Coronavirus disease is an infectious disease triggered by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) that belongs to the family of viruses that cause viral pneumonia. Despite the spreading of the COVID-19 in Kenya with a positivity of 12.9% as at 26 August 2021, there was no reliable deterministic Mathematical model that described the dynamics of COVID-19 incorporating underlying health conditions and impact of screening and treatment. In this study, we propose a SIRS (Susceptible-Infected –Recovered-Susceptible) classical mathematical model which is modified to incorporate the exposed and the treated individuals where COVID-19 is modelled. The model stratifies the population into two categories depending whether they have underlying health conditions or not, and describes disease transmission within or between the groups. Five compartments are considered in the model for each group that is; Susceptible individuals, exposed population, Infected individuals, treated population and the Recovered population. The Next generation matrix method was used to determine the basic reproduction number denoted 𝑅𝑜 of the proposed model. The results obtained indicates that the Disease Free Equilibrium is locally asymptotically stable whenever 𝑅𝑜∗ <1 and globally asymptotically stable if 𝑅0∗≤1. On the other hand, Endemic Equilibrium it is globally asymptotically stable if 𝑅𝑜∗ >1.The results obtained showed that increasing the rate of screening and treatment on the exposed population and weakening the disease transmission route between the susceptible, exposed and infected population are crucial to curb the spread of COVID-19 virus. The Government of Kenya should advocate treatment and screening of the exposed and infected individuals. Further research should consider incorporating vaccination.