Abstract
A mathematical model describing the growth of tumor cells and the effect of impulsive therapy is studied in this paper. The governing equations and parameters related to the proposed model are based on the experimental and clinical outcome. Employing the quasi-steady-state approximation in delineating the dynamics of tumor–immune under different cytokines, a four-dimensional deterministic system is obtained. We explore the steady states, local and global stability criteria, transcritical bifurcation and boundary separation for the given model. The tumor cells are characterized by their growth rate and the tumor control region is determined in the parametric space. An impulsive differential equation is considered to determine the interval for perfect dosing of dendritic cell vaccination to boost the immune response. The effect of dendritic cell vaccination is determined by taking into account both perfect and imperfect therapeutics and the optimal number for therapeutics is computed. Our model demonstrates that the dendritic cell vaccination boosts the immune system and eradicates the tumor cell population.
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