Mathematical Modelling and Applications

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Mathematical Modelling and Simulation of the Factors Associated with Targeted Cells, Virus-Producing Cells, and Infected Cells

Received: 28 June 2023    Accepted: 14 July 2023    Published: 24 July 2023
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Abstract

Mathematical modeling and simulation of the effective parameters in targeted, virus-producing, and infected cells were carried out. The research involved mathematical models that represent the targeted cell population, the virus-producing cell population, and the infected cell population, respectively. The numerical simulation was carried out using Wolfram Mathematica, version 12, where the pertinent parameters in the various models were varied within a specified range to study their effect on the dynamic system. The simulated results revealed that the production of the target infected cells, the elimination rate of infected cells, the elimination rate of virus cells, the elimination rate of tissue cells, the infected cell rate constant, and the constant rate of infection affect the various cell populations. The novelty of this research is the fact that the interaction between macrophage and other cells was modeled and direct numerical simulation was carried out to ascertain the effect of pertinent parameters on the system using Wolfram Mathematica. The results revealed that the production rate of tissue and infected cells affects the targeted tissue cells growth, the elimination rate affects the rate of infected cells, and the infected cell rate constant also affects the dynamic system. In addition, the virus’s increase per infected cell affects the system, and finally, the elimination rate of tissue cell affects the system.

DOI 10.11648/j.mma.20230801.12
Published in Mathematical Modelling and Applications (Volume 8, Issue 1, March 2023)
Page(s) 13-19
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Modeling, Simulation, Cells, Virus, Infected Cells, Effective Parameters

References
[1] Saltelli, A., Bammer, G., Bruno, I., Charters, E., Di Fiore, M., Didier, E.,... & Kay, J. (2020). Samuele Lo Piano, Deborah Mayo, Roger PielkeJr, TommasoPortaluri, Theodore M. Porter, ArnaldPuy, Ismael Rafols, Jerome R. Ravetz, Erik Reinert, Daniel Sarewitz, Philip B. Stark, Andrew Stirling, Jeroen van der Sluijs, and Paolo Vineis, 482-484.
[2] Boianelli, A., Nguyen, V. K., Ebensen, T., Schulze, K., Wilk, E., Sharma, N. & Hernandez-Vargas, E. A. (2015). Modeling influenza virus infection: a roadmap forinfluenza research. Viruses, 7 (10), 5274-5304.
[3] Burg, D., Rong, L., Neumann, A. U., & Dahari, H. (2009). Mathematical modeling ofviral kinetics under immune control during primary HIV-1 infection. Journal of Theoretical Biology, 259 (4), 751-759.
[4] Stafford, M. A., Corey, L., Cao, Y., Daar, E. S., Ho, D. D., &Perelson, A. S. (2000). Modeling plasma virus concentration during primary HIV infection. Journal of theoretical biology, 203 (3), 285-301.
[5] Mukhopadhyay, B., & Bhattacharyya, R. (2009). A nonlinear mathematical model ofvirus-tumor-immune system interaction: deterministic and stochastic analysis. Stochastic Analysis and Applications, 27 (2), 409-429.
[6] Bunonyo, K. W., Odinga, T., & Ikimi, C. G. (2022). Modeling Tumor Cell Proliferationand Therapeutic Treatment Simulation. Central Asian Journal of Medical and Natural Science, 3 (6), 576-586.
[7] Bunonyo, K. W., & Ebiwareme, L. (2022). Tumor growth mathematical modeling andapplication of chemo-immunotherapy and radiotherapy treatments. International Journalof Statistics and Applied Mathematics, 7 (2): 125-139; https://doi.org/10.22271/maths.2022.v7.i2b.806,
[8] Layden, T. J., Layden, J. E., Ribeiro, R. M., & Perelson, A. S. (2003). Mathematicalmodeling of viral kinetics: a tool to understand and optimize therapy. Clinics in liver disease, 7 (1), 163-178.
[9] Bunonyo, K. W., Ebiwareme, L., & Awomi, P. Z. (2023). Temperature effect on drugdiffusion in the stomach and bloodstream compartments. World Journal of Biology Pharmacy and Health Sciences, 13 (02), 178-188.
[10] Wodarz, D., & Nowak, M. A. (2002). Mathematical models of HIV pathogenesis andtreatment. BioEssays, 24 (12), 1178-1187.
[11] Ghafari, A., and N. Naserifar. "Mathematical modeling and lyapunov-based drugadministration in cancer chemotherapy." (2009): 151-158.
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  • APA Style

