COVID-19, an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), starting from Wuhan city of China, plagued the world in the later part of 2019. We developed a deterministic model to study the transmission dynamics of the disease with two categories of the Susceptibles (ie immigrant Susceptibles and local Susceptible). The model is shown to have a globally stable disease-free equilibrium point whenever the basic reproduction number ${\mathcal{R}}_0$ is less than unity. The endemic equilibrium is also shown to be globally stable for ${\mathcal{R}}_0>1$ under some conditions. The spread of the disease is also shown to be highly sensitive to use of PPEs and personal hygiene $(d)$, transmission probability $(\beta )$, average number of contacts of infected person per unit time (day) $(c)$, the rate at which the exposed develop clinical symptoms $(\delta )$ and the rate of recovery $(\rho )$. Numerical simulation of the model is also done to illustrate the analytical results established.