  In late 2019, a novel coronavirus, the SARS-CoV-2 outbreak was identified in
Wuhan, China and later spread to every corner of the globe. Whilst the number
of infection-induced deaths in Ghana, West Africa are minimal when compared
with the rest of the world, the impact on the local health service is still
significant. Compartmental models are a useful framework for investigating
transmission of diseases in societies. To understand how the infection will
spread and how to limit the outbreak. We have developed a modified SEIR
compartmental model with nine compartments (CoVCom9) to describe the dynamics
of SARS-CoV-2 transmission in Ghana. We have carried out a detailed
mathematical analysis of the CoVCom9, including the derivation of the basic
reproduction number, $\mathcal{R}_{0}$. In particular, we have shown that the
disease-free equilibrium is globally asymptotically stable when
$\mathcal{R}_{0}<1$ via a candidate Lyapunov function. Using the SARS-CoV-2
reported data for confirmed-positive cases and deaths from March 13 to August
10, 2020, we have parametrised the CoVCom9 model. The results of this fit show
good agreement with data. We used Latin hypercube sampling-rank correlation
coefficient (LHS-PRCC) to investigate the uncertainty and sensitivity of
$\mathcal{R}_{0}$ since the results derived are significant in controlling the
spread of SARS-CoV-2. We estimate that over this five month period, the basic
reproduction number is given by $\mathcal{R}_{0} = 3.110$, with the 95\%
confidence interval being $2.042 \leq \mathcal{R}_0 \leq 3.240$, and the mean
value being $\mathcal{R}_{0}=2.623$. Of the 32 parameters in the model, we find
that just six have a significant influence on $\mathcal{R}_{0}$, these include
the rate of testing, where an increasing testing rate contributes to the
reduction of $\mathcal{R}_{0}$.
