Analyzing the Competition of HIV-1 Phenotypes with Quantum Game Theory

Year 2022, Volume: 35 Issue: 3, 1190 - 1198, 01.09.2022

Bilge Özlüer Başer

https://doi.org/10.35378/gujs.772616

Abstract

HIV-1 (Human Immunodeficiency Virus) is a virus that causes AIDS (Acquired Immunodeficiency Syndrome), which damages the immune system by reducing people's resistance to infections and diseases. Antiretroviral treatment methods are based on drug designs developed using inhibitors that suppress the dynamics that enable the maturation of the virus. However, studies are needed to improve treatment methods against infection because HIV-1 is frequently mutated and mutant viruses develop resistance to the treatment used. Therefore, it is important to model the evolutionary development of the virus. For this purpose, the developmental process and spread of HIV-1 are modeled as a game with the players of phenotypes in this study. The related searches known to be made so far have been carried out based on the rules of classical physics. However, games of survival are being played on the molecular level, where the rules of quantum mechanics work. Since the HIV-1 game is being played on the molecular level, the behaviors of the virus phenotypes are examined from the perspective of quantum computation.

Keywords

Quantum game theory, Evolutionary game theory, HIV-1 phenotypes

References

• [1] Castiglione, F., Pappalardo, F., Bernasch, M. and Motta, S., “Optimization of haart with genetic algorithms and agent-based models of hiv infection”, Bioinformatics, 23(24): 3350-3355, (2007).
• [2] Harada, K., “Self-destruction Dynamics of HIV-1 Quasi-species Population in the Presence of Mutagenic Activities”, Procedia Computer Science, 22: 1259-1265, (2013).
• [3] Goshu, A.T. and Dessie, Z.G., “Modelling Progression of HIV/AIDS Disease Stages Using Semi-Markov Processes”, Journal of Data Science, 11: 269-280, (2013).
• [4] Wu, Y., Zhang, M., Wu, J., Zhao, X. and Xia, L., “Evolutionary game theoretic strategy for optimal drug delivery to influence selection pressure in treatment of HIV-1”, Journal of Mathematical Biology, 3(64): 495-512, (2012).
• [5] Khazaei, B., Sartakhti, J.S., Manshaei, M.H., Zhu, Q., Sadeghi, M. and Mousavi, S.R., “HIV-1 infected T-cells dynamics and prognosis: An evolutionary game theory model”, Computer Methods and Programs in Biomedicine, 152: 1-14, (2017).
• [6] Fisher, R. A., The Genetical Theory of Natural Selection, 1st ed., Oxford Clarendon Press, Oxford, (1930).
• [7] Hidalgo, E.G., “Quantum Games and the Relationships between Quantum Mechanics and Game Theory”, arXiv:0803.0292v2 [quant-ph], (2016).
• [8] Smith, J.M., Evolution and the Theory of Games, 1st ed., Cambridge University Press, Oxford, (1982).
• [9] https://oyc.yale.edu/sites/default/files/ess_handout_0_0.pdf. Access date: 05.12.2018.
• [10] Smith, J.M., On Evolution, 1st ed., Edinburgh University Press, Edinburgh, (1972).
• [11] Smith, J.M. and Price, G.R., “The Logic of Animal Conflict”, Nature, 246: 15-18, (1973).
• [12] Eisert, J., Wilkens, M. and Lewenstein, M., “Quantum Games and Quantum Strategies”, Physical Review Letters, 83(15): 3077-3080, (1999).
• [13] Dawkins, R., The Selfish Gene, 4th ed., Oxford University Press, Oxford, (2016).
• [14] Dahl, G.B. and Landsburg S.E., “Quantum Strategies”, arXiv:1110.4678v1 [math.OC], (2011).
• [15] Blaquiere, A., “Wave Mechanics as a Two-Player Game”, Dynamical Systems and Microphysics, 33-69, (1980).
• [16] Meyer, D.A., “Quantum Strategies”, Physical Review Letters, 82: 1052-1055, (1999).
• [17] http://hamilton.uchicago.edu/~sethi/Teaching/P243-W2020/final-papers/price.pdf. Access date: 14.07.2021.
• [18] Marinatto, L. and Weber, T., “A Quantum Approach to Static Games of Complete Information”, Physics Letters, A 272: 291-303, (2000).
• [19] Du, J., Li, H., Xu, X., Shi, M., Wu, J., Zhou, X. and Han, R., “Experimental Realization of Quantum Games on a Quantum Computer”, Physical Review Letters, 88, 137902, (2002).
• [20] Iqbal, A. and Toor, A.H., “Evolutionarily Stable Strategies in Quantum Games”, Physics Letters, A 280/5-6: 249-256, (2001).
• [21] Iqbal, A. and Toor, A.H, “Equilibria of Replicator Dynamics in Quantum Games”, quant-ph/0106135v2, (2004).
• [22] Grabbe, J.O., “An Introduction to Quantum Game Theory”, arXiv:quant-ph/0506219v1, (2005).
• [23] Flitney, A.P., Game Theory: Strategies, Equilibria and Theorems, 1st ed., Haugen I.N. and Nielsen A.S., Nova Science Publishers, New York, 1-40, (2009).