Dehingia, K.Hosseini, K.Salahshour, S.Baleanu, D.Matematik2024-02-092024-02-092022Dehingia, 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.52349-5103https://doi.org/10.1007/s40819-022-01433-yThis 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. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.eninfo:eu-repo/semantics/closedAccessDiscrete-Time DelayHopf BifurcationNumerical ResolutionSteady-State AnalysisTumor-Macrophages InteractionArticle8510.1007/s40819-022-01433-y2-s2.0-85137201470N/AQ2