impact of lockdown to the controlling and spreading of infectious disease COVID-19. The epidemic model incorporates constant recruitment, experiencing infectious force in the latent period and the infected period. The equilibrium states are computed. Under some conditions, results for local asymptotic stability and global stability of disease-free and endemic equilibrium are established by using the stability theory of ordinary differential equations. It is seen that when the basic reproduction number , the dynamical system is stable and diseases die out from the system and when , the disease persists in the dynamical system. When , trans critical bifurcation is appeared. The numerical simulations are carried out to validate the analytical results.