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.

Assessing Public Health and Social Measures Against COVID-19 in Japan From March to June 2021

“…This is particularly true for PEM; the risk of an epidemic wave could have been greatly reduced if PEM had been implemented before a substantial increase in the COVID-19 incidence and if the PEM covered the areas or regions with increasing virus transmission. It must be remembered that the estimated relative reduction in R t found in the present study is conditional on implementation at a given timing; in general, the effectiveness of PHSM is greater if implemented earlier (76,77).…”

Analytical and numerical study of infection progression under social distancing measures

“…The model delivers closed-form mathematical expressions for the time dependence of infected (I) [2], detected cases (D) [3], and fatalities (F) [3]. These main infection progression data (I(t), D(t), F(t)) are well reproduced (for a majority of COVID-19 hotspots) through joint analytical and numerical analysis, capturing empirically observed COVID-19 growth signatures of detected cases, that is its three distinct growth signatures (exponential, superlinear, and sublinear regime).…”

“…The growth signatures and associated scaling laws are utilized [2] to pinpoint regions where analytical derivations are most effective for i) assessing the nearly constant value of the scaling exponent in the superlinear regime; ii) understanding the relationship between the duration of this regime and strength of social distancing (α); iii) recognizing changes in the reproduction number from infection outburst to its extinguishing; vi) constraining the main parameter quantifying the effect of social distancing (α), by analyzing the time duration of the sublinear regime. The combination of α and the time of social measures introduction [3] defines a new parameter -protection time, essential for public policy decision making. For instance, our study not only suggests that rigorous measures can be often substituted by more relaxed ones imposed at earlier times, but provides a direct analytical expression to quantify this balance.…”

“…For instance, our study not only suggests that rigorous measures can be often substituted by more relaxed ones imposed at earlier times, but provides a direct analytical expression to quantify this balance. We also provide simple analytical expressions [3] to estimate the peak's timing, the epidemic wave's tipping points, and the maximum of detected cases per day. Additionally, our model is applied to infer key infection parameters [2], such as case fatality, infected fatality, and attack rates.…”