Bank of Canada : A Macroeconomic Model of an Epidemic with Silent Transmission and Endogenous Self-isolation

As the world continues to grapple with the global spread of COVID-19, there is increasing evidence that most mild and asymptomatic cases of the disease tend to go undiagnosed or unreported. We study the interaction between epidemics and economic decisions in a model where there is silent transmission of the virus. Agents in our model solve a time allocation problem by deciding how much time to devote to production of a market good, production of a home good, social leisure and leisure at home. Their probability of becoming infected with the virus depends on the time spent in each of these activities.

We find that when agents are rational (i.e., they are aware of the initial outbreak and understand the dynamics of population health), they partially shield themselves from the epidemic by reallocating time from riskier activities (producing the market good and social leisure) to less risky activities (staying at home). Agents reallocate their time in such a way that the total expected number of cases directly generated by one infected person stabilizes around one. That is, agents balance avoiding exponential growth of the number of infections with their preference to spend more time outside of their home.

Rational behaviour strongly diminishes the severity of the epidemic (as measured by the number of total infections) but exacerbates the depth and length of the economic recession that the epidemic causes. We find that in addition to isolating individuals with symptoms, implementing detection and isolation policies targeted at asymptomatic or mildly symptomatic cases can reduce the severity of the recession brought on by the COVID-19 pandemic. Given that both economic and health outcomes of the epidemic are substantially worse when agents are not rational, detection and isolation of asymptomatic and mildly symptomatic infected individuals is even more important.