Mathematical study of transmission dynamics of SARS-CoV-2 with waning immunity

The aim of this work is to provide a new mathematical model that studies transmission dynamics of Coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The model captures the dynamics of the disease taking into consideration some measures and is represented by a system of nonlinear ordinary differential equations including seven classes, which are susceptible class (S), exposed class (E), asymptomatic infected class (A), severely infected class (V), hospitalized class (H), hospitalized class but in ICU (C) and recovered class (R). We prove positivity and boundedness of solutions, compute the basic reproduction number, and investigate asymptotic stability properties of the proposed model. As a consequence, dynamical properties of the model are established fully and some mitigation and prevention measures of COVID-19 outbreaks are also suggested. Furthermore, the model is fitted to COVID-19 confirmed cases in South Africa during the Omicron wave from November 27, 2021 to January 20, 2022 which helped determine the model parameters value for our numerical simulation. A set of numerical experiments using real data is conducted to support and illustrate the theoretical findings. Numerical simulation results show that fast waning of infection-induced immunity can increase the occurrence of outbreaks.