A Transmission Dynamics Model of COVID-19 With Consideration of the Vulnerability of a Population

Abstract

A well documented characteristic of COVID-19 is that whereas certain infected individuals recover without ever showing symptoms, others regarded as vulnerable, usually age with comorbidities tend to succumb to more or less severe symptoms. To address pertinent issues, we formulate an $SEI_{A}I_{S}RS$ Transmission Dynamics model of COVID-19 where $I_{A}$ and $I_{S}$ respectively represent asymptomatic and symptomatic classes thus allowing the inclusion of parameters which are vulnerability sensitive. We define a vulnerability factor, $\phi$ and show that the model is globally asymptotically stable at the disease-free equilibrium when $\mathcal{R}_{0}<1$ and $\phi$ is appropriately bounded above. We also show that the model is globally asymptotically stable at the endemic equilibrium when $\mathcal{R}_{0}>1$ and $\phi$ is appropriately bounded below. Finally, we employ numerical analysis using Ghana data, to further illustrate the effect of vulnerability related parameter  values on the trajectories of key variables of the model. We thereby demonstrated that  if a dominantly young population is of sufficiently low vulnerability then $\mathcal{R}_{0}<1$, and the Transmission Dynamics exhibits global asymptotic stability at the disease-free equilibrium.