Optimal immunisation policies for epidemics

Abakuks, Andris

doi:10.1017/s0001867800039963

Cited by 21 publications

(40 citation statements)

References 4 publications

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“…Our work extends that of Abakuks (1972Abakuks ( , 1973Abakuks ( , 1974, Morton and Wickwire (1974), and Wickwire (1975) by examining the kind of resource constraints mentioned earlier. Specifically, the simple SIR model with mass action contact is revisited, and the following question is asked: "Given that there is a limited amount of control resources available during an outbreak, what control policy minimizes the total outbreak size?"…”

supporting

confidence: 56%

“…The main reason we have chosen to analyze model (1) is that it allows us to extend the work of Abakuks (1972Abakuks ( , 1973Abakuks ( , 1974, Morton and Wickwire (1974), and Wickwire (1975) to the case when there are limited resources. This being said, it is worth mentioning some of the major assumptions implicit in model (1).…”

Section: Model and Setupmentioning

confidence: 99%

“…Although an analysis of the time-optimal application of outbreak controls is of clear practical value, surprisingly little analysis has been done for the basic SIR model (Abakuks 1972(Abakuks , 1973(Abakuks , 1974Behncke 2000;Greenhalgh 1988; Morton and Wickwire 1974;Wickwire 1975Wickwire , 1977. In addition, many of the previous results that have been published have not been fully assimilated by practicing epidemiologists and public health officials.…”

mentioning

confidence: 99%

“…In Abakuks (1972), Abakuks determined the optimal vaccination strategy for the same model and found that the optimal strategy was to vaccinate N susceptibles at the start of the epidemic, where N depends on the precise form of the objective function. In Abakuks (1974), Abakuks then determined the optimal vaccination strategy for the same model but under the assumption that, at any instant, either all or none of the susceptibles are vaccinated. He found that the optimal control had the same basic form as the optimal control for the isolation model.…”

mentioning

confidence: 99%

“…He found that the optimal control had the same basic form as the optimal control for the isolation model. Shortly after the publication of Abakuks (1973Abakuks ( , 1974, Wickwire published Morton and Wickwire (1974) and Wickwire (1975) where he studied the same questions but with two notable differences. Firstly, he removed the unrealistic assumption that an arbitrary number of individuals can be isolated or vaccinated instantaneously, and instead modeled these processes under the assumption that some finite rate of isolation or vaccination is possible.…”

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confidence: 99%

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Optimal control of epidemics with limited resources

2010

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We extend the existing work on the time-optimal control of the basic SIR epidemic model with mass action contact rate. Previous results have focused on minimizing an objective function that is a linear combination of the cost associated with using control and either the outbreak size or the infectious burden. We instead, provide analytic solutions for the control that minimizes the outbreak size (or infectious burden) under the assumption that there are limited control resources. We provide optimal control policies for an isolation only model, a vaccination only model and a combined isolation-vaccination model (or mixed model). The optimal policies described here contain many interesting features especially when compared to previous analyses. For example, under certain circumstances the optimal isolation only policy is not unique. Furthermore the optimal mixed policy is not simply a combination of the optimal isolation only policy and the optimal vaccination only policy. The results presented here also highlight a number of areas that warrant further study and emphasize that time-optimal control of the basic SIR model is still not fully understood.

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confidence: 56%

Section: Model and Setupmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

mentioning

confidence: 99%

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Optimal control of epidemics with limited resources

2010

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Optimal Immunity Control and Final Size Minimization by Social Distancing for the SIR Epidemic Model

Bliman

Duprez

Privat

et al. 2021

J Optim Theory Appl

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The aim of this article is to understand how to apply partial or total containment to SIR epidemic model during a given finite time interval in order to minimize the epidemic final size, that is the cumulative number of cases infected during the complete course of an epidemic. The existence and uniqueness of an optimal strategy are proved for this infinite-horizon problem, and a full characterization of the solution is provided. The best policy consists in applying the maximal allowed social distancing effort until the end of the interval, starting at a date that is not always the closest date and may be found by a simple algorithm. Both theoretical results and numerical simulations demonstrate that it leads to a significant decrease in the epidemic final size. We show that in any case the optimal intervention has to begin before the number of susceptible cases has crossed the herd immunity level, and that its limit is always smaller than this threshold. This problem is also shown to be equivalent to the minimum containment time necessary to stop at a given distance after this threshold value.

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Nash-MFG equilibrium in a SIR model with time dependent newborn vaccination

Hubert

Turinici

2018

Ricerche mat

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We study the newborn, non compulsory, vaccination in a SIR model with vital dynamics. The evolution of each individual is modeled as a Markov chain. His/Her vaccination decision optimizes a criterion depending on the time-dependent aggregate (societal) vaccination rate and the future epidemic dynamics. We prove the existence of a Nash-Mean Field Games equilibrium among all individuals in the population. Then we propose a novel numerical approach to find the equilibrium and test it numerically.

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Optimal immunisation policies for epidemics

Cited by 21 publications

References 4 publications

Optimal control of epidemics with limited resources

Optimal control of epidemics with limited resources

Optimal Immunity Control and Final Size Minimization by Social Distancing for the SIR Epidemic Model

Nash-MFG equilibrium in a SIR model with time dependent newborn vaccination

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