Author:
Turner Leo, ,Burbanks Andrew,Cerasuolo Marianna
Abstract
<abstract><p>Prostate cancer is the fifth most common cause of death from cancer, and the second most common diagnosed cancer in men. In the last few years many mathematical models have been proposed to describe the dynamics of prostate cancer under treatment. So far one of the major challenges has been the development of mathematical models that would represent <italic>in vivo</italic> conditions and therefore be suitable for clinical applications, while being mathematically treatable. In this paper, we take a step in this direction, by proposing a nonlinear distributed-delay dynamical system that explores neuroendocrine transdifferentiation in human prostate cancer <italic>in vivo</italic>. Sufficient conditions for the existence and the stability of a tumour-present equilibrium are given, and the occurrence of a Hopf bifurcation is proven for a uniform delay distribution. Numerical simulations are provided to explore differences in behaviour for uniform and exponential delay distributions. The results suggest that the choice of the delay distribution is key in defining the dynamics of the system and in determining the conditions for the onset of oscillations following a switch in the stability of the tumour-present equilibrium.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Computational Mathematics,General Agricultural and Biological Sciences,Modelling and Simulation,General Medicine
Reference37 articles.
1. F. Bray, J. Ren, E. Masuyer, J. Ferlay, Global estimates of cancer prevalence for 27 sites in the adult population in 2008, Int. J. Cancer, 132 (2012), 1133–1145. doi: 10.1002/ijc.27711.
2. W. H. Organisation, Cancer Today, available from: https://gco.iarc.fr/today, Last Accessed: 2020-06-05.
3. P. J. Hensley, N. Kyprianou, Modeling prostate cancer in mice: limitations and opportunities, J. Androl., 33 (2012), 133–144. doi: 10.2164/jandrol.111.013987.
4. J. Horoszewicz, S. Leong, T. Ming-Chu, Z. Wajsman, M. Friedman, L. Papsidero, et al., The LNCaP cell line - a new model for studies on human prostatic carcinoma, Prog. Clin. Biol. Res., 37 (1980), 115–132.
5. T. Phan, S. Crook, A. Bryce, C. Maley, E. Kostelich, Y. Kuang, Mathematical modeling of prostate cancer and clinical application, Appl. Sci., 10 (2020), 2721. doi: 10.3390/app10082721.
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