ArticleJournal of mathematical biology2016
Asymptotic dynamics of some t-periodic one-dimensional model with application to prostate cancer immunotherapy.
Article in Journal of mathematical biology, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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Who cites it
2 citing papers in PubMed, 8 citations in OpenAlex.
- Mathematical model of hormone sensitive prostate cancer treatment using leuprolide: A small step towards personalization.PloS one · 2022Article
- Mathematical Prostate Cancer Evolution: Effect of Immunotherapy Based on Controlled Vaccination Strategy.Computational and mathematical methods in medicine · 2020Article
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Authors and funding
3 authors at 2 institutions in 2 countries.
Funding
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Abstract
In the case of some specific cancers, immunotherapy is one of the possible treatments that can be considered. Our study is based on a mathematical model of patient-specific immunotherapy proposed in Kronik et al. (PLoS One 5(12):e15,482, 2010). This model was validated for clinical trials presented in Michael et al. (Clin Cancer Res 11(12):4469-4478, 2005). It consists of seven ordinary differential equations and its asymptotic dynamics can be described by some t-periodic one-dimensional dynamical system. In this paper we propose a generalised version of this t-periodic system and study the dynamics of the proposed model. We show that there are three possible types of the model behaviour: the solution either converges to zero, or diverges to infinity, or it is periodic. Moreover, the periodic solution is unique, and it divides the phase space into two sub-regions. The general results are applied to the PC specific case, which allow to derive conditions guaranteeing successful as well as unsuccessful treatment. The results indicate that a single vaccination is not sufficient to cure the cancer.
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