Long-term regulation of prolonged epidemic outbreaks in large populations via adaptive control: a singular perturbation approach

TL;DR

This paper develops a control-theoretic framework using singular perturbation methods to regulate epidemic outbreaks, achieving stable infection plateaus through adaptive feedback in a simplified SIR model.

Contribution

It introduces a novel adaptive control approach for epidemic regulation, modeling social distancing as a nonlinear integral controller and analyzing its stability and robustness.

Findings

The Quasi-Steady-State can be globally asymptotically stable.

The model effectively captures effects of population size, vaccination, and second waves.

The approach provides a systematic way to tune NPIs for epidemic control.

Abstract

Initial hopes of quickly eradicating the COVID-19 pandemic proved futile, and the goal shifted to controlling the peak of the infection, so as to minimize the load on healthcare systems. To that end, public health authorities intervened aggressively to institute social distancing, lock-down policies, and other Non-Pharmaceutical Interventions (NPIs). Given the high social, educational, psychological, and economic costs of NPIs, authorities tune them, alternatively tightening up or relaxing rules, with the result that, in effect, a relatively flat infection rate results. For example, during the summer in parts of the United States, daily infection numbers dropped to a plateau. This paper approaches NPI tuning as a control-theoretic problem, starting from a simple dynamic model for social distancing based on the classical SIR epidemics model. Using a singular-perturbation approach, the plateau becomes a Quasi-Steady-State (QSS) of a reduced two-dimensional SIR model regulated by adaptive dynamic feedback. It is shown that the QSS can be assigned and it is globally asymptotically stable. Interestingly, the dynamic model for social distancing can be interpreted as a nonlinear integral controller. Problems of data fitting and parameter identifiability are also studied for this model. The paper also discusses how this simple model allows for meaningful study of the effect of population size, vaccinations, and the emergence of second waves.