Dehingia, KaushikHosseini, KamyarSalahshour, SoheilBaleanu, D.2024-02-092024-02-092022Dehingia, Kaushik...et.al. (2022). "A Detailed Study on a Tumor Model with Delayed Growth of Pro-Tumor Macrophages", International Journal of Applied and Computational Mathematics, Vol.8, No.523495103https://hdl.handle.net/20.500.12416/7131This paper investigates a tumor-macrophages interaction model with a discrete-time delay in the growth of pro-tumor M2 macrophages. The steady-state analysis of the governing model is performed around the tumor dominant steady-state and the interior steady-state. It is found that the tumor dominant steady-state is locally asymptotically stable under certain conditions, and the stability of the interior steady-state is affected by the discrete-time delay; as a result, the unstable system experiences a Hopf bifurcation and gets stabilized. Furthermore, the transversality conditions for the existence of Hopf bifurcations are derived. Several graphical representations in two and three-dimensional postures are given to examine the validity of the results provided in the current study.eninfo:eu-repo/semantics/openAccessDiscrete-Time DelayHopf BifurcationNumerical ResolutionSteady-State AnalysisTumor-Macrophages İnteractionArticle8510.1007/s40819-022-01433-y