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International Conference on Information Technology and Applied Mathematics

ICITAM 2019: Recent Advances in Intelligent Information Systems and Applied Mathematics pp 598–609Cite as

Dynamics of Effector -Tumor- Interleukin-2 Interactions with Monod-Haldane Immune Response and Treatments

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 863))

Abstract

In this paper, we modify and study a deterministic mathematical model governing interactions between tumor cell (TCs), effector-cells (ECs) and interleukin-2 with treatments. We investigate local stability at equilibria. The system exhibits transcritical bifurcation at tumor free equilibrium which is proved analytically by using Sotomayer’s theorem and illustrated numerically. Our study demonstrates that tumor is being eradicated after administration of external treatments. We execute extensive computer simulations and analyze with biological relevance.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, India

    Parthasakha Das & Pritha Das

  2. Department of Mathematics, Sivnath Sastri College, Kolkata, India

    Sayan Mukherjee

Authors
  1. Parthasakha Das
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  2. Sayan Mukherjee
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  3. Pritha Das
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Corresponding author

Correspondence to Parthasakha Das .

Editor information

Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico

    Oscar Castillo

  2. Haldia Institute of Technology, Haldia, West Bengal, India

    Dipak Kumar Jana

  3. Maulana Abul Kalam Azad University of Technology, Haringhata, India

    Debasis Giri

  4. Haldia Institute of Technology, Haldia, India

    Arif Ahmed

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Das, P., Mukherjee, S., Das, P. (2020). Dynamics of Effector -Tumor- Interleukin-2 Interactions with Monod-Haldane Immune Response and Treatments. In: Castillo, O., Jana, D., Giri, D., Ahmed, A. (eds) Recent Advances in Intelligent Information Systems and Applied Mathematics. ICITAM 2019. Studies in Computational Intelligence, vol 863. Springer, Cham. https://doi.org/10.1007/978-3-030-34152-7_46

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