Optimal control

Optimal control of epidemics

From the perspective of control theory, an epidemic is viewed as a dynamical system with controlled variables. Its model is an instrument for designing a control action that will achieve the desired outcome. Depending on the context, different assumptions on the model and different control objectives can be formulated. In the context of the COVID-19 pandemic, with vaccines scarce or unavailable in many countries, intervention policies based on social distancing measures were the core containment tool. Considering the dramatic effect that extended lockdowns have on people and countries' economies, a minimum-time control using social distancing measures and considering hospital capacity restrictions is presented in [ACMM+21].

The SIR model is arguably the simplest epidemiological model. However, it already exhibits many of the nonlinear characteristics that are present in more elaborate models. In [CM21], we make the model more realistic by adding features such as inaccurate and partial state measurements and input and measurement delays. Delays in measurements and policy implementation have proved to be critical in the success or failure of government strategies. The former correspond to the time taken for the tests to be carried out, processed, verified, and made available in centralized databases. The latter correspond to the time it takes the population to adopt restrictions such as quarantine, social distancing habits, and mask use. A recent approach to the compensation of delays consists of modifying an observer to predict future states. The stability of the estimation-error dynamics is addressed from both the perspective of classical frequency-domain quasipolynomial analysis, and from the perspective of time-domain Lyapunov-Krasowskii analysis.