Mathematical model of COVID-19 transmission dynamics incorporating booster vaccine program and environmental contamination

Abstract

COVID-19 is one of the greatest human global health challenges that cause economic meltdown in many nations. In this study, we develop a SIR-type model which captures both human-to-human and environment-to-human-to-environment transmissions that allow the recruitment of coronaviruses in the environment in the midst of booster vaccine program. Theoretically, we prove some basic properties of the full model as well as investigate the existence of SARS-CoV-2-free and endemic equilibria. The SARS-CoV-2-free equilibrium for the special case, where the constant inflow of coronavirus into the environment by any other means, Ω is suspended (Ω = 0) is globally asymptotically stable when the effective reproduction number 𝑅0𝑐 < 1 and unstable if otherwise. Whereas in the presence of free-living Coronaviruses in the environment (Ω > 0), the endemic equilibrium using the centre manifold theory is shown to be stable globally whenever 𝑅0𝑐 > 1. The model is extended into an optimal control system and analyzed analytically using Pontryagin’s Maximum Principle. Results from the optimal control simulations show that strategy E for implementing the public health advocacy, booster vaccine program, treatment of isolated people and disinfecting or fumigating surfaces and dead bodies before burial is the most effective control intervention for mitigating the spread of Coronavirus. Importantly, based on the available data used, the study also revealed that if at least 70% of the constituents followed the aforementioned public health policies, then herd immunity could be achieved during the COVID-19 pandemic in the community.