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Applying optimal control theory to complex epidemiological models to inform real-world disease management.

ABSTRACT: Mathematical models provide a rational basis to inform how, where and when to control disease. Assuming an accurate spatially explicit simulation model can be fitted to spread data, it is straightforward to use it to test the performance of a range of management strategies. However, the typical complexity of simulation models and the vast set of possible controls mean that only a small subset of all possible strategies can ever be tested. An alternative approach-optimal control theory-allows the best control to be identified unambiguously. However, the complexity of the underpinning mathematics means that disease models used to identify this optimum must be very simple. We highlight two frameworks for bridging the gap between detailed epidemic simulations and optimal control theory: open-loop and model predictive control. Both these frameworks approximate a simulation model with a simpler model more amenable to mathematical analysis. Using an illustrative example model, we show the benefits of using feedback control, in which the approximation and control are updated as the epidemic progresses. Our work illustrates a new methodology to allow the insights of optimal control theory to inform practical disease management strategies, with the potential for application to diseases of humans, animals and plants. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

SUBMITTER: Bussell EH

PROVIDER: S-EPMC6558566 | biostudies-literature | 2019 Jul

REPOSITORIES: biostudies-literature

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Applying optimal control theory to complex epidemiological models to inform real-world disease management.

Bussell E H EH Dangerfield C E CE Gilligan C A CA Cunniffe N J NJ

Philosophical transactions of the Royal Society of London. Series B, Biological sciences 20190701 1776

Mathematical models provide a rational basis to inform how, where and when to control disease. Assuming an accurate spatially explicit simulation model can be fitted to spread data, it is straightforward to use it to test the performance of a range of management strategies. However, the typical complexity of simulation models and the vast set of possible controls mean that only a small subset of all possible strategies can ever be tested. An alternative approach-optimal control theory-allows the ...[more]

PMID: 31104600

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Project description:The IUCN (International Union for Conservation of Nature) Red List categories and criteria are the most widely used framework for assessing the relative extinction risk of species. The criteria are based on quantitative thresholds relating to the size, trends, and structure of species' distributions and populations. However, data on these parameters are sparse and uncertain for many species and unavailable for others, potentially leading to their misclassification or classification as data deficient. We devised an approach that combines data on land-cover change, species-specific habitat preferences, population abundance, and dispersal distance to estimate key parameters (extent of occurrence, maximum area of occupancy, population size and trend, and degree of fragmentation) and hence predict IUCN Red List categories for species. We applied our approach to nonpelagic birds and terrestrial mammals globally (?15,000 species). The predicted categories were fairly consistent with published IUCN Red List assessments, but more optimistic overall. We predicted 4.2% of species (467 birds and 143 mammals) to be more threatened than currently assessed and 20.2% of data deficient species (10 birds and 114 mammals) to be at risk of extinction. Incorporating the habitat fragmentation subcriterion reduced these predictions 1.5-2.3% and 6.4-14.9% (depending on the quantitative definition of fragmentation) for threatened and data deficient species, respectively, highlighting the need for improved guidance for IUCN Red List assessors on the application of this aspect of the IUCN Red List criteria. Our approach complements traditional methods of estimating parameters for IUCN Red List assessments. Furthermore, it readily provides an early-warning system to identify species potentially warranting changes in their extinction-risk category based on periodic updates of land-cover information. Given our method relies on optimistic assumptions about species distribution and abundance, all species predicted to be more at risk than currently evaluated should be prioritized for reassessment.

Dataset Information

Applying optimal control theory to complex epidemiological models to inform real-world disease management.

Publications

Applying optimal control theory to complex epidemiological models to inform real-world disease management.

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