Precaution, Social Distancing and Tests in a Model of Epidemic Disease

I develop an extension of a canonical epidemiology model in which the policy in place determines the probability of transmission of an epidemic disease. I use the model to evaluate the effects of isolating symptomatic individuals, of increasing social distancing and of tests of different quality: a poor quality test that can only discriminate between healthy and infected individuals (such as polymerase chain reaction -PCR- or Rapid Diagnostic Test), and a high quality test that is able to discriminate between immune and vulnerable healthy, and infected individuals (such as a serology test like Neutralization Assay). I find that isolating symptomatic individuals has a large effect at delaying and reducing the pick of infections. The combination of this policy with the poor quality test represents only a negligible improvement, whereas with the high quality test there is an additional delaying and reduction in the pick of infections. Social distancing alone cannot achieve similar effects without incurring in enormous output losses. I explore the combined effect of social distancing at early stages of the epidemic with a following period of tests and find that the best outcome is obtained with a light reduction of human interaction for about three months together with a subsequent test of the population over 40 days.