Analysis and analytical simulation for a biophysical fractional diffusive cancer model with virotherapy using the Caputo operator

Mohammed Alabedalhadi; Mohammed Shqair; Ibrahim Saleh; Mohammed Alabedalhadi; Mohammed Shqair; Ibrahim Saleh

doi:10.3934/biophy.2023028

AIMS Biophysics

2023, Volume 10, Issue 4: 503-522. doi: 10.3934/biophy.2023028

Previous Article Next Article

Research article Special Issues

Analysis and analytical simulation for a biophysical fractional diffusive cancer model with virotherapy using the Caputo operator

1.
Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan
2.
College of Science, Zarqa University, Zarqa, Jordan

Received: 03 August 2023 Revised: 25 September 2023 Accepted: 27 September 2023 Published: 18 December 2023

In this paper, a biophysical fractional diffusive cancer model with virotherapy is thoroughly analyzed and analytically simulated. The goal of this biophysical model is to represent both the dynamics of cancer development and the results of virotherapy, which uses viruses to target and destroy cancer cells. The Caputo sense is applied to the fractional derivatives. We look at the governing model's existence and uniqueness. For analytical solutions, the Laplace residual power series approach is used. The study investigates the model's dynamic behavior, shedding light on the development of cancer and the effects of virotherapy. The research advances our knowledge of cancer modeling and treatment options. Numerical simulations show the agreement between the analytical results and the related numerical solutions, proving the usefulness of the analytical solution.
- cancer model,
- biophysics,
- immune response,
- Caputo fractional derivative,
- Laplace residual power series
Citation: Mohammed Alabedalhadi, Mohammed Shqair, Ibrahim Saleh. Analysis and analytical simulation for a biophysical fractional diffusive cancer model with virotherapy using the Caputo operator[J]. AIMS Biophysics, 2023, 10(4): 503-522. doi: 10.3934/biophy.2023028

Related Papers:

Abstract

In this paper, a biophysical fractional diffusive cancer model with virotherapy is thoroughly analyzed and analytically simulated. The goal of this biophysical model is to represent both the dynamics of cancer development and the results of virotherapy, which uses viruses to target and destroy cancer cells. The Caputo sense is applied to the fractional derivatives. We look at the governing model's existence and uniqueness. For analytical solutions, the Laplace residual power series approach is used. The study investigates the model's dynamic behavior, shedding light on the development of cancer and the effects of virotherapy. The research advances our knowledge of cancer modeling and treatment options. Numerical simulations show the agreement between the analytical results and the related numerical solutions, proving the usefulness of the analytical solution.

