Modelling the Dynamics of COVID-19 Disease with Contact Tracing and Isolation in Ghana

Abstract

We have formulated a mathematical model to investigate the transmission dynamics of the current novel COVID-19 disease outbreak in Ghana. The coronavirus originated from Wuhan,, China. Majority of people who contact the disease experience mild to moderate respiratory illness and recover. The elderly and people with underlying health issues experience severe complications. A plethora of measures have been taken by the government of Ghana to curtail the disease. The model considers, among other things, quarantining and testing of immigrants, contact tracing and isolation in the form of quarantining or hospitalization, as control measures in mitigating the spread of the pandemic. Our model considers the following classes: susceptible, exposed, infectious, quarantine, treatment and recovery class. The steady-state solution was calculated and the basic reproduction number for this model calculated and used as a threshold to determine the asymptotic behaviour of the model. Our analytical and numerical results show a close dependence of the basic reproductive number on epidemic parameters. The aim of this paper was to incorporate the various intervention strategies into the model and ascertain their impact on COVID-19. Some of the methods employed in the analysis include the Next Generation Matrix and the Jacobian Matrix. Our simulations results correlate well with data and indicate that early quarantine and a high quarantine rate are crucial to the control of COVID-19. Thus, current preventative measures, such as isolation, contact tracing and treatment are, indeed, critical components in the control of COVID-19 until appropriate cure or vaccine is found.