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

To understand the spread of Covid-19, we analyse 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, R₀, to a target value <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20122580v2_inline65.gif"/></alternatives></inline-formula>, but in distinct ways, which we implement in our model equations. We find that for the same <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20122580v2_inline66.gif"/></alternatives></inline-formula>, TQ is more efficient in controlling the pandemic than SD. However, for TQ to be effective, it has to be based on contact tracing and our study quantifies the required ratio of tests-per-day to the number of new cases-per-day. Our analysis shows that the largest eigenvalue of the linearised dynamics provides a simple understanding of the disease progression, both pre- and post-intervention, and explains observed data for many countries. We propose an accurate way of specifying initial conditions for the numerics (from insufficient data) using the fact that the early time exponential growth is well-described by the dominant eigenvector of the linearized equations. Weak intervention strategies (that reduce R₀ but not sufficiently) reduce the peak values of infections and the asymptotic affected population and we provide analytic expressions for these in terms of the disease parameters. We apply them in the Indian context to obtain heuristic projections for the course of the pandemic, noting that the predictions strongly depend on the assumed fraction of asymptomatic carriers.