Transmission Dynamics of COVID-19 and Impact on Public Health Policy

B Shayak; Mohit Manoj Sharma; Richard H Rand; Awadhesh Kumar Singh; Anoop Misra

The first attempt to model the spread of an epidemic though a set of differential equations was by WILLIAM KERMACK and ANDERSON MCKENDRICK in 1927 [23] who constructed a third order nonlinear model. Their basic variables were x, the number of people susceptible to the epidemic, y the number of people infected by it and z, the number of people recovered from it (or killed by it). Their pioneering study formed the basis of the S-I-R (susceptible-infected-recovered) model which has since been applied to influenza [24] , dengue [25] and Ebola virus outbreaks [26] . Numerous modifications to the basic model have been proposed over the years; the one which is most relevant for us is the addition of delay [27, 28] . In these works, the delay represents the incubation period i.e. the gap between a person's being exposed to the pathogen and his/her turning infectious. These and similar models may be considered as lumped-parameter models, in the sense that they feature a small number of parameters which represent averages over various kinds of population, for example the young and the old, the healthy and the constitutionally infirm. The advantage of these models is that they are considerably simple, easy to use, and yet capable of yielding the broad trajectory of the epidemic in a region with high accuracy.