DYNAMICAL SYSTEMS

Below are some applied projects to which I have contributed. You may ask: how can a physicist contribute to projects involving biology or epidemiology? Well... physicists are good at solving puzzles, and we can propose creative solutions!
"...If our small minds, for some convenience, divide this glass of wine, this universe, into parts -- physics, biology, geology, astronomy, psychology, and so on -- remember that nature does not know it!.." >>RF

Can we cure prions?

Prions are proteins that cause fatal neurodegenerative diseases! Therapeutics to stop prion proliferation have been studied experimentally; however, it is not clear how the combination of different types of treatments can decrease the growth rate of prions in the brain. In this article, we combine the implementation of pharmacological chaperones and interferons to develop a novel model using a nonlinear system of ordinary differential equations and study the quantitative effects of these two treatments on the growth rate of prions. This mathematical model can be used to identify and optimize the best combination of treatments within their safe ranges.

From: Garzon, D. N., Y. Castillo, M. G. Navas-Zuloaga, and A. Ghosh, "Dynamics of Prion Proliferation Under Combined Treatment of Pharmacological Chaperones and Interferons," J. Theor. Biol. 527, 110797 (2021). https://doi.org/10.1016/j.jtbi.2021.110797

Fig. Detailed dynamical model of prion proliferation that includes the incorporation of the treatments: antibodies and interferons.

LIST OF PAPERS

Ghosh, A., Castillo Castillo, Y.A., Garzon, D. N., Arriola, L. and Mubayi, A. (2024) ‘COVID-19 transmission dynamics in close-contacts facilities: Optimizing control strategies’, Computational and Mathematical Biophysics, 12(1).
Garzon, D. N., Arellano, P., Toro-Álava, J., Román-Carrión, J.L., Ordoñez, J.E., Andrade, P., Mendoza-Ochoa, C., Ayala, P., Oleas, M., Vizcaino, A. and Jiménez-Orellana, N.M. (2024) ‘First record of a mosasaurid (Squamata: Mosasauridae) from the Upper Cretaceous of Ecuador’, Spanish Journal of Palaeontology, 39.
Garzon, D. N., Castillo, Y., Navas-Zuloaga, M.G., Darwin, L., Culik, N., Hardin, A., Yang, A., Ghosh, A., Castillo-Garsow, C., Arriola, L. and Ríos-Soto, K. (2021) ‘Dynamics of prion proliferation under combined treatment of pharmacological chaperones and interferons’, Journal of Theoretical Biology, 527, 110797. arXiv:2107.01618.
Garzon, D. N., Chipatinza, C., Andrade, A. and Matamoros, E. (2017) ‘Lycalopex culpaeus reissii, el segundo cánido más grande de Sudamérica’, Bionatura, 2(3), pp. 400–403.