DYNAMICAL SYSTEMS

I am interested in Dynamical Systems. You can find below some applied projects to which I have contributed. You may ask, how can a Physicist contribute to projects that involve Biology or Epidemiology? Well...Physicists are good at solving puzzles and we can propose creative solutions to solve problems!
Let me quote Prof. Feynman here "...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!.."

I used to be part of the Interdisciplinary Group of Complex Systems at Yachay Tech.

Dynamics of proteins in the brain

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 non-linear 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 the treatments within their safe ranges.

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