Compartmental Modelling Approach for Accessing the Role of Non-Pharmaceutical Measures in the Spread of COVID-19

Abstract

Epidemic diseases are well known to be fatal and cause great loss worldwide—economically, socially and mentally. Even after around nine months, since the Coronavirus Disease 2019 (COVID-19) began to spread, people are getting infected all over the world. This is one of the areas where human medical advancements fail because by the time the disease is identified and its treatment is figured out, most of the population is already exposed to it. In such cases, it becomes easier to take steps if the dynamics of the disease and its sensitivity to various factors is known. This chapter deals with developing a mathematical model for the spread of Coronavirus disease, by employing a number of parameters that affect its spread. A compartmental modelling approach using ordinary differential equation has been used to formulate the set of equations that describe the model. We have used the next generation matrix method to find the basic reproduction number of the system and proved that the system is locally asymptotically stable at the disease-free equilibrium for $R_0<1$. Stability and existence of endemic equilibrium have been discussed, followed by sensitivity of infective classes to parameters like proportion of vaccinated individuals and precautionary measures like social distancing. It is expected that after the vaccine is developed and is available to use, as the proportion of vaccinated individuals will increase, the infection will decrease in the population which can gradually lead to herd immunity. Since, the vaccine is still under development, non-intervention measures play a major role in coping with the disease. The disease generally transmits when the water droplets from an infected individuals’ mouth or nose are inhaled by a healthy individual. The best measures that should be adopted are social distancing, washing one’s hands frequently, and covering one’s mouth with mask, quarantine and lockdowns. Thus, as more and more precautionary measures are taken, it would gradually reduce the infection which has also been proved numerically by the sensitivity analysis of ‘w’ in our dynamical analysis.