In this paper, we study the dynamical effects of timely and delayed diagnosis on the spread of COVID-19 in Ghana during its initial phase by using reported data from March 12 to June 19, 2020. The estimated basic reproduction number, ℛ0, for the proposed model is 1.04. One of the main focus of this study is global stability results. Theoretically and numerically, we show that the disease persistence depends on ℛ0. We carry out a local and global sensitivity analysis. The local sensitivity analysis shows that the most positive sensitive parameter is the recruitment rate, followed by the relative transmissibility rate from the infectious with delayed diagnosis to the susceptible individuals. And that the most negative sensitive parameters are: self-quarantined, waiting time of the infectious for delayed diagnosis and the proportion of the infectious with timely diagnosis. The global sensitivity analysis using the partial rank correlation coefficient confirms the directional flow of the local sensitivity analysis. For public health benefit, our analysis suggests that, a reduction in the inflow of new individuals into the country or a reduction in the inter community inflow of individuals will reduce the basic reproduction number and thereby reduce the number of secondary infections (multiple peaks of the infection). Other recommendations for controlling the disease from the proposed model are provided in Section 7.
