Novel use of online optimization in a mathematical model of COVID-19 to guide the relaxation of pandemic mitigation measures.

Since early 2020, non-pharmaceutical interventions (NPIs)-implemented at varying levels of severity and based on widely-divergent perspectives of risk tolerance-have been the primary means to control SARS-CoV-2 transmission. This paper aims to identify how risk tolerance and vaccination rates impact the rate at which a population can return to pre-pandemic contact behavior. To this end, we developed a novel mathematical model and we used techniques from feedback control to inform data-driven decision-making. We use this model to identify optimal levels of NPIs across geographical regions in order to guarantee that hospitalizations will not exceed given risk tolerance thresholds. Results are shown for the state of Colorado, United States, and they suggest that: coordination in decision-making across regions is essential to maintain the daily number of hospitalizations below the desired limits; increasing risk tolerance can decrease the number of days required to discontinue NPIs, at the cost of an increased number of deaths; and if vaccination uptake is less than 70%, at most levels of risk tolerance, return to pre-pandemic contact behaviors before the early months of 2022 may newly jeopardize the healthcare system. The sooner we can acquire population-level vaccination of greater than 70%, the sooner we can safely return to pre-pandemic behaviors.

Stability Analysis of an Eight Parameter SIR-Type Model Including Loss of Immunity, and Disease and Vaccination Fatalities

We revisit here a landmark five-parameter SIR-type model, which is maybe the simplest example where a complete picture of all cases, including non-trivial bistability behavior, may be obtained using simple tools. We also generalize it by adding essential vaccination and vaccination-induced death parameters, with the aim of revealing the role of vaccination and its possible failure. The main result is Theorem 1, which describes the stability behavior of our model in all possible cases.