scholarly journals On the design of treatment schedules that avoid chemotherapeutic resistance

2018 ◽  
Author(s):  
Y. Ma ◽  
P.K. Newton
Keyword(s):  
Cell Population ◽  
Evolutionary Game ◽  
Maximum Tolerated Dose ◽  
Payoff Matrix ◽  
Theory Model ◽  
Release Mechanism ◽  
Trajectory Design ◽  
Chemotherapeutic Resistance ◽  
Competitive Release ◽  
Resistant Cells

We introduce a method of designing treatment schedules for a model three-component replicator dynamical system that avoids chemotherapeutic resistance by controlling and managing the competitive release of resistant cells in the tumor. We use an evolutionary game theory model with prisoner’s dilemma payoff matrix that governs the competition among healthy cells, chemo-sensitive cells, and chemo-resistant cells and the goal is to control the evolution of chemo-resistance via the competitive release mechanism. The method is based on nonlinear trajectory design and energy transfer methods first introduced in the orbital mechanics literature for Hamiltonian systems. By using the structure of the trajectories defined by solutions of the replicator system for different constant chemotherapeutic concentrations (which produces a curvilinear coordinate system spanning the full region), we construct periodic (closed) orbits by switching the chemo-dose at carefully chosen times and appropriate levels to design schedules that are superior to both maximum tolerated dose (MTD) schedules and low-dose metronomic (LDM) schedules, both of which ultimately lead to fixation of either sensitive cells or resistant cells. By keeping the three sub-populations of cells in competition with each other, neither the sensitive cell population nor the resitant cell population are able to dominate as we balance the populations indefinitely (closed periodic orbits), thereby avoiding fixation of the cancer cell population and re-growth of a resistant tumor. The schedules we design have the feature that they maintain a higher average population fitness than either the MTD or the LDM schedules.PACS numbers: 87.23.Kg; 87.55.de; 87.19.Xj; 87.19.lr

scholarly journals Nonlinear dynamics of chemotherapeutic resistance

2018 ◽  
Author(s):  
Y. Ma ◽  
P.K. Newton
Keyword(s):  
Evolutionary Game ◽  
Payoff Matrix ◽  
Phase Portraits ◽  
Chemotherapeutic Resistance ◽  
Continuous Therapy ◽  
Fitness Functions ◽  
Competitive Release ◽  
Basin Boundaries ◽  
Sensitive Population ◽  
Average Fitness

We use a three-component replicator dynamical system with healthy cells, sensitive cells, and resistant cells, with a prisoner’s dilemma payoff matrix from evolutionary game theory to understand the phenomenon of competitive release, which is the main mechanism by which tumors develop chemotherapeutic resistance. By comparing the phase portraits of the system without therapy compared to continuous therapy above a certain threshold, we show that chemotherapeutic resistance develops if there are pre-exisiting resistance cells in the population. We examine the basin boundaries of attraction associated with the chemo-sensitive population and the chemo-resistant population for increasing values of chemo-concentrations and show their spiral intertwined structure. We also examine the fitness landscapes both with and without continuous therapy and show that with therapy, the average fitness as well as the fitness functions of each of the subpopulations initially increases, but eventually decreases monotonically as the resistant subpopulation saturates the tumor.

scholarly journals Optimizing chemo-scheduling based on tumor growth rates

2018 ◽  
Author(s):  
Jeffrey West ◽  
Paul Newton
Keyword(s):  
Tumor Growth ◽  
Low Dose ◽  
Cell Kinetics ◽  
Evolutionary Game ◽  
Maximum Tolerated Dose ◽  
General Concept ◽  
Theory Model ◽  
Moran Process ◽  
Evolutionary Features ◽  
Gompertzian Growth

