Mathematical modelling of the COVID‑19 pandemic with demographic efects

Document Type : Original Article

Authors

1 Department of Mathematics and Statistics, Fourah Bay College, University of Sierra Leone, Freetown, Sierra Leone.

2 Department of Mathematics, Ecole Normale Superieure Université Marien Ngouabi, Brazzaville, Congo.

3 Department of Physical Sciences, Jaramogi Oginga Odinga University of Science and Technology, Bondo, Kenya.

Abstract

In this paper, a latent infection susceptible–exposed–infectious–recovered model with
demographic efects is used to understand the dynamics of the COVID-19 pandemics.
We calculate the basic reproduction number (R0) by solving the diferential 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 R0 < 1 or
R0 ≤ 1 and R0 > 1 or R0 ≥ 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.

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