ArticleMathematical biosciences2017
Time-optimal control strategies in SIR epidemic models.
Article in Mathematical biosciences, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 21 papers.
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Who cites it
21 citing papers in PubMed.
- A Fokker-Planck framework for control of epidemics.Journal of mathematical biology · 2026Article
- Analysis of an SIR model: preventive measures, bounded multiplicative random perturbations and optimal control strategies.Scientific reports · 2026Article
- Reframing Optimal Control Problems for Infectious Disease Management in Low-Income Countries.Bulletin of mathematical biology · 2023Article
- Highly coordinated nationwide massive travel restrictions are central to effective mitigation and control of COVID-19 outbreaks in China.Proceedings. Mathematical, physical, and engineering sciences · 2022Article
- Optimal control of the SIR model with constrained policy, with an application to COVID-19.Mathematical biosciences · 2022Article
- Effects of Vaccination Efficacy on Wealth Distribution in Kinetic Epidemic Models.Entropy (Basel, Switzerland) · 2022Article
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- Optimal control-based vaccination and testing strategies for COVID-19.Computer methods and programs in biomedicine · 2021Article
- Safety-Critical Control of Compartmental Epidemiological Models With Measurement Delays.IEEE control systems letters · 2021Article
- On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies.Journal of mathematical biology · 2021Article
- Control with uncertain data of socially structured compartmental epidemic models.Journal of mathematical biology · 2021Article
- Optimal control of the SIR model in the presence of transmission and treatment uncertainty.Mathematical biosciences · 2021Article
- Application of Optimal Control of Infectious Diseases in a Model-Free Scenario.SN computer science · 2021Article
- Optimal Immunity Control and Final Size Minimization by Social Distancing for the SIR Epidemic Model.Journal of optimization theory and applications · 2021Article
- Piecewise-constant optimal control strategies for controlling the outbreak of COVID-19 in the Irish population.Mathematical biosciences · 2020Article
- A new modelling of the COVID 19 pandemic.Chaos, solitons, and fractals · 2020Article
- Optimal quarantine control of an infectious outbreak.Chaos, solitons, and fractals · 2020Article
- An optimal predictive control strategy for COVID-19 (SARS-CoV-2) social distancing policies in Brazil.Annual reviews in control · 2020Article
- Beyond just "flattening the curve": Optimal control of epidemics with purely non-pharmaceutical interventions.Journal of mathematics in industry · 2020Article
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4 authors.
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Abstract
We investigate the time-optimal control problem in SIR (Susceptible-Infected-Recovered) epidemic models, focusing on different control policies: vaccination, isolation, culling, and reduction of transmission. Applying the Pontryagin's Minimum Principle (PMP) to the unconstrained control problems (i.e. without costs of control or resource limitations), we prove that, for all the policies investigated, only bang-bang controls with at most one switch are admitted. When a switch occurs, the optimal strategy is to delay the control action some amount of time and then apply the control at the maximum rate for the remainder of the outbreak. This result is in contrast with previous findings on the unconstrained problems of minimizing the total infectious burden over an outbreak, where the optimal strategy is to use the maximal control for the entire epidemic. Then, the critical consequence of our results is that, in a wide range of epidemiological circumstances, it may be impossible to minimize the total infectious burden while minimizing the epidemic duration, and vice versa. Moreover, numerical simulations highlighted additional unexpected results, showing that the optimal control can be delayed also when the control reproduction number is lower than one and that the switching time from no control to maximum control can even occur after the peak of infection has been reached. Our results are especially important for livestock diseases where the minimization of outbreaks duration is a priority due to sanitary restrictions imposed to farms during ongoing epidemics, such as animal movements and export bans.
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