Mathematical modelling of the COVID-19 pandemic with demographic effects

Abstract

In this paper, a latent infection susceptible–exposed–infectious–recovered model with demographic effects is used to understand the dynamics of the COVID-19 pandemics. We calculate the basic reproduction number ( $${R}_{0}$$ R 0 ) by solving the differential equations of the model and also using next-generation matrix method. We also prove the global stability of the model using the Lyapunov method. We showed that when the $${R}_{0}<1$$ R 0 < 1 or $${R}_{0}\le 1$$ R 0 ≤ 1 and $${R}_{0}>1$$ R 0 > 1 or $${R}_{0}\ge 1$$ R 0 ≥ 1 the disease-free and endemic equilibria asymptotic stability exist theoretically. We provide numerical simulations to demonstrate the detrimental impact of the direct and latent infections for the COVID-19 pandemic.