Revisiting SIR in the age of COVID-19: Explicit Solutions and Control Problems

Autor:	Borkar, Vivek S., Manjunath, D.
Rok vydání:	2020
Předmět:	Mathematics - Optimization and Control Electrical Engineering and Systems Science - Systems and Control Physics - Physics and Society
Druh dokumentu:	Working Paper
Popis:	The non-population conserving SIR (SIR-NC) model to describe the spread of infections in a community is proposed and studied. Unlike the standard SIR model, SIR-NC does not assume population conservation. Although similar in form to the standard SIR, SIR-NC admits a closed form solution while allowing us to model mortality, and also provides different, and arguably a more realistic, interpretation of the model parameters. Numerical comparisons of this SIR-NC model with the standard, population conserving, SIR model are provided. Extensions to include imported infections, interacting communities, and models that include births and deaths are presented and analyzed. Several numerical examples are also presented to illustrate these models. Two control problems for the SIR-NC epidemic model are presented. First we consider the continuous time model predictive control in which the cost function variables correspond to the levels of lockdown, the level of testing and quarantine, and the number of infections. We also include a switching cost for moving between lockdown levels. A discrete time version that is more amenable to computation is then presented along with numerical illustrations. We then consider a multi-objective and multi-community control where we can define multiple cost functions on the different communities and obtain the minimum cost control to keep the value function corresponding to these control objectives below a prescribed threshold. Comment: SIAM Journal of Control and Optimization 2020
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2010.06445 Zobrazit plný text záznamu View this record from Arxiv