Mathematical Analysis of COVID-19 model with Vaccination and Partial Immunity to Reinfection

Abstract

COVID-19 is an infectious respiratory disease caused by a new virus, called SARS-CoV-2. Since its
inception, it has been a major cause of deaths and illnesses in the general population across the globe. In
this paper, we have formulated and theoretically analyzed a non-linear deterministic model for COVID-19
transmission dynamics by incorporating vaccination of the susceptible population. The system properties,
such as the boundedness of solutions, the basic reproduction number R0, the local stability of disease-free
equilibrium(DFE), and endemic equilibrium (EE) points, are explored. Besides, the Lyapunov function is
utilized to prove the global stability of both DFE and EE. The bifurcation analysis was carried out by utilizing
the center manifold theory. Then, the model is fitted with real COVID-19 cumulative data of infected cases
in Kenya as from March 30, 2020, to March 30, 2022. Furthermore, sensitivity analysis was performed for
the proposed model to ascertain the relative significance of model parameters to COVID-19 transmission
dynamics. The simulations revealed that the spread of COVID-19 can be curtailed not only via vaccination
of susceptible populations but also increased administration of COVID-19 booster vaccine to the vaccinated
persons and early detection and treatment of asymptomatic individuals.