Designing combination therapies using multiple optimal controls

Sharp, John; Browning, Alexander P; Mapder, Tarunendu; Baker, Christopher M.; Burrage, Kevin; Simpson, Matthew J.

doi:10.1016/j.jtbi.2020.110277

Cited by 25 publications

(24 citation statements)

References 81 publications

(106 reference statements)

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“…3, we simulate a persister producing bacteria colony under antibiotic treatment, demonstrating the distinct advantage persisters afford bacteria (10,14,17). Our stochastic model of persister production can be used to improve the efficacy of antimicrobial therapies using optimal control from an optimal treatment perspective (52,(57)(58)(59). Furthermore, recent experimental and mathematical work examines the potential of so-called evolutionarily informed therapy or drug sequencing (53,54,60), where a sequence of drugs is administered to sequentially induce susceptibility and overcome drug resistance.…”

Section: Discussionmentioning

confidence: 99%

Persistence as an optimal hedging strategy

Browning

Sharp

Mapder

et al. 2019

Preprint

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AbstractBacteria invest in a slow-growing subpopulation, called persisters, to ensure survival in the face of uncertainty. This hedging strategy, which we term cellular hedging, is remarkably similar to financial hedging where diversifying an investment portfolio protects against economic uncertainty. We provide a new theoretical foundation for understanding cellular hedging by unifying the study of biological population dynamics and the mathematics of financial risk management. Our approach explicitly incorporates environmental volatility as a stochastic process, and we study the persister strategy that maximises the expected per-capita growth rate by formulating a stochastic optimal control problem. We demonstrate that persistence is only advantageous in the presence of environmental volatility. Analytical and simulation results probe the optimal persister strategy, revealing results that are consistent with experimental observations and suggest new opportunities for experimental investigation. Overall, we provide a new way of conceptualising and modelling cellular decision making by unifying previously disparate theory from mathematical biology and finance.

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Section: Discussionmentioning

confidence: 99%

Persistence as an optimal hedging strategy

Browning

Sharp

Mapder

et al. 2019

Preprint

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“…In this section we briefly review the Pontryagin Maximum Principle approach to such an optimal control problem, and the standard implementation of the FBSM for solving the resulting two-point boundary value problem. The FBSM is readily extended to problems with multiple state variables, multiple controls, state constraints and free end-times [43,49,70,71], however for this overview we restrict ourselves to the single variable, single control, fixed end-time case for clarity.…”

Section: Forward-backward Sweep Methodsmentioning

confidence: 99%

“…We construct the linear model to examine the behaviour of the acceleration techniques as applied to a simple idealised set of control problems. We include the AML model, variations upon which have been considered in the literature [24,70,71], to examine how the acceleration techniques perform when applied to problems more reflective of those considered in applied optimal control. For each model, we consider three distinct control problems; continuous control, bang-bang control and continuous control with fixed endpoint.…”

Section: Control Problemsmentioning

confidence: 99%

“…Here, we have only considered systems subject to a single control. While this is reflective of the vast majority of applications featured in the control literature, there are instances where we are interested in applying multiple controls simultaneously [9,19,71]. The FBSM can be readily applied to solve problems with multiple controls [71]; a logical extension of this work is to adapt the acceleration methods or identify suitable alternative methods for accelerating convergence of the FBSM for problems with multiple controls.…”

Section: Summary and Outlook 823mentioning

confidence: 99%

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Implementation and acceleration of optimal control for systems biology

Sharp

Burrage

Simpson

2021

Preprint

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Optimal control theory provides insight into complex resource allocation decisions. The forward-backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems (TPBVPs) arising from the application of Pontryagin's Maximum Principle (PMP) in optimal control. In this review we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualising the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Further, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021.

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“…The optimality system is solved numerically using forward-backward sweep numerical method [28,31,24]. First, the initial guess of the optimal control is determined.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Optimal vaccination strategy for dengue transmission in Kupang city, Indonesia

Ndii

Mage

Messakh

et al. 2020

Heliyon

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Dengue is a public health problem with around 390 million cases annually and is caused by four distinct serotypes. Infection by one of the serotypes provides lifelong immunity to that serotype but have a higher chance of attracting the more dangerous forms of dengue in subsequent infections. Therefore, a perfect strategy against dengue is required. Dengue vaccine with 42-80% efficacy level has been licensed for the use in reducing disease transmission. However, this may increase the likelihood of obtaining the dangerous forms of dengue. In this paper, we have developed single and two-serotype dengue mathematical models to investigate the effects of vaccination on dengue transmission dynamics. The model is validated against dengue data from Kupang city, Indonesia. We investigate the effects of vaccination on seronegative and seropositive individuals and perform a global sensitivity analysis to determine the most influential parameters of the model. A sensitivity analysis suggests that the vaccination rate, the transmission probability and the biting rate have greater effects on the reduction of the proportion of dengue cases. Interestingly, with vaccine implementation, the mosquito-related parameters do not have significant impact on the reduction in the proportion of dengue cases. If the vaccination is implemented on seronegative individuals only, it may increase the likelihood of obtaining the severe dengue. To reduce the proportion of severe dengue cases, it is better to vaccinate seropositive individuals. In the context of Kupang City where the majority of individuals have been infected by at least one dengue serotype, the implementation of vaccination strategy is possible. However, understanding the serotype-specific differences is required to optimise the delivery of the intervention.

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Designing combination therapies using multiple optimal controls

Cited by 25 publications

References 81 publications

Persistence as an optimal hedging strategy

Persistence as an optimal hedging strategy

Implementation and acceleration of optimal control for systems biology

Optimal vaccination strategy for dengue transmission in Kupang city, Indonesia

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