Effectiveness of lock down to curtail the spread of corona virus: A mathematical model

Abstract

In this paper, we have considered a mathematical model that deals with the effectiveness of the measures that may be helpful for reducing the spread of the COVID-19 virus in the society. Here we have illustrated the importance of lock down in controlling and maintaining the spread of the COVID-19 virus. The impact of the virus on the susceptible population has been considered in the model. Also, we have taken into account the susceptible population, which by taking preventive measures viz., by having strong immunity, maintaining social distancing, wearing PPE kits and masks etc., is able to reduce the possibility of getting infected from the virus. Local as well as global stability of the equilibrium points of the model have been studied using Lyapunov function and the geometrical approach techniques. Basic reproduction number has also been obtained by using the next generation matrix. To show the effectiveness of the model, different cases obtained by varying the parameters involved in the model have been considered. A comparison between the actual number of infected cases in India and that obtained by the proposed model, showing the effectiveness of the proposed model, has also been carried out.

Keywords: Basic reproduction number; Lyapunov function; Next generation matrix; Routh–Hurwitz criterion.