AbstractWe review the classic tumor growth and regression laws of Skipper and Schable based on fixed exponential growth assumptions, and Norton and Simon’s law based on a Gompertzian growth assumption. We then discuss ways to optimize chemotherapeutic scheduling using a Moran process evolutionary game-theory model of tumor growth that incorporates more general dynamical and evolutionary features of tumor cell kinetics. Using this model, and employing the quantitative notion of Shannon entropy which assigns high values to low-dose metronomic (LDM) therapies, and low values to maximum tolerated dose (MTD) therapies, we show that low-dose metronomic strategies can outperform maximum tolerated dose strategies, particularly for faster growing tumors. The general concept of designing different chemotherapeutic strategies for tumors with different growth characteristics is discussed.

scholarly journals The role of synergy and antagonism in designing multidrug adaptive chemotherapy schedules

2020 ◽  
Author(s):  
P.K. Newton ◽  
Y. Ma
Keyword(s):  
Tumor Cell ◽  
Drug Interactions ◽  
Cell Population ◽  
Tumor Recurrence ◽  
Fitness Landscape ◽  
Evolutionary Game ◽  
Cell Populations ◽  
Sensitive Cell ◽  
Stable States ◽  
Competitive Release

Chemotherapeutic resistance via the mechanism of competitive release of resistant tumor cell subpopulations is a major problem associated with cancer treatments and one of the main causes of tumor recurrence. Often, chemoresistance is mitigated by using multidrug schedules (two or more combination therapies) that can act synergistically, additively, or antagonistically on the heterogeneous population of cells as they evolve. In this paper, we develop a three-component evolutionary game theory model to design two-drug adaptive schedules (timing and dose levels associated with C1(t) and C2(t)) that mitigate chemoresistance and delay tumor recurrence in an evolving collection of tumor cells with two resistant subpopulations: R1 (sensitive to drug 1, resistant to drug 2), and R2 (sensitive to drug 2, resistant to drug 1). A key parameter, e, takes us from synergistic (e > 0), to additive (e = 0), to antagonistic (e < 0) drug interactions. In addition to the two resistant populations, the model includes a population of chemosensitive cells, S that have higher baseline fitness but are not resistant to either drug. Using the nonlinear replicator dynamical system with a payoff matrix of Prisoner’s Dilemma (PD) type (enforcing a cost to resistance), we investigate the nonlinear dynamics of the three-component system (S, R1, R2), along with an additional tumor growth model whose growth rate is a function of the fitness landscape of the tumor cell populations. We show that antagonistic drug interactions generally result in slower rates of adaptation of the resistant cells than synergistic ones, making them more effective in combating the evolution of resistance. We then design closed loops in the three-component phase space by shaping the fitness landscape of the cell populations (i.e. altering the evolutionary stable states of the game) using appropriately designed time-dependent schedules (adaptive therapy), altering the dosages and timing of the two drugs using information gleaned from constant dosing schedules. We show that the bifurcations associated with the evolutionary stable states are transcritical, and we detail a typical antagonistic bifurcation that takes place between the sensitive cell population S and the R1 population, and a synergistic bifurcation that takes place between the sensitive cell population S and the R2 population for fixed values of C1 and C2. These bifurcations help us further understand why antagonistic interactions are more effective at controlling competitive release of the resistant population than synergistic interactions in the context of an evolving tumor.

scholarly journals IsoMaTrix: a framework to visualize the isoclines of matrix games and quantify uncertainty in structured populations

2020 ◽  
Author(s):  
Jeffrey West ◽  
Yongqian Ma ◽  
Artem Kaznatcheev ◽  
Alexander R A Anderson
Keyword(s):  
Spatial Configuration ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Structured Populations ◽  
Continuous Treatment ◽  
Supplementary Information ◽  
Matrix Games ◽  
Spatial Games ◽  
Competitive Release ◽  
Zero Growth

