Analysis of a delay-induced mathematical model of cancer

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