Covid-19: an analysis of an extended SEIR model and a comparison of different intervention strategies

Das, Arghya; Dhar, Abhishek; Goyal, Srashti; Kundu, Anupam

Modeling accurately the evolution and intervention strategies for the Covid-19 pandemic, that has now affected almost every country in the world, is a challenging problem. We present here an analysis of an extended Susceptible-Exposed-Infected-Recovered (SEIR) model, that takes into account the presence of aymptomatic carriers, and explore the effects of different intervention strategies such as social distancing (SD) and testing-quarantining (TQ). The two intervention strategies (SD and TQ) try to reduce the disease reproductive number ($R_0>1$) to a target value ($R_0^{\rm target}<1 $), but in distinct ways, which we implement in our model equations. We find that for the same target value, $R_0^{\rm target}<1 $, TQ is more efficient in controlling the pandemic than lockdowns that only implement SD. However, for TQ to be effective, it has has to be based on contact tracing and the ratio of tests/per day to the number of new cases/per day has to be scaled with the mean number of contacts that an infectious person has, which would be high in regions with high population density and low levels of social distancing. We point out that, apart from $R_0$, an important quantity is the largest eigenvalue of the linearized dynamics which provides a more complete understanding of the disease progression both pre- and post- intervention and explains observed data. Weak extended intervention strategies (that reduce $R_0$ but not to a value less than $1$) can reduce the peak values of infections and the asymptotic affected population. We provide simple expressions for these in terms of the disease parameters and apply them in the Indian context to obtain heuristic projections for the course of the pandemic. Looking at real data, we find that for many countries, several broad qualitative features are captured well by the model.