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Mathematical and numerical analysis of a mathematical model of mixed immunotherapy and chemotherapy of cancer

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  • In this study, a previously published mathematical model of mixed immunotherapy and chemotherapy of tumors is considered. The stability analysis of the tumor-free equilibrium obtained in the previous study of this model is flawed. In this paper, a suitable analysis is performed to correct this error, and the parameter conditions for the stability of the tumor-free equilibrium are obtained. The stability condition gives an indicator of the host's ability to fight a cancer. The parameter conditions are examined using experimental data from clinical studies to show that the immune system is able to control a small tumor, and the host's ability to fight a cancer depends on individual variation. A numerical method based on the continuation technique is employed for one-parameter bifurcation analysis of the mathematical model with periodically pulsed therapies. The unstable fixed point curve provides a good approximation of the maximum tumor burden as a function of the dosage. Chemotherapy-induced lymphocyte damage, which may cause treatment failure, is observed in the numerical simulation. The numerical method also produces a set of combined chemotherapy and immunotherapy dosages from which an efficient and safe combination of dosages can be determined.
    Mathematics Subject Classification: Primary: 37N25, 34H20, 92B05; Secondary: 34D20.


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