Analysis of a delay-induced mathematical model of cancer

Advances in Continuous and Discrete Models
Anusmita Das1, Kaushik Dehingia1, Hemanta Kumar Sarmah1, K. Hosseini2, Khadijeh Sadri2, Soheil Salahshour3
1Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India
2Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
3Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

Tóm tắt

AbstractIn this paper, the dynamical behavior of a mathematical model of cancer including tumor cells, immune cells, and normal cells is investigated when a delay term is induced. Though the model was originally proposed by De Pillis et al. (Math. Comput. Model. 37:1221–1244, 2003), to make the model more realistic, we have added a delay term into the model, and it has incorporated novelty in our present work. The stability of existing equilibrium points in the delay-induced system is studied in detail. Global stability conditions of the tumor-free equilibrium point have been found. It is shown that due to this delay effect, the coexisting equilibrium point may lose its stability through a Hopf bifurcation. The implicit function theorem is applied to characterize a complex function in a neighborhood of delay terms. Additionally, the presence of Hopf bifurcation is demonstrated when the transversality conditions are satisfied. The length of delay for which the solutions preserve the stability of the limit cycle is estimated. Finally, through a series of numerical simulations, the theoretical results are formally examined.

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Advances in Continuous and Discrete Models

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