<p>In this paper, we create a fractal fractional order mathematical model to investigate cancer dynamics involving virotherapy. The fractional-order dynamical system’s solutions are explored for their non-negativeness and boundedness. The equilibrium and stability of the fractal fractional order (FFM) model are computed. The system’s sensitivity analysis looks at how various parameters influence or regulate disease transmission. We show the endemic equilibrium point’s global asymptotic stability. Finally, we use numerical simulations to support our theoretical findings. These simulations are used to evaluate the memory effect introduced by the fractal fractional order derivative technique, analyze the trajectory of model solutions, and investigate the impact of parameters on cancer dynamics incorporating virotherapy. The numerical results further reveal that the fractional order derivative represents the long-term memory effect, which has no effect on the stability of the steady points. However, when the fractional order derivative decreases, solutions tend to approach equilibrium more quickly. Results also suggest that virotherapy improves when immune cells are highly stimulated, allowing the patient’s body to produce activated immune cells. Additionally, numerical simulations are performed on various fractal fractional-order chaotic systems to validate the efficacy of the given results. The data indicate that the chaotic character of virotherapy may lead to tumor regrowth. The fractional model behaves differently than the integer order model, and the approach is smooth and dependable across a wide range of dynamical models.</p>

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Mathematical analysis and chaotic behavior of cancer treatment with virotherapy by using fractional integral sustainable approach

  • Kottakkaran Sooppy Nisar,
  • Muhammad Farman,
  • Evren Hincal

摘要

In this paper, we create a fractal fractional order mathematical model to investigate cancer dynamics involving virotherapy. The fractional-order dynamical system’s solutions are explored for their non-negativeness and boundedness. The equilibrium and stability of the fractal fractional order (FFM) model are computed. The system’s sensitivity analysis looks at how various parameters influence or regulate disease transmission. We show the endemic equilibrium point’s global asymptotic stability. Finally, we use numerical simulations to support our theoretical findings. These simulations are used to evaluate the memory effect introduced by the fractal fractional order derivative technique, analyze the trajectory of model solutions, and investigate the impact of parameters on cancer dynamics incorporating virotherapy. The numerical results further reveal that the fractional order derivative represents the long-term memory effect, which has no effect on the stability of the steady points. However, when the fractional order derivative decreases, solutions tend to approach equilibrium more quickly. Results also suggest that virotherapy improves when immune cells are highly stimulated, allowing the patient’s body to produce activated immune cells. Additionally, numerical simulations are performed on various fractal fractional-order chaotic systems to validate the efficacy of the given results. The data indicate that the chaotic character of virotherapy may lead to tumor regrowth. The fractional model behaves differently than the integer order model, and the approach is smooth and dependable across a wide range of dynamical models.