scholarly journals Ongoing surveillance protects tanoak whilst conserving biodiversity: applying optimal control theory to a spatial simulation model of sudden oak death

2019 ◽  
Author(s):  
E.H. Bussell ◽  
N.J. Cunniffe
Keyword(s):  
Optimal Control ◽  
Disease Management ◽  
Control Theory ◽  
Predictive Control ◽  
Optimal Control Theory ◽  
Control Strategies ◽  
Management Strategies ◽  
Simulation Models ◽  
Sudden Oak Death ◽  
Ongoing Surveillance

AbstractThe sudden oak death epidemic in California is spreading uncontrollably. Large-scale eradication has been impossible for some time. However, small-scale disease management could still slow disease spread. Although empirical evidence suggests localised control could potentially be successful, mathematical models have said little about such management. By approximating a detailed, spatially-explicit simulation model of sudden oak death with a simpler, mathematically-tractable model, we demonstrate how optimal control theory can be used to unambiguously characterise effective time-dependent disease management strategies. We focus on protection of tanoak, a tree species which is culturally and ecologically important, but also highly susceptible to sudden oak death. We identify management strategies to protect tanoak in a newly-invaded forest stand, whilst also conserving biodiversity. We find that thinning of bay laurel is essential early in the epidemic. We apply model predictive control, a feedback strategy in which both the approximating model and the control are repeatedly updated as the epidemic progresses. Adapting optimal control strategies in this way is vital for effective disease management. This feedback strategy is robust to parameter uncertainty, limiting loss of tanoak in the worst-case scenarios. However, the methodology requires ongoing surveillance to re-optimise the approximating model. This introduces an optimal level of surveillance to balance the high costs of intensive surveys against improved management resulting from better estimates of disease progress. Our study shows how detailed simulation models can be coupled with optimal control theory and model predictive control to find effective control strategies for sudden oak death. We demonstrate that control strategies for sudden oak death must depend on local management goals, and that success relies on adaptive strategies that are updated via ongoing disease surveillance. The broad framework allowing the use of optimal control theory on complex simulation models is applicable to a wide range of systems.

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

2018 ◽  
Author(s):  
E.H. Bussell ◽  
C.E. Dangerfield ◽  
C.A. Gilligan ◽  
N.J. Cunniffe
Keyword(s):  
Optimal Control ◽  
Disease Management ◽  
Control Theory ◽  
Simulation Model ◽  
Optimal Control Theory ◽  
Management Strategies ◽  
Simulation Models ◽  
Open Loop ◽  
Small Subset ◽  
Control Disease

SummaryMathematical 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 very 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 plants, animals and humans.

scholarly journals Applying optimal control theory to a spatial simulation model of sudden oak death: ongoing surveillance protects tanoak while conserving biodiversity

2020 ◽  
Vol 17 (165) ◽  
pp. 20190671 ◽  
Author(s):  
E. H. Bussell ◽  
N. J. Cunniffe
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Simulation Model ◽  
Optimal Control Theory ◽  
Disease Surveillance ◽  
Management Strategies ◽  
Sudden Oak Death ◽  
Disease Spread ◽  
Important Species ◽  
Ongoing Surveillance

Sudden oak death has devastated tree populations across California. However, management might still slow disease spread at local scales. We demonstrate how to unambiguously characterize effective, local management strategies using a detailed, spatially explicit simulation model of spread in a single forest stand. This pre-existing, parameterized simulation is approximated here by a carefully calibrated, non-spatial model, explicitly constructed to be sufficiently simple to allow optimal control theory (OCT) to be applied. By lifting management strategies from the approximate model to the detailed simulation, effective time-dependent controls can be identified. These protect tanoak—a culturally and ecologically important species—while conserving forest biodiversity within a limited budget. We also consider model predictive control, in which both the approximating model and optimal control are repeatedly updated as the epidemic progresses. This allows management which is robust to both parameter uncertainty and systematic differences between simulation and approximate models. Including the costs of disease surveillance then introduces an optimal intensity of surveillance. Our study demonstrates that successful control of sudden oak death is likely to rely on adaptive strategies updated via ongoing surveillance. More broadly, it illustrates how OCT can inform effective real-world management, even when underpinning disease spread models are highly complex.

