The economic impact of lockdown and bounded treatment capability for an epidemic without vaccine

The COVID-19 virus continues to circulate in many countries, despite successful attempts to curb previous waves, and hence the issue of effective control both of the epidemic and its economic consequences remains a matter of lively debate. Although the estimated development time for an effective vaccine proved to be relatively accurate, many governments were still unable to devise a clear and coherent control policy during the pre-vaccination period. Policy responses often vacillated between two seemingly conflicting strategies—protecting the economy versus containing the spread of the epidemic by all available means, including mobility restrictions and social and economic lockdown. In the setup of a multidimensional and non-linear optimal control model, we describe the performance of a capital accumulation-based economy in which the revenue generated from production relies on both capital and labor. Using analytical means, we characterize intertemporal policies that ensure an optimal tradeoff between: (i) the level of lockdown, the purpose of which is to contain the epidemic and prevent the national health system from becoming overwhelmed; (ii) the level of investment in treatments; (iii) the level of consumption; and (iv) consequential impacts on labor availability and capital accumulation. We show that the fear of infection alone can be highly capital-destructive. Finally, given an incompressible consumption level, we identify thresholds for the initial endowment in capital below which the stock of capital decreases over time and can eventually become fully depleted.