Abstract   Evolutionary game theory describes frequency-dependent selection for fixed, heritable strategies in a population of competing individuals using a payoff matrix. We present a software package to aid in the construction, analysis, and visualization of three-strategy matrix games. The IsoMaTrix package computes the isoclines (lines of zero growth) of matrix games, and facilitates direct comparison of well-mixed dynamics to structured populations on a lattice grid. IsoMaTrix computes fixed points, phase flow, trajectories, (sub)velocities, and uncertainty quantification for stochastic effects in spatial matrix games. We describe a result obtained via IsoMaTrix’s spatial games functionality, which shows that the timing of competitive release in a cancer model (under continuous treatment) critically depends on the initial spatial configuration of the tumor. Availability The code is available at: https://github.com/mathonco/isomatrix. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals A Study of Taxi Service Mode Choice Based on Evolutionary Game Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Zhu Bai ◽  
Mingxia Huang ◽  
Shuai Bian ◽  
Huandong Wu
Keyword(s):  
Game Theory ◽  
Evolutionary Game Theory ◽  
Mode Choice ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Game Model ◽  
Stable States ◽  
Taxi Service ◽  
Service Mode ◽  
The Impact

The emergence of online car-hailing service provides an innovative approach to vehicle booking but has negatively influenced the taxi industry in China. This paper modeled taxi service mode choice based on evolutionary game theory (EGT). The modes included the dispatching and online car-hailing modes. We constructed an EGT framework, including determining the strategies and the payoff matrix. We introduced different behaviors, including taxi company management, driver operation, and passenger choice. This allowed us to model the impact of these behaviors on the evolving process of service mode choice. The results show that adjustments in taxi company, driver, and passenger behaviors impact the evolutionary path and convergence speed of our evolutionary game model. However, it also reveals that, regardless of adjustments, the stable states in the game model remain unchanged. The conclusion provides a basis for studying taxi system operation and management.

An Analysis of Quality Liability Insurance for Prefabricated Components Using Evolutionary Game Theory

2021 ◽  
Author(s):  
Yan Liu ◽  
Chenyao Lv ◽  
Hong Xian Li ◽  
Yan Li ◽  
Zhen Lei ◽  
...  
Keyword(s):  
Game Theory ◽  
Evolutionary Game Theory ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Liability Insurance ◽  
Insurance Companies ◽  
Social Benefits ◽  
Simulation Calculation ◽  
The Government

Managing quality risks of prefabricated components is one of the challenges for prefabricated construction. The Quality Liability Insurance for Prefabricated Components (QLIPC) is an effective approach to transfer such risks; however, limited research has been conducted regarding the development of QLIPC. This study introduces an Evolutionary Game Theory (EGT)-based approach incorporating decisions from both the government and insurance companies. In the EGT model, a payoff matrix under disparate strategies is constructed, and the evolutionary stable strategies (ESS) are deduced. The simulation calculation is then carried out by MATLAB using sample virtual data to demonstrate the analysis. The results show that the government should act as the game promoter because the QLIPC can reduce governance cost and has significant social benefits. This research contributes a theoretical framework to analyze the QLIPC development using the EGT theory, and it could help the government to make long-term strategies for developing the QLIPC market.

Exponential Families and Game Dynamics

1982 ◽  
Vol 34 (2) ◽  
pp. 374-405 ◽  
Author(s):  
Ethan Akin
Keyword(s):  
Game Theory ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Exponential Families ◽  
Von Neumann ◽  
Rational Player ◽  
Large Populations ◽  
Pure Strategies ◽  
Classical Game ◽  
Classical Game Theory

A symmetric game consists of a set of pure strategies indexed by {0, …, n} and a real payoff matrix (aij). When two players choose strategies i and j the payoffs are aij and aji to the i-player and j-player respectively. In classical game theory of Von Neumann and Morgenstern [16] the payoffs are measured in units of utility, i.e., desirability, or in units of some desirable good, e.g. money. The problem of game theory is that of a rational player who seeks to choose a strategy or mixture of strategies which will maximize his return. In evolutionary game theory of Maynard Smith and Price [13] we look at large populations of game players. Each player's opponents are selected randomly from the population, and no information about the opponent is available to the player. For each one the choice of strategy is a fixed inherited characteristic.

