Authors: Samuel B. Apima 1 and Jacinta M. Mutwiwa 2
1Department of Mathematics and Statistics, Kaimosi Friends University College, Kenya.
2Department of Mathematics, Kibabii University, Kenya.

Abstract
COVID-19, a novel coronavirus, is a respiratory infection which is spread between humans through small droplets expelled when a person with COVID-19 sneezes, coughs, or speaks. An SEIQR model to investigate the spread of COVID-19 was formulated and analysed. The disease free equilibrium point for formulated model was shown to be globally asymptotically stable. The endemic states were shown to exist provided that the basic reproduction number is greater than unity. By use of Routh-Hurwitz criterion and suitable Lyapunov functions, the endemic states are shown to be locally and globally asymptotically stable respectively. This means that any perturbation of the model by the introduction of infectives the model solutions will converge to the endemic states whenever reproduction number is greater than one, thus the disease transmission levels can be kept quite low or manageable with minimal deaths at the peak times of the re-occurrence.

Keywords:
Basic reproduction number, endemic states, locally asymptotically stable, globally asympto- tically stable.