Bifurcation analysis of a delayed mathematical model for tumor growth |
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Affiliation: | 1. Department of Mathematics, Bankura University, Bankura 722155, India;2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India;1. nInstituto Politécnico Nacional, CITEDI-IPN, Av. del IPN No. 1310, Mesa de Otay, Tijuana 22510, B.C., México;2. Instituto Tecnológico de Tijuana, Blvd. Limón Padilla s/n, Mesa de Otay, Tijuana 22454, B.C., México |
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Abstract: | In this study, we present a modified mathematical model of tumor growth by introducing discrete time delay in interaction terms. The model describes the interaction between tumor cells, healthy tissue cells (host cells) and immune effector cells. The goal of this study is to obtain a better compatibility with reality for which we introduced the discrete time delay in the interaction between tumor cells and host cells. We investigate the local stability of the non-negative equilibria and the existence of Hopf-bifurcation by considering the discrete time delay as a bifurcation parameter. We estimate the length of delay to preserve the stability of bifurcating periodic solutions, which gives an idea about the mode of action for controlling oscillations in the tumor growth. Numerical simulations of the model confirm the analytical findings. |
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