Mathematical Analysis of COVID-19 Transmission Dynamics Model in Ghana with Double-Dose Vaccination and Quarantine

Abstract

The discovery of vaccines for COVID-19 has been helpful in the fight against the spread of the disease. Even with these vaccines, the virus continues to spread in many countries, with some vaccinated persons even reported to have been infected, calling for administration of booster vaccines. The need for continued use of nonpharmaceutical interventions to complement the administration of vaccines cannot therefore be overemphasized. This study presents a novel mathematical model to study the impact of quarantine and double-dose vaccination on the spread of the disease. The local stability analysis of the COVID-19-free and endemic equilibria is examined using the Lyapunov second technique. The equilibria are found to be locally asymptotically stable if <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:msub> <a:mrow> <a:mi mathvariant="script">R</a:mi> </a:mrow> <a:mrow> <a:mn>0</a:mn> </a:mrow> </a:msub> <a:mo>&lt;</a:mo> <a:mn>1</a:mn> </a:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" id="M2"> <d:msub> <d:mrow> <d:mi mathvariant="script">R</d:mi> </d:mrow> <d:mrow> <d:mn>0</d:mn> </d:mrow> </d:msub> <d:mo>&gt;</d:mo> <d:mn>1</d:mn> </d:math> , respectively. Besides other analytical results, numerical simulations are performed to illustrate the analytical results established in the paper.