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

2019 ◽  
Vol 374 (1776) ◽  
pp. 20180284 ◽  
Author(s):  
E. H. Bussell ◽  
C. E. Dangerfield ◽  
C. A. Gilligan ◽  
N. J. Cunniffe
Keyword(s):  
Infectious Disease ◽  
Optimal Control ◽  
Disease Management ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Management Strategies ◽  
Disease Outbreaks ◽  
Theme Issue ◽  
Infectious Disease Outbreaks ◽  
And Control

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’.

Intelligent energy management for hybrid fuel cell/battery system

2016 ◽  
Vol 35 (5) ◽  
pp. 1850-1864 ◽  
Author(s):  
Moussa Boukhnifer ◽  
Nadir Ouddah ◽  
Toufik Azib ◽  
Ahmed Chaibet
Keyword(s):  
Optimal Control ◽  
Fuel Cell ◽  
Control Theory ◽  
Energy Management ◽  
Optimal Control Theory ◽  
Hybrid Electric Vehicle ◽  
Minimum Principle ◽  
Management Strategies ◽  
Hybrid Architecture ◽  
Content Type

Purpose The purpose of this paper is to propose two energy management strategies (EMS) for hybrid electric vehicle, the power system is an hybrid architecture (fuel cell (FC)/battery) with two-converters parallel configuration. Design/methodology/approach First, the authors present the EMS uses a power frequency splitting to allow a natural frequency decomposition of the power loads and second the EMS uses the optimal control theory, based on the Pontryagin’s minimum principle. Findings Thanks to the optimal approach, the control objectives will be easily achieved: hydrogen consumption is minimized and FC health is protected. Originality/value The simulation results show the effectiveness of the control strategy using optimal control theory in term of improvement of the fuel consumption based on a comparison analysis between the two strategies.

scholarly journals Application of Optimal Control Theory to Newcastle Disease Dynamics in Village Chicken by Considering Wild Birds as Reservoir of Disease Virus

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Furaha Chuma ◽  
Gasper Godson Mwanga ◽  
Verdiana Grace Masanja
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Disease Virus ◽  
Newcastle Disease ◽  
Optimal Control Theory ◽  
Control Strategies ◽  
Wild Birds ◽  
Village Chicken ◽  
Environmental Hygiene ◽  
The Village

In this study, an optimal control theory was applied to a nonautonomous model for Newcastle disease transmission in the village chicken population. A notable feature of this model is the inclusion of environment contamination and wild birds, which act as reservoirs of the disease virus. Vaccination, culling, and environmental hygiene and sanitation time dependent control strategies were adopted in the proposed model. This study proved the existence of an optimal control solution, and the necessary conditions for optimality were determined using Pontryagin’s Maximum Principle. The numerical simulations of the optimal control problem were performed using the forward–backward sweep method. The results showed that the use of only the environmental hygiene and sanitation control strategy has no significant effect on the transmission dynamics of the Newcastle disease. Additionally, the combination of vaccination and environmental hygiene and sanitation strategies reduces more number of infected chickens and the concentration of the Newcastle disease virus in the environment than any other combination of control strategies. Furthermore, a cost-effective analysis was performed using the incremental cost-effectiveness ratio method, and the results showed that the use of vaccination alone as the control measure is less costly compared to other control strategies. Hence, the most effective way to minimize the transmission rate of the Newcastle disease and the operational costs is concluded to be the timely vaccination of the entire population of the village chicken, improvement in the sanitation of facilities, and the maintenance of a hygienically clean environment.

Multiscale Regularization of Flooding Optimization for Smart Field Management

SPE Journal ◽  
2008 ◽  
Vol 13 (02) ◽  
pp. 195-204 ◽  
Author(s):  
Martha E. Lien ◽  
D. Roald Brouwer ◽  
Trond Mannseth ◽  
Jan-Dirk Jansen
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Objective Function ◽  
Optimal Control Theory ◽  
Degrees Of Freedom ◽  
Management Strategies ◽  
Multiscale Methods ◽  
Regularization Methods ◽  
Production Rates ◽  
Numerical Examples

