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<p>This paper presents a mathematical model aimed at understanding the dynamics of Pancreatic cancer, specifically the interactions among Pancreatic cancer cells (PCC), Pancreatic stellate cells (PSC), effector cells, and cytokines, with a focus on the therapeutic role of small interfering RNA (siRNA) treatment. The model integrates fractional calculus through the Atangana-Baleanu fractional derivative to capture the memory-dependent behaviors of the tumor microenvironment, accounting for delayed and long-term cytokine interactions and immune responses that are crucial for cancer progression. The existence and uniqueness of solutions are demonstrated using the Arzelà-Ascoli and Banach’s Fixed Point theorems, ensuring the reliability of the model. Stability analysis is conducted for the disease-free equilibrium (DFE), and global stability is evaluated using Ulam-Hyers stability theory. Reproduction Number and sensitivity analysis has been calculated for the disease-free equilibrium point. Numerical simulations are performed with the fourth-order Runge–Kutta method, providing insights into the growth rates of PCC and PSC, cytokine production, and effector cell apoptosis under varying parameter conditions. A comparison of the fractional derivative model with the traditional ODE model reveals notable differences in the rate of change of certain system variables, suggesting that the fractional approach offers a more gradual evolution of tumor dynamics. The results show that siRNA therapy can effectively inhibit tumor progression within specific biological parameter ranges.</p>

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Fractional Calculus Approach to Pancreatic Cancer Therapy: Modeling Tumor and Immune Interactions with siRNA Treatment

  • 期刊论文

  • 发表日期：

    2025年3月12日

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  • Akanksha Singh,
  • Anil Chavada,
  • Nimisha Pathak

摘要

This paper presents a mathematical model aimed at understanding the dynamics of Pancreatic cancer, specifically the interactions among Pancreatic cancer cells (PCC), Pancreatic stellate cells (PSC), effector cells, and cytokines, with a focus on the therapeutic role of small interfering RNA (siRNA) treatment. The model integrates fractional calculus through the Atangana-Baleanu fractional derivative to capture the memory-dependent behaviors of the tumor microenvironment, accounting for delayed and long-term cytokine interactions and immune responses that are crucial for cancer progression. The existence and uniqueness of solutions are demonstrated using the Arzelà-Ascoli and Banach’s Fixed Point theorems, ensuring the reliability of the model. Stability analysis is conducted for the disease-free equilibrium (DFE), and global stability is evaluated using Ulam-Hyers stability theory. Reproduction Number and sensitivity analysis has been calculated for the disease-free equilibrium point. Numerical simulations are performed with the fourth-order Runge–Kutta method, providing insights into the growth rates of PCC and PSC, cytokine production, and effector cell apoptosis under varying parameter conditions. A comparison of the fractional derivative model with the traditional ODE model reveals notable differences in the rate of change of certain system variables, suggesting that the fractional approach offers a more gradual evolution of tumor dynamics. The results show that siRNA therapy can effectively inhibit tumor progression within specific biological parameter ranges.