Covid-19: analysis of a modified SEIR model, a comparison of different intervention strategies and projections for India.

Modeling accurately the evolution and intervention strategies for the Covid-19 pandemic is a challenging problem. We present here an analysis of an extended Susceptible-Exposed-Infected-Recovered (SEIR) model that accounts for asymptomatic carriers, and explore the effect 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 $R_0$ 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 $R_0^{\rm target} <1$, TQ is more efficient in controlling the pandemic than lockdowns that only implement SD. However, for TQ to be effective, it has to be based on contact tracing and the ratio of tests/day to the number of new cases/day has to be scaled with the mean number of contacts of an infectious person, which would be high in densely populated regions with low levels of SD. We point out that, apart from $R_0$, an important quantity is the largest eigenvalue of the linearised dynamics which provides a more complete understanding of the disease progression, both pre- and post- intervention, and explains observed data for many countries. Weak 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 analytic 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. We find that the predictions strongly depend on the assumed fraction of asymptomatic carriers.