scholarly journals Explore Knowledge-Sharing Strategy and Evolutionary Mechanism for Integrated Project Team Based on Evolutionary Game Model

2019 ◽  
Vol 2019 ◽  
pp. 1-23
Author(s):  
Yanchao Du ◽  
Hengyu Zhou ◽  
Yongbo Yuan ◽  
Xiaoxue Liu
Keyword(s):  
Knowledge Sharing ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Evolutionary Mechanism ◽  
Interaction Behavior ◽  
Sharing Strategy ◽  
Overall Performance ◽  
Integrated Project ◽  
Cost Efficient ◽  
Knowledge Absorption

Integrated Project Delivery (IPD) has become increasingly popular in the architecture, engineering, and construction industries. However, the current practice status by the construction industry fails to deliver the desired results. In that backdrop, how to promote cooperation within and improve the overall performance of integrated project team has received wide attention. Herein, knowledge-sharing plays a critical role in cooperation and overall performance. However, to the best of our knowledge, the research on knowledge-sharing strategy interaction and evolutionary mechanism is rare. To make up for the deficiency of the studies existing, a novel model is proposed by taking advantage of evolutionary game theory, to capture the interaction behavior of knowledge-sharing and explore its evolutionary mechanism. Six parameters of knowledge stock, knowledge-sharing degree, heterogeneous knowledge proportion, synergy effect, knowledge absorption coefficient, and knowledge-sharing cost efficient that are critical to knowledge-sharing are extracted and defined. The payoff matrix is constructed by analyzing the benefits and costs of knowledge-sharing. Then, a replicator dynamic system is established based on payoff matrix, to determine the evolutionary tendency of knowledge-sharing behavior. Finally, numerical simulations are conducted to explore the influences of all parameters on the knowledge-sharing strategy. The findings in this research reveal that strategy interaction behavior is significantly influenced by proportion of strategy of choosing to share knowledge in both game players. The authors also find that strategy interaction behavior has a strong negative correlation with knowledge-sharing cost efficient, but has a positive correlation with knowledge stock, heterogeneous knowledge proportion, degree of knowledge-sharing, knowledge absorption coefficient, and synergetic effect coefficient. This research can provide the evolutionary mechanism and broaden our understanding of relationship between project performance and knowledge-sharing and can offer valuable guidance on improving cooperation and performance of project teams.

scholarly journals The Trilateral Evolutionary Game of Agri-Food Quality in Farmer-Supermarket Direct Purchase: A Simulation Approach

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xin Su ◽  
Haolong Liu ◽  
Shunqi Hou
Keyword(s):  
Quality Assurance ◽  
Food Quality ◽  
Evolutionary Game ◽  
Quality Standards ◽  
Payoff Matrix ◽  
Legal Rights ◽  
Evolutionary System ◽  
Key Factors ◽  
Stable States ◽  
High Quality

The prevalence of opportunistic behaviors in agri-food production and circulation results in frequent quality accidents in emerging economies. Numerous researches have discussed effective countermeasures to this problem, but few of them focus on the effectiveness and stability of quality assurance systems. Owing to the bounded rationality and information asymmetry, the dynamic quality game among producers, marketers, and consumers has significant characteristics of complexity. This paper aims at discussing the farmer-supermarket direct purchase’s contributions to ensure the agri-food quality and analyzing the effectiveness, stability, and key factors of this new industrial organization. Based on the evolutionary game theory, we establish the trilateral-game payoff matrix, build up the replicator dynamic equations, and discuss possible evolutionary stable states. The simulation results show that the evolutionary system converges to desired stability faster, when the high-quality agri-food’s market premium increases and the penalty for violating quality standards increases. Furthermore, when farmers share more high-quality agri-food’s market premiums and marketers compensate more for violating the quality standards than before, the evolutionary system also converges to desired stability faster. Therefore, the quality information tracing technology, farmers and marketers’ fair distribution of profits and risks, and consumers’ capabilities to safeguard their legal rights are the three key factors to maintain the effectiveness and stability of quality assurance systems.

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