Optimal treatment strategies for delayed cancer-immune system with multiple therapeutic approach

Parthasakha Das, Samhita Das, Ranjit Kumar Upadhyay and Pritha Das

Chaos, Solitons & Fractals, 2020, vol. 136, issue C

Abstract: In this article, we propose and analyze an optimal control problem of a delayed tumor-immune model in presence of a multi immuno-chemotherapeutic drug. Local dynamics of drug-free steady states are studied and Hopf-bifurcation is observed with delay bifurcation parameter. By formulating a quadratic control based functional, an optimal control problem is constructed with treatments as control variables. The formulation of the functional is aimed at minimizing the proliferation rate of tumor cells and the detrimental effects of injected drugs. Additionally, maximizing the effector cells and maintaining an attributed level of normal cells are also a priority. By applying Pontryagin’s maximum principle, the sufficient and necessary conditions of optimality system are established. The sensitivity analysis of cost functional is performed with different combinations of control variables. The cost-effectiveness analysis is carried out to determine the most cost-effective strategy. The numerical results verify analytical findings and demonstrate that a multi-therapeutic treatment protocol can alleviate tumor burden within a few months of drug administration.

Keywords: Tumor-immune interactions; Hopf-bifurcation; Optimal control; Sensitivity analysis; Cost-effectiveness analysis (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302071

DOI: 10.1016/j.chaos.2020.109806

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