CoSIR: Optimal control of SIR epidemic dynamics by mapping to Lotka-Volterra System

Multiple macro-phenomena such as disease epidemics, online information propagation, and economic activity can be well-approximated using simple dynamical systems. Shaping these phenomena with adaptive control of key levers has long been the holy grail of policymakers. In this paper, we focus on optimal control of transmission rate in epidemic systems following the widely applicable SIR dynamics. We first demonstrate that the SIR model with infectious patients and susceptible contacts (i.e., product of transmission rate and susceptible population) interpreted as predators and prey respectively reduces to a Lotka-Volterra (LV) predator-prey model. The modified SIR system (LVSIR) has a stable equilibrium point, an “energy” conservation property, and exhibits bounded cyclic behavior. We exploit this mapping using a control-Lyapunov approach to design a novel adaptive control policy (CoSIR) that nudges the SIR model to the desired equilibrium. Combining CoSIR policy with data-driven estimation of parameters and adjustments for discrete transmission levels yields a control strategy with practical utility. Empirical comparison with periodic lockdowns on simulated and real COVID-19 data demonstrates the efficacy and adaptability of our approach. ### Competing Interest Statement The authors have declared no competing interest. ### Clinical Trial Our work does not involve clinical trials ### Funding Statement No external funding ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: No special approvals were required for this work. All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes All data used for our experiments are publicly available. Data sources include, (i)Public Health England COVID-19 data (ii)Covid19india data (iii)The New York Times COVID-19 data