Abstract

Within the context of SEIR models, we consider a lockdown that is both imposed and lifted at an early stage of an epidemic. We show that, in these models, although such a lockdown may delay deaths, it eventually does not avert a significant number of fatalities. Therefore, in these models, the efficacy of a lockdown cannot be gauged by simply comparing figures for the deaths at the end of the lockdown with the projected figure for deaths by the same date without the lockdown. We provide a simple but robust heuristic argument to explain why this conclusion should generalize to more elaborate compartmental models. We qualitatively discuss some important effects of a lockdown, which go beyond the scope of simple models, but could cause it to increase or decrease an epidemic's final toll. Given the significance of these effects in India, and the limitations of currently available data, we conclude that simple epidemiological models cannot be used to reliably quantify the impact of the Indian lockdown on fatalities caused by the COVID-19 pandemic.

Highlights

  • SEIR model to obtain specific analytic results, we explain in section 3 that our results should qualitatively generalize to more complicated models

  • To the extent that we rely on epidemiological models at all, one of the few reliable lessons we should take away is that lockdowns should not be evaluated by comparing fatalities by a fixed date

  • We start by considering the simplest epidemiological models — the SEIR models

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Summary

Lockdowns in the SEIR model

We start by considering the simplest epidemiological models — the SEIR models. It is possible to obtain simple analytic results in these models. A SEIR model was reportedly used in the BCG study, and the INDSCI-SIM model can be thought of as an extended SEIR model.

Setting
Definition of scenarios
A numerical example
A heuristic explanation and general compartmental models
The SEIR Model
General compartmental models
Real-world caveats
Possible negative long-term impacts of a lockdown
Possible positive long-term impacts of a lockdown
Conclusion and discussion
Findings
A The INDSCI-SIM model
Full Text
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