An analytical framework for understanding infection progression under social mitigation measures

Abstract

While there has been much computational work on the effect of intervention measures, such as vaccination or quarantine, the influence of social distancing on the epidemics' outbursts is not well understood. We present a realistic, analytically solvable, framework for COVID-19 dynamics in the presence of social distancing measures. The model is a generalization of the compartmental SEIR model that accounts for the effects of these measures. We derive a closed-form mathematical expressions for the time dependence of epidemiological observables, in particular, the detected cases and fatalities. These analytical solutions indicate simple quantitative relations between the model variables and epidemiological observables, which give insights into cause-effect connections that underlie the outburst dynamics but are obscured in more standard (numerical) approaches. While the obtained results and conclusions are based on the study of the COVID-19 pandemic, the presented analysis has general applicability to infection outbursts. Our findings are particularly important in the emergence of new pandemics when effective pharmaceutical treatments are unavailable, and one must rely on well-timed and appropriately chosen social mitigation measures.

Robust Global Trends during Pandemics: Analysing the Interplay of Biological and Social Processes

“…[3,4] and references therein), a rigorous quantitative analysis of these factors' intrinsic interactions is still visibly lacking [5,6]. Thus, understanding the big picture behind the underlying stochastic processes of infection progression [7] and the impact of fatality resulting during such events and post-infection [8] is vital. In contrast to many other stochastic processes in physics, biology and society, the evolution of epidemics occurs at the interplay of crucial biological and social factors, which are governed by their own (natural) laws.…”