References

[1]	Zeeshan A, Majeed A, Ellahi R (2016) Effect of magnetic dipole on viscous ferro-fluid past a stretching surface with thermal radiation. J Mol Liq 215: 549-554. https://doi.org/10.1016/j.molliq.2015.12.110
[2]	Ramli N, Ahmad S, Pop I Slip effects on MHD flow and heat transfer of ferrofluids over a moving flat plate, AIP Conference Proceedings (2017). https://doi.org/10.1063/1.4995847
[3]	Rashad AM (2017) Impact of anisotropic slip on transient three dimensional MHD flow of ferrofluid over an inclined radiate stretching surface. J Egypt Math Soc 25: 230-237. https://doi.org/10.1016/j.joems.2016.12.001
[4]	Hussanan A, Salleh MZ, Khan I (2018) Microstructure and inertial characteristics of a magnetite ferrofluid over a stretching/shrinking sheet using effective thermal conductivity model. J Mol Liq 255: 64-75. https://doi.org/10.1016/j.molliq.2018.01.138
[5]	Fukuhara H, Ino Y, Todo T (2016) Oncolytic virus therapy: a new era of cancer treatment at dawn. Cancer Sci 107: 1373-1379. https://doi.org/10.1111/cas.13027
[6]	Tian JP (2011) The replicability of oncolytic virus: defining conditions in tumor virotherapy. Math Biosci Eng 8: 841-860. http://dx.doi.org/10.3934/mbe.2011.8.841
[7]	Younoussi ME, Hajhouji Z, Hattaf K, et al. (2021) A new fractional model for cancer therapy with M1 oncolytic virus. Complexity 2021: 99344070. https://doi.org/10.1155/2021%2F9934070
[8]	Kumar S, Kumar A, Samet B, et al. (2020) A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment. Chaos Soliton Fract 141: 110321. https://doi.org/10.1016/j.chaos.2020.110321
[9]	Gómez-Aguilar JF, López-López MG, Alvarado-Martínez VM, et al. (2017) Chaos in a cancer model via fractional derivatives with exponential decay and Mittag-Leffler law. Entropy 19: 681. https://doi.org/10.3390/e19120681
[10]	Zhang Z, ur Rahman G, Gómez-Aguilar JF, et al. (2022) Dynamical aspects of a delayed epidemic model with subdivision of susceptible population and control strategies. Chaos Soliton Fract 160: 112194. https://doi.org/10.1016/j.chaos.2022.112194
[11]	Zhang L, ur Rahman M, Haidong Q, et al. (2022) Fractal-fractional anthroponotic cutaneous Leishmania model study in sense of Caputo derivative. Alex Eng J 61: 4423-4433. https://doi.org/10.1016/j.aej.2021.10.001
[12]	Chu YM, Rashid S, Karim S, et al. (2023) New configurations of the fuzzy fractional differential Boussinesq model with application in ocean engineering and their analysis in statistical theory. CMES-Comp Model Eng 137: 1573-1611. https://doi.org/10.32604/cmes.2023.027724
[13]	Shen WY, Chu YM, ur Rahman M, et al. (2021) Mathematical analysis of HBV and HCV co-infection model under nonsingular fractional order derivative. Results Phys 28: 104582. https://doi.org/10.1016/j.rinp.2021.104582
[14]	Umar M, Sabir Z, Raja MAZ, et al. (2021) Neuro-swarm intelligent computing paradigm for nonlinear HIV infection model with CD4⁺ T-cells. Math Comput Simulat 188: 241-253. https://doi.org/10.1016/j.matcom.2021.04.008
[15]	Alharbey RA, Aljahdaly NH (2022) On fractional numerical simulation of HIV infection for CD⁸⁺ T-cells and its treatment. Plos One 17: e0265627. https://doi.org/10.1371/journal.pone.0265627
[16]	Xiao T, Tang YL, Zhang QF (2021) The existence of sign-changing solutions for Schrödinger-Kirchhoff problems in R³. AIMS Math 6: 6726-6733. http://dx.doi.org/10.3934/math.2021395
[17]	Liu X, Arfan M, Ur Rahman M, et al. (2023) Analysis of SIQR type mathematical model under Atangana-Baleanu fractional differential operator. Comput Method Biomec 26: 98-112. https://doi.org/10.1080/10255842.2022.2047954
[18]	Sami A, Ali A, Shafqat R, et al. (2023) Analysis of food chain mathematical model under fractal fractional Caputo derivative. Math Biosci Eng 20: 2094-2109. http://dx.doi.org/10.3934/mbe.2023097
[19]	Haidong Q, Rahman MU, Arfan M (2023) Fractional model of smoking with relapse and harmonic mean type incidence rate under Caputo operator. J Appl Math Comput 69: 403-420. https://doi.org/10.1007/s12190-022-01747-6
[20]	Chu YM, Khan MS, Abbas M, et al. (2022) On characterizing of bifurcation and stability analysis for time fractional glycolysis model. Chaos Soliton Fract 165: 112804. https://doi.org/10.1016/j.chaos.2022.112804
[21]	Jin F, Qian ZS, Chu YM, et al. (2022) On nonlinear evolution model for drinking behavior under Caputo-Fabrizio derivative. J Appl Anal Comput 12: 790-806. http://dx.doi.org/10.11948/20210357
[22]	Chu YM, Khan MF, Ullah S, et al. (2023) Mathematical assessment of a fractional-order vector–host disease model with the Caputo–Fabrizio derivative. Math Method Appl Sci 46: 232-247. https://doi.org/10.1002/mma.8507
[23]	Aljahdaly NH, Ashi HA (2021) Exponential time differencing method for studying prey-predator dynamic during mating period. Comput Math Method M 2021: 2819145. https://doi.org/10.1155/2021/2819145
[24]	Wodarz D (2003) Gene therapy for killing p53-negative cancer cells: use of replicating versus nonreplicating agents. Hum Gene Ther 14: 153-159. https://doi.org/10.1089/104303403321070847
[25]	Jenner AL, Kim PS, Frascoli F (2019) Oncolytic virotherapy for tumours following a Gompertz growth law. J Theor Biol 480: 129-140. https://doi.org/10.1016/j.jtbi.2019.08.002
[26]	Marelli G, Howells A, Lemoine NR, et al. (2018) Oncolytic viral therapy and the immune system: a double-edged sword against cancer. Front Immunol 9: 866. https://doi.org/10.3389/fimmu.2018.00866
[27]	Komarova NL, Wodarz D (2014) Targeted Cancer Treatment in Silico.Springer.
[28]	Wodarz D (2001) Viruses as antitumor weapons: defining conditions for tumor remission. Cancer Res 61: 3501-3507.
[29]	Wodarz D, Komarova N (2009) Towards predictive computational models of oncolytic virus therapy: basis for experimental validation and model selection. PloS One 4: e4271. https://doi.org/10.1371/journal.pone.0004271
[30]	Aljahdaly NH, Almushaity NA (2023) A diffusive cancer model with virotherapy: Studying the immune response and its analytical simulation. AIMS Math 8: 10905-10928. https://doi.org/10.3934/math.2023553
[31]	Al-Johani N, Simbawa E, Al-Tuwairqi S (2019) Modeling the spatiotemporal dynamics of virotherapy and immune response as a treatment for cancer. Commun Math Biol Neurosci 2019: 28. https://doi.org/10.28919/cmbn%2F4294
[32]	Simbawa E, Al-Johani N, Al-Tuwairqi S (2020) Modeling the spatiotemporal dynamics of oncolytic viruses and radiotherapy as a treatment for cancer. Comput Math Method M 2020: 3642654. https://doi.org/10.1155/2020/3642654
[33]	Gómez-Aguilar JF, Rosales-García JJ, Bernal-Alvarado JJ, et al. (2012) Fractional mechanical oscillators. Rev Mex Fís 58: 348-352.
[34]	Burqan A, Shqair M, El-Ajou A, et al. (2023) Analytical solutions to the coupled fractional neutron diffusion equations with delayed neutrons system using Laplace transform method. AIMS Math 8: 19297-19312. https://doi.org/10.3934/math.2023984
[35]	Shqair M, Ghabar I, Burqan A (2023) Using Laplace residual power series method in solving coupled fractional neutron diffusion equations with delayed neutrons system. Fractal Fract 7: 219. https://doi.org/10.3390/fractalfract7030219
[36]	Al-Smadi M, Freihat A, Khalil H, et al. (2017) Numerical multistep approach for solving fractional partial differential equations. Int J Comp Meth 14: 1750029. https://doi.org/10.1142/S0219876217500293
[37]	Oqielat MN, Eriqat T, Al-Zhour Z, et al. (2023) Construction of fractional series solutions to nonlinear fractional reaction–diffusion for bacteria growth model via Laplace residual power series method. Int J Dynam Control 11: 520-527. https://doi.org/10.1007/s40435-022-01001-8

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)