Spread and control of COVID-19: A mathematical model

Abstract

A mathematical model is proposed in this paper to study the transmission and control of COVID-19. The mathematical model is formulated using system of nonlinear ordinary differential equations. The model includes disease-related parameters such as contact rate, disease-induced death rates, immigration rate and transition rates along with parameters for control measures such as implementation of social distancing practices, isolation and quarantine rates. From the stability analysis of the model, it is shown that if the social distancing is practiced by the large number of susceptible population, then the disease will not spread, and it may eventually die out. Further, it is derived from the analysis of the model that if most of the infected populations are isolated or quarantined, then the spread of the disease can be eventually controlled. However, from the analysis of the model, it is observed that if there is constant immigration of asymptomatic infected persons, then the disease will continue to spread and will remain pandemic. For controlling the disease, two more parameters, that is, vaccination and testing rates, are introduced in the original mathematical model and from the numerical analysis of this model, it has been shown that the control strategy involving vaccination and testing in combination can have synergistic effect for minimizing the COVID-19 infected cases.