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 itsinception, it has been a major cause of deaths and illnesses in the general population across the globe. Inthis paper, we have formulated and theoretically analyzed a non-linear deterministic model for COVID-19transmission 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-freeequilibrium(DFE), and endemic equilibrium (EE) points, are explored. Besides, the Lyapunov function isutilized to prove the global stability of both DFE and EE. The bifurcation analysis was carried out by utilizingthe center manifold theory. Then, the model is fitted with real COVID-19 cumulative data of infected casesin Kenya as from March 30, 2020, to March 30, 2022. Furthermore, sensitivity analysis was performed forthe proposed model to ascertain the relative significance of model parameters to COVID-19 transmissiondynamics. The simulations revealed that the spread of COVID-19 can be curtailed not only via vaccinationof susceptible populations but also increased administration of COVID-19 booster vaccine to the vaccinatedpersons and early detection and treatment of asymptomatic individuals.