Summary Smart fields can provide enhanced oil recovery through the combined use of optimization and data assimilation. In this paper, we focus on the dynamic optimization of injection and production rates during waterflooding. In particular, we use optimal control theory in order to find an optimal well management strategy over the life of the reservoir that maximizes an objective function (e.g., recovery or net present value). Optimal control requires the determination of a potentially large number of (groups of) well rates for a potentially large number of time periods. However, the optimal number of well groups and time steps is not known a priori. Moreover, taking these numbers too large can slow down the optimization process and increase the chance of achieving a suboptimal solution. We investigate the use of multiscale regularization methods to achieve grouping of the control settings of the wells in both space and time. Starting out with a very coarse grouping, the resolution is subsequently refined during the optimization. The regularization is adaptive in that the multiscale parameterization is chosen based on the gradients of the objective function. Results for the numerical examples studied indicate that the regularization may lead to significantly simpler optimum strategies, while resulting in a better or similar cumulative oil production. Introduction We consider the secondary recovery phase of a heterogeneous oil reservoir, where water is injected into the reservoir for pressure maintenance and sweep improvement. In a smart field scenario, we consider injectors and producers with both single and multiple completions. The flow rates of the different well completions can be adjusted individually. In the following, an individual well completion will be referred to as "well segment." This implies that in case of conventional single-completion wells the term "well segment" is therefore equivalent to "well." Ideally, the injected water will displace the remaining oil in the reservoir on its way from the injection wells to the production wells. Rock heterogeneities will, however, influence the path of the injected water. The water will mainly flow in the high-permeability channels, which causes only part of the oil to be produced. Recently, smart field concepts have been proposed as a means to improve control over the waterfront through detailed adjustments of the injection and production rates in time using a combination of model-based flooding optimization and model updating (Brouwer et al. 2004; Sarma et al. 2005b). For the optimization part, these "closed-loop" reservoir management strategies rely on optimal control theory, which has been proposed before as a flooding optimization method by various authors (Asheim 1988; Virnovski 1991; Sudaryanto 1998; Brouwer et al. 2004; Sarma et al. 2005a). However, optimization by means of optimal control theory is computationally expensive, and detailed management of every individual well segment of a smart field at every moment in time is economically and technically demanding. Moreover, there may not be enough information in the system to determine the optimal production strategy uniquely. Hence, we seek to develop management strategies with a restricted number of degrees of freedom, which at the same time maintain the advantages of the smart field technology. In this paper, multiscale estimation techniques are utilized to attempt to find the optimal well management level. These are hierarchical regularization methods where the number of degrees of freedom in the estimation is gradually increased as the optimization proceeds. Multiscale methods were first applied for solving partial differential equations to speed up convergence (Brandt 1977; Briggs 1987). Later, through the development of wavelets, multiscale approaches have also been widely used within inverse problems (Emsellem and de Marsily 1971; Chavent and Liu 1989; Liu 1993; Yoon et al. 2001). The outline of the paper is as follows: First, the theory behind the solution of the problem in terms of optimal control and gradient-based optimization is presented. Thereafter we present methods to regularize the optimization problem in terms of multiscale reparameterization of the control variable. Finally, the performance of the proposed regularization strategies is illustrated through a line of numerical examples before we summarize and conclude.

scholarly journals Optimal Control Analysis of Cholera Dynamics in the Presence of Asymptotic Transmission

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 60
Author(s):  
Emmanuel A. Bakare ◽  
Sarka Hoskova-Mayerova
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Mathematical Models ◽  
Optimal Control Theory ◽  
Numerical Experiments ◽  
Control Strategies ◽  
Optimal Strategies ◽  
Control Analysis ◽  
Multiple Control ◽  
Mortality And Morbidity

Many mathematical models have explored the dynamics of cholera but none have been used to predict the optimal strategies of the three control interventions (the use of hygiene promotion and social mobilization; the use of treatment by drug/oral re-hydration solution; and the use of safe water, hygiene, and sanitation). The goal here is to develop (deterministic and stochastic) mathematical models of cholera transmission and control dynamics, with the aim of investigating the effect of the three control interventions against cholera transmission in order to find optimal control strategies. The reproduction number Rp was obtained through the next generation matrix method and sensitivity and elasticity analysis were performed. The global stability of the equilibrium was obtained using the Lyapunov functional. Optimal control theory was applied to investigate the optimal control strategies for controlling the spread of cholera using the combination of control interventions. The Pontryagin’s maximum principle was used to characterize the optimal levels of combined control interventions. The models were validated using numerical experiments and sensitivity analysis was done. Optimal control theory showed that the combinations of the control intervention influenced disease progression. The characterisation of the optimal levels of the multiple control interventions showed the means for minimizing cholera transmission, mortality, and morbidity in finite time. The numerical experiments showed that there are fluctuations and noise due to its dependence on the corresponding population size and that the optimal control strategies to effectively control cholera transmission, mortality, and morbidity was through the combinations of all three control interventions. The developed models achieved the reduction, control, and/or elimination of cholera through incorporating multiple control interventions.

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