On the efficiency of restrictive sanitary barriers to contain the progress of COVID-19: A simple mathematical modeling

Abstract

In May 2020, COVID-19 advanced aggressively towards countryside reaching most Brazilian municipalities. A measure frequently applied by Brazilian municipality authorities is the implementation of restrictive sanitary barriers that limit the flow of people to prevent viruses from reaching their municipalities through imported cases. Such barriers, however, have shown to be insufficient in many municipalities and new reports of first cases occur every day. In this informative text, use simple mathematical examples to explain the reason of this inefficiency and point out situations in which the barrier presents some expressive effect. All barriers, even the most rigorous, have some permeability in which people cross it and have contact with citizens. This permeability, associated with the low level of social distance, is an explanation for early cases of COVID-19 in the municipalities that adopted access restrictions. Barriers that generate positive impacts in the epidemic prevalence curves  are very difficult to implement and, therefore, a safe alternative is to reduce rates of local contagion  by means of social distancing and individual protection.