Mathematical analysis of COVID-19 model incorporating vaccination of susceptible and isolation of symptomatic individuals

COVID-19 is undoubtedly the most dangerous and highly contagious disease in 21st century. Intensive researches have and are being done to unearth effective vaccines to deal with future pandemics. In this research, we developed a deterministic model for COVID-19 driven by asymptomatic and symptomatic individuals taking into consideration the indispensable role of vaccination in combating disease transmission. The dissection of the proposed model was conferred in terms of the associated reproduction number R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}$$\end{document}, which is determined by utilizing the next-generation matrix (NGM) approach and forms the basis upon which the model’s stability analysis is established. The analysis showed that COVID-19 free equilibrium (CFE) is locally asymptotically stable for R0<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}<1$$\end{document} and unstable if R0>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}>1$$\end{document}. The local stability of endemic equilibrium was explored using center manifold theorem where the method utilized by Castilo-Chavez and Song was implemented and revealed that backward bifurcation was driven by the vaccine efficacy. The results revealed that increased administration levels of vaccine, increased identification and treatment of the asymptomatic and strict adherence to isolation for the symptomatic individuals would curtail COVID-19 infections from burgeoning to catastrophic levels that would overrun the capacity of health care support system.