Abstract
Motivated by the Covid-19 epidemic, we build a SIR model with private decisions on social distancing and population heterogeneity in terms of infection-induced fatality rates, and calibrate it to UK data to understand the quantitative importance of these assumptions. Compared to our model, the calibrated benchmark version with constant mean contact rate significantly over-predicts the mean contact rate, the death toll, herd immunity and prevalence peak. Instead, the calibrated counterfactual version with endogenous social distancing but no heterogeneity massively under-predicts these statistics. We use our calibrated model to understand how the impact of mitigating policies on the epidemic may depend on the responses these policies induce across the various population segments. We find that policies that shut down some of the essential sectors have a stronger impact on the death toll than on infections and herd immunity compared to policies that shut down non-essential sectors. Furthermore, there might not be an after-wave after policies that shut down some of the essential sectors are lifted. Restrictions on social distancing can generate welfare gains relative to the case of no intervention. Milder but longer restrictions on less essential activities might be better in terms of these welfare gains than stricter but shorter restrictions, whereas the opposite might be the case for restrictions on more essential activities. Finally, shutting down some of the more essential sectors might generate larger welfare gains than shutting down the less essential sectors.
Highlights
The current coronavirus epidemic has forcefully brought onto centre stage the need to understand how social distancing influences the evolution of an epidemic and vice versa
Regarding the effects of various second-best government interventions on social distancing, our results suggest that the length of a lockdown that shuts down nonessential sectors such as services has a significant effect on the death toll, and the “flattening of the curve”, and on the behavioural responses of low-risk individuals when such policies are lifted
We have calibrated the model to UK data on reported deaths prior to the introduction of the UK lockdown to study various hypothetical scenarios of government intervention regarding social distancing
Summary
The current coronavirus epidemic has forcefully brought onto centre stage the need to understand how social distancing influences the evolution of an epidemic and vice versa. Regarding the effects of various second-best government interventions on social distancing, our results suggest that the length of a lockdown that shuts down nonessential sectors such as services has a significant effect on the death toll, and the “flattening of the curve”, and on the behavioural responses of low-risk individuals when such policies are lifted These behavioural responses, in turn, could contribute to an after-wave. The reason is that such mitigating policies will not affect social distancing by low-risk susceptible individuals during the lockdown To understand the latter finding, observe first that in the SIR model there is no after-wave when the mean contact rate times the proportion in the population of the susceptible to infection individuals times the basic reproduction number is (weakly) lower than one. We conclude and point to possible extensions of our model and directions for future research
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