Jitendra Singh,
- Assistant Professor, Guru Tegh Bahadur 4th Centenary Engineering College G-8 Area, Rajouri Garden, New Delhi, Delhi, India
Abstract
This study investigates tumor-immune interactions within the context of chemotherapy using a mathematical model. The model’s solutions are proven to exist, be unique, non-negative, and bounded. Both untreated and chemotherapy-treated systems are examined for equilibrium points, with local stability analyzed using the Routh–Hurwitz criterion and global stability established through a Lyapunov function. A quadratic optimal control strategy is applied to minimize tumor cells while limiting chemotherapy’s side effects on healthy and immune cells. The existence of an optimal control is demonstrated, and the necessary conditions for optimality are derived using Pontryagin’s maximum principle. The optimal control system is solved numerically via the forward-backward sweep method and the fourth-order Runge–Kutta scheme. Results reveal that tumor suppression improves with enhanced immune cell recruitment, triggered by tumor antigenicity, Finally, a comparative analysis shows that optimal control leads to more effective tumor management than uncontrolled scenarios, highlighting the potential of mathematical modeling and control strategies in improving cancer treatment outcomes.
Keywords: Tumor Cells, Immune Cells, Chemotherapy Mathematical Modeling; Optimal Control.
[This article belongs to International Journal of Biomedical Innovations and Engineering ]
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International Journal of Biomedical Innovations and Engineering
| Volume | 04 | |
| Issue | 02 | |
| Received | 28/04/2026 | |
| Accepted | 01/07/2026 | |
| Published | 09/10/2026 | |
| Publication Time | 164 Days |