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’.
9Mathematical models provide a rational basis to inform how, where and when to control disease. Assuming 10 an accurate spatially-explicit simulation model can be fitted to spread data, it is straightforward to use it to test 11 the performance of a range of management strategies. However, the typical complexity of simulation models 12 and the vast set of possible controls mean that only a small subset of all possible strategies can ever be tested. 13 An alternative approach -optimal control theory -allows the very best control to be identified unambiguously. 14 However, the complexity of the underpinning mathematics means that disease models used to identify this 15 optimum must be very simple. We highlight two frameworks for bridging the gap between detailed epidemic 16 simulations and optimal control theory: open-loop and model predictive control. Both these frameworks 17 approximate a simulation model with a simpler model more amenable to mathematical analysis. Using an 18 illustrative example model we show the benefits of using feedback control, in which the approximation and 19 control are updated as the epidemic progresses. Our work illustrates a new methodology to allow the insights 20 of optimal control theory to inform practical disease management strategies, with the potential for application 21 to diseases of plants, animals and humans. 22 1 Introduction 23 Mathematical modelling plays an increasingly important role in informing policy and management decisions 24 concerning invading diseases [1, 2]. However, model-based identification of effective and cost-efficient controls 25 can be difficult, particularly when models include highly detailed representations of disease transmission 26 processes. There is a variety of mathematical tools for designing optimal strategies, but no standard for putting 27 the results from mathematically motivated simplifications into practice. An open question is how to incorporate 28 enough realism into a model to allow accurate predictions of the impact of control measures, whilst ensuring 29 that the truly optimal strategy can still be identified [3]. In this paper we identify the difficulties -as well as 30 potential solutions -in achieving a practically useful optimal strategy, highlighting the potential roles of open 31 loop and model predictive control by way of a simple example. 32Realistic landscape-scale modelling 33 The optimisation of epidemic interventions involves determining the management strategy that minimises 34 impacts of disease. This minimisation can be difficult when resources are limited and there are economic costs 35 associated with both control measures and disease. Methods that simulate the expected course of an epidemic 36 and explicitly model effects of interventions allow us to quantify the potential impact of a given strategy [4]. 37These simulation models accurately capture the dynamics of the real system and so have become important 38 tools in designing intervention strategies to inform policy decisions. Examples include...
Epidemics can particularly threaten certain sub-populations. For example, for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the elderly are often preferentially protected. For diseases of plants and animals, certain sub-populations can drive mitigation because they are intrinsically more valuable for ecological, economic, socio-cultural or political reasons. Here, we use optimal control theory to identify strategies to optimally protect a ‘high-value’ sub-population when there is a limited budget and epidemiological uncertainty. We use protection of the Redwood National Park in California in the face of the large ongoing state-wide epidemic of sudden oak death (caused by Phytophthora ramorum ) as a case study. We concentrate on whether control should be focused entirely within the National Park itself, or whether treatment of the growing epidemic in the surrounding ‘buffer region’ can instead be more profitable. We find that, depending on rates of infection and the size of the ongoing epidemic, focusing control on the high-value region is often optimal. However, priority should sometimes switch from the buffer region to the high-value region only as the local outbreak grows. We characterize how the timing of any switch depends on epidemiological and logistic parameters, and test robustness to systematic misspecification of these factors due to imperfect prior knowledge.
Epidemics can particularly threaten certain sub-populations. For example, for SARS-CoV-2, the elderly are often preferentially protected. For diseases of plants and animals, certain sub-populations can drive mitigation because they are intrinsically more valuable for ecological, economic, socio-cultural or political reasons. Here we use optimal control theory to identify strategies to optimally protect a "high value" sub-population when there is a limited budget and epidemiological uncertainty. We use protection of the Redwood National Park in California in the face of the large ongoing state-wide epidemic of sudden oak death (caused by Phytophthora ramorum) as a case study. We concentrate on whether control should be focused entirely within the National Park itself, or whether treatment of the growing epidemic in the surrounding "buffer region" can instead be more profitable. We find that, depending on rates of infection and the size of the ongoing epidemic, focusing control on the high value region is often optimal. However, priority should sometimes switch from the buffer region to the high value region only as the local outbreak grows. We characterise how the timing of any switch depends on epidemiological and logistic parameters, and test robustness to systematic misspecification of these factors due to imperfect prior knowledge.
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