    Kubugha Wilcox Bunonyo, Liberty Ebiwareme. (2023). Mathematical Modelling and Simulation of the Factors Associated with Targeted Cells, Virus-Producing Cells, and Infected Cells. Mathematical Modelling and Applications, 8(1), 13-19. https://doi.org/10.11648/j.mma.20230801.12

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    ACS Style

    Kubugha Wilcox Bunonyo; Liberty Ebiwareme. Mathematical Modelling and Simulation of the Factors Associated with Targeted Cells, Virus-Producing Cells, and Infected Cells. Math. Model. Appl. 2023, 8(1), 13-19. doi: 10.11648/j.mma.20230801.12

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    AMA Style

    Kubugha Wilcox Bunonyo, Liberty Ebiwareme. Mathematical Modelling and Simulation of the Factors Associated with Targeted Cells, Virus-Producing Cells, and Infected Cells. Math Model Appl. 2023;8(1):13-19. doi: 10.11648/j.mma.20230801.12

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  • @article{10.11648/j.mma.20230801.12,
      author = {Kubugha Wilcox Bunonyo and Liberty Ebiwareme},
      title = {Mathematical Modelling and Simulation of the Factors Associated with Targeted Cells, Virus-Producing Cells, and Infected Cells},
      journal = {Mathematical Modelling and Applications},
      volume = {8},
      number = {1},
      pages = {13-19},
      doi = {10.11648/j.mma.20230801.12},
      url = {https://doi.org/10.11648/j.mma.20230801.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20230801.12},
      abstract = {Mathematical modeling and simulation of the effective parameters in targeted, virus-producing, and infected cells were carried out. The research involved mathematical models that represent the targeted cell population, the virus-producing cell population, and the infected cell population, respectively. The numerical simulation was carried out using Wolfram Mathematica, version 12, where the pertinent parameters in the various models were varied within a specified range to study their effect on the dynamic system. The simulated results revealed that the production of the target infected cells, the elimination rate of infected cells, the elimination rate of virus cells, the elimination rate of tissue cells, the infected cell rate constant, and the constant rate of infection affect the various cell populations. The novelty of this research is the fact that the interaction between macrophage and other cells was modeled and direct numerical simulation was carried out to ascertain the effect of pertinent parameters on the system using Wolfram Mathematica. The results revealed that the production rate of tissue and infected cells affects the targeted tissue cells growth, the elimination rate affects the rate of infected cells, and the infected cell rate constant also affects the dynamic system. In addition, the virus’s increase per infected cell affects the system, and finally, the elimination rate of tissue cell affects the system.},
     year = {2023}
    }
    

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    T1  - Mathematical Modelling and Simulation of the Factors Associated with Targeted Cells, Virus-Producing Cells, and Infected Cells
    AU  - Kubugha Wilcox Bunonyo
    AU  - Liberty Ebiwareme
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    N1  - https://doi.org/10.11648/j.mma.20230801.12
    DO  - 10.11648/j.mma.20230801.12
    T2  - Mathematical Modelling and Applications
    JF  - Mathematical Modelling and Applications
    JO  - Mathematical Modelling and Applications
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    PB  - Science Publishing Group
    SN  - 2575-1794
    UR  - https://doi.org/10.11648/j.mma.20230801.12
    AB  - Mathematical modeling and simulation of the effective parameters in targeted, virus-producing, and infected cells were carried out. The research involved mathematical models that represent the targeted cell population, the virus-producing cell population, and the infected cell population, respectively. The numerical simulation was carried out using Wolfram Mathematica, version 12, where the pertinent parameters in the various models were varied within a specified range to study their effect on the dynamic system. The simulated results revealed that the production of the target infected cells, the elimination rate of infected cells, the elimination rate of virus cells, the elimination rate of tissue cells, the infected cell rate constant, and the constant rate of infection affect the various cell populations. The novelty of this research is the fact that the interaction between macrophage and other cells was modeled and direct numerical simulation was carried out to ascertain the effect of pertinent parameters on the system using Wolfram Mathematica. The results revealed that the production rate of tissue and infected cells affects the targeted tissue cells growth, the elimination rate affects the rate of infected cells, and the infected cell rate constant also affects the dynamic system. In addition, the virus’s increase per infected cell affects the system, and finally, the elimination rate of tissue cell affects the system.
    VL  - 8
    IS  - 1
    ER  - 

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Author Information
  • Department of Mathematics and Statistics, Federal University Otuoke, Yenagoa, Nigeria

  • Department of Mathematics, Rivers State University, Port Harcourt, Nigeria

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