Chaos synchronization and Nelder-Mead search for parameter estimation in nonlinear pharmacological systems: Estimating tumor antigenicity in a model of immunotherapy

Pillai, Nikhil; Craig, Morgan; Dokoumetzidis, Aristides; Schwartz, Sorell L.; Bies, Robert R.; Freedman, I.

doi:10.1016/j.pbiomolbio.2018.06.006

Cited by 7 publications

(4 citation statements)

References 23 publications

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“…Then in [ 45 ] the effects of control parameters on chaos synchronization by optical feedback is presented. Finally, other interesting papers are shown in [ 46 , 47 ], where the synchronization of an uncertain fractional order chaotic system is presented and the chaos synchronization of nonlinear pharmacological system is presented, respectively.…”

Section: Related Workmentioning

confidence: 99%

Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique

Muñoz‐Pacheco

Volos

Serrano

et al. 2021

Entropy

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In this paper, the stabilization and synchronization of a complex hidden chaotic attractor is shown. This article begins with the dynamic analysis of a complex Lorenz chaotic system considering the vector field properties of the analyzed system in the Cn domain. Then, considering first the original domain of attraction of the complex Lorenz chaotic system in the equilibrium point, by using the required set topology of this domain of attraction, one hidden chaotic attractor is found by finding the intersection of two sets in which two of the parameters, r and b, can be varied in order to find hidden chaotic attractors. Then, a backstepping controller is derived by selecting extra state variables and establishing the required Lyapunov functionals in a recursive methodology. For the control synchronization law, a similar procedure is implemented, but this time, taking into consideration the error variable which comprise the difference of the response system and drive system, to synchronize the response system with the original drive system which is the original complex Lorenz system.

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Section: Related Workmentioning

confidence: 99%

Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique

Muñoz‐Pacheco

Volos

Serrano

et al. 2021

Entropy

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“…Nelder Mead (NM) search is a "direct search" (i.e., derivative-free) optimization algorithm originally designed for finding locally optimal solutions to deterministic, unconstrained problems 22 . NM search has also been used for parameter estimation/calibration for simulations, e.g., 23,24 .…”

Section: 4)mentioning

confidence: 99%

“…21 § Even mathematical models that include a seasonality component do so in an "arbitrary" fashion, that is, without specific environmental data. Environment-driven seasonality has been found to be critical to many diseases, including influenza, 22 malaria, 23 and cholera. 24 We hypothesize that GW transmission is driven in large part by environmental patterns, which directly or indirectly affects the behaviors of humans and dogs as well as the life cycle or availability of the parasite or other .…”

Section: Introductionmentioning

confidence: 99%

Agent-Based Simulation for Seasonal Guinea Worm Disease in Chad Dogs

Perini

Keskinocak

et al. 2020

The American Journal of Tropical Medicine and Hygiene

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The campaign to eradicate dracunculiasis (Guinea worm [GW] disease) and its causative pathogen Dracunculus medinensis (GW) in Chad is challenged by infections in domestic dogs, which far outnumber the dwindling number of human infections. We present an agent-based simulation that models transmission of GW between a shared water source and a large population of dogs. The simulation incorporates various potential factors driving the infections including external factors and two currently used interventions, namely, tethering and larvicide water treatments. By defining and estimating infectivity parameters and seasonality factors, we test the simulation model on scenarios where seasonal patterns of dog infections could be driven by the parasite's life cycle alone or with environmental factors (e.g., temperature and rainfall) that could also affect human or dog behaviors (e.g., fishing versus farming seasons). We show that the best-fitting model includes external factors in addition to the pathogen's life cycle. From the simulation, we estimate that the basic reproductive number, R 0 , is approximately 2.0; our results also show that an infected dog can transmit the infection to 3.6 other dogs, on average, during the month of peak infectivity (April). The simulation results shed light on the transmission dynamics of GWs to dogs and lay the groundwork for reducing the number of infections and eventually interrupting transmission of GW.

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“…Since classical methods have low accuracy and are computationally expensive, one can look for methods which are robust and can overcome these issues. Controlled chaos synchronization is one approach that may be appropriate to address these problems [ 13 ].…”

Section: Introductionmentioning

confidence: 99%

Estimating parameters of nonlinear dynamic systems in pharmacology using chaos synchronization and grid search

Pillai

Schwartz

et al. 2019

J Pharmacokinet Pharmacodyn

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Bridging fundamental approaches to model optimization for pharmacometricians, systems pharmacologists and statisticians is a critical issue. These fields rely primarily on Maximum Likelihood and Extended Least Squares metrics with iterative estimation of parameters. Our research combines adaptive chaos synchronization and grid search to estimate physiological and pharmacological systems with emergent properties by exploring deterministic methods that are more appropriate and have potentially superior performance than classical numerical approaches, which minimize the sum of squares or maximize the likelihood. We illustrate these issues with an established model of cortisol in human with nonlinear dynamics. The model describes cortisol kinetics over time, including its chaotic oscillations, by a delay differential equation. We demonstrate that chaos synchronization helps to avoid the tendency of the gradient-based optimization algorithms to end up in a local minimum. The subsequent analysis illustrates that the hybrid adaptive chaos synchronization for estimation of linear parameters with coarse-to-fine grid search for optimal values of non-linear parameters can be applied iteratively to accurately estimate parameters and effectively track trajectories for a wide class of noisy chaotic systems. Electronic supplementary material The online version of this article (10.1007/s10928-019-09629-4) contains supplementary material, which is available to authorized users.

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Chaos synchronization and Nelder-Mead search for parameter estimation in nonlinear pharmacological systems: Estimating tumor antigenicity in a model of immunotherapy

Cited by 7 publications

References 23 publications

Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique

Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique

Agent-Based Simulation for Seasonal Guinea Worm Disease in Chad Dogs

Estimating parameters of nonlinear dynamic systems in pharmacology using chaos synchronization and grid search

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