Containment strategy for an epidemic based on fluctuations in the SIR model

The COVID-19 pandemic has created a challenging situation where governing authorities are faced with the complex decision of what the appropriate measures are given the existing information, and how much containment can be justified given the uncertainties involved with the future development of the spread of infection. A typical course of action usually involves waiting until a critical condition is reached and then using this to justify implementing severely restrictive measures. Building on the key observation that the stochastic evolution of a process such as the spread of infection has a finite extinction probability even when it is expected to grow exponentially on average, we propose a strategy of containment that falls in between the relatively mild measures that are typically deemed more acceptable by the public and more popular by the politicians, and the maximally restrictive lock-down strategies, which some countries have had to implement to avert catastrophic spread of infection. Our proposed strategy involves dividing cities and regions in countries and implementing containment at the level of such sub-populations. Since our analysis is based on small numbers (with the relevant data taken from the reported infection cases in Germany on 17 March 2020), it also means that it is doubly beneficial to impose drastic isolation measures for relatively small communities (villages, cities, parts of large cities) early on even if it seems disproportionate at the time, to forego the likely need for future drastic measures.