Stability Analysis of a Mathematical Modeling of Spread and Control of Corona Virus Disease (Covid-19) Incorporating Vaccination Class

Abstract

In this paper some mathematical models of COVID 19 were extended by incorporating vaccination, social distancing, and proper use of face mask and hand sanitizers for the spread and control of Corona virus (COVID-19). The analysis of the Disease-Free Equilibrium (DFE) and Endemic Equilibrium (EE) points were carried out. The trace -determinant approaches for local stability and Castilo-chaves for global stability were used in the stability and sensitivity analyses. At the stability of the equilibrium points, we find out that the basic reproduction number which implies the (DFE) is locally asymptotically stable, but global asymptotic stability of (EE) exists at . Sensitivity analysis identifies the model's most sensitive parameters; which are responsible for disease transmission and control. Visualization of the effect of the key parameters on the basic reproduction number was carried out. The data visualization demonstrates that vaccination and recovery rate are crucial parameters for eradicating COVID-19 from the population, while contact rate, lack of social distancing, and improper use of facemasks and hand sanitizers are crucial for COVID-19 persistence. The risks of close proximity to infected people should indeed be made known to the general public. The government needs to step up its vaccination efforts.