A Mathematical Model and Sensitivity Assessment of COVID-19 Outbreak for Ghana and Egypt

TLDR: A Susceptible, Exposed, Asymptomatic, Quarantined asymPTomatic, Severely infected, Hospitalized, Recovered, Deceased, and Partially quarantined susceptible individuals is proposed.

Abstract: Following the outbreak of COVID-19 in December 2019, and the eventual spread to other parts of the world; has pushed governments and health authorities to take drastic socioeconomic, sociocultural and sociopolitical measures to curb the spread of the virus, SARS-CoV-2. In this paper, we propose a Susceptible, Exposed, Asymptomatic, Quarantined asymptomatic, Severely infected, Hospitalized, Recovered, Deceased, and Partially quarantined susceptible individuals; thus $(S E A Q I_s H RR^{A} D S_p )$ model to describe the dynamics of COVID-19. We fit the model to real data from Ghana and Egypt to estimate model parameters. We calculate the control and basic reproduction numbers for Egypt and Ghana. Projections for the disease control in Ghana and Egypt are presented. The sensitivity analysis suggests that: a continuous increase in the rate of diagnoses, the rate of quarantine through doubling enhanced contact tracing, and stringent safety measures in hospitals (and/or isolation centres); with a constant supply of effective personal protective equipment's (PPEs) will help reduce the control reproduction number $\mathcal{R}_{c}$, to less than unity as the lockdown measures are been lifted. Adding natural recovery to the model shows that an increase in natural recovery from the asymptomatic stage reduces the control reproduction number. We also noticed that the choice of a force of infection influences the control reproduction number.