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Stability analysis and numerical simulations for interactions of tumor-immune system with drug delivery

Author

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  • Yadav, Manisha
  • Singh, Paramjeet

Abstract

This paper presents a five-dimensional mathematical model that describes the complex interactions between tumor cells, components of the immune system, and the effects of administering drugs to specific cellular locations. We have included logistic growth to elucidate tumor cell proliferation and the framework is defined by a system of nonlinear differential equations. Furthermore, we investigate the presence and stability of equilibria with and without drug. In both cases, the model have two distinct equilibria: a tumor-free state and a tumorous equilibrium. However, in the absence of drug, we observe that each equilibrium is characterized by a distinct center manifold. The dynamic behavior of these equilibrium has been explained via stability analysis. Finally, we established the presence of bifurcation along with sensitivity analysis. Further, we provide empirical validation for the observed dynamics using numerical simulations to support our theoretical findings. Thus, through this comprehensive approach our research adds to an extensive knowledge of the complex interplay between tumor dynamics, drug therapy, and stability phenomena.

Suggested Citation

  • Yadav, Manisha & Singh, Paramjeet, 2025. "Stability analysis and numerical simulations for interactions of tumor-immune system with drug delivery," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077924015236
    DOI: 10.1016/j.chaos.2024.115971
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