Abstract
The COVID-19 pandemic and subsequent lockdowns highlight the close and delicate relationship between a country’s public health and economic health. Models that combine macroeconomic factors with traditional epidemic dynamics to calculate the impacts of a disease outbreak are therefore extremely useful for policymakers seeking to evaluate the best course of action in such a crisis. We developed a macroeconomic SIR model that considers herd immunity, behavior-dependent transmission rates, remote workers, and the indirect externalities of lockdowns. It is formulated as an exit time control problem where a social planner is able to prescribe separate levels of the lockdown low-risk and high-risk portions of the adult population. The model predicts that by considering the possibility of reaching herd immunity, high-risk individuals are able to leave lockdown sooner than in models where herd immunity is not considered. Additionally, a behavior-dependent transmission rate (which represents increased personal caution in response to increased infection levels) can lower both output loss and total mortality. Overall, the model-determined optimal lockdown strategy, combined with individual actions to slow virus transmission, is able to reduce total mortality to one-third of the model-predicted no-lockdown level of mortality.
Highlights
The COVID-19 global pandemic has led to massive lockdowns to slow the spread of the virus
We presented a realistic model of pandemic modeling that incorporates previously unconsidered factors such as natural herd immunity, behavior-dependent transmission rates, and indirect deaths due to lockdown, and thereby extends previous models, resulting in markedly different lockdown recommendations
The most notable difference was shorter lockdowns, due to the hope of reaching herd immunity and the cost of indirect deaths as an additional penalty on lengthy lockdowns. This strategy did result in lower levels of output loss, but it resulted in higher mortality rates, especially among the high-risk population
Summary
The COVID-19 global pandemic has led to massive lockdowns to slow the spread of the virus. The task is to find the optimal balance between public health and economic growth Models such as those proposed by [1,2] have used a macroeconomic approach and variations on the susceptible-infectious-recovered (SIR) epidemic model proposed by [3] to solve an optimization problem determining the lockdown policy that minimizes both the loss of life and the effects on output. We expand on these previous models by presenting our original work, which considers more factors affecting epidemic progression.
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