ArticleJournal of mathematical biology2022
A Fokker-Planck feedback control framework for optimal personalized therapies in colon cancer-induced angiogenesis.
Article in Journal of mathematical biology, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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Who cites it
5 citing papers in PubMed.
- A Fokker-Planck framework for control of epidemics.Journal of mathematical biology · 2026Article
- A novel mathematical model of seasonality in Oropouche virus transmission in Amazonas, Brazil.Journal of mathematical biology · 2026Article
- Article
- An evolutionary differential game for regulating the role of monoclonal antibodies in treating signalling pathways in oesophageal cancer.Royal Society open science · 2024Article
- Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer.International journal of molecular sciences · 2022Article
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3 authors.
Funding
Abstract
In this paper, a new framework for obtaining personalized optimal treatment strategies in colon cancer-induced angiogenesis is presented. The dynamics of colon cancer is given by a Itó stochastic process, which helps in modeling the randomness present in the system. The stochastic dynamics is then represented by the Fokker-Planck (FP) partial differential equation that governs the evolution of the associated probability density function. The optimal therapies are obtained using a three step procedure. First, a finite dimensional FP-constrained optimization problem is formulated that takes input individual noisy patient data, and is solved to obtain the unknown parameters corresponding to the individual tumor characteristics. Next, a sensitivity analysis of the optimal parameter set is used to determine the parameters to be controlled, thus, helping in assessing the types of treatment therapies. Finally, a feedback FP control problem is solved to determine the optimal combination therapies. Numerical results with the combination drug, comprising of Bevacizumab and Capecitabine, demonstrate the efficiency of the proposed framework.
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