C. Rodriguez
University of Guadalajara, Mexico
Title: Mathematical Analysis of Epidemiological Models and their Forecasts
Biography
Dr. Carlos Oscar Rodriguez Leal is a physicist-mathematician, who did his doctorate in physics in the University of Guadalajara. He is also a self-taught philosopher and has experience in the application and modeling of mathematics, physics, AI and machine learning in specific areas of medicine, such as epidemiological models and neuroscience. He has published papers and books, and participated in international conferences on mathematics, physics, philosophy and medicine.
Abstract
In this article I present analyses of the existence and uniqueness, as well as the convergence, consistency, and stability, of various analytical (such as Lie algebras) and approximate methods (both existing -deterministic and stochastic-, such as numerical methods, machine learning, and neural networks, and some I have developed -discrete Taylor series, Rodriguez's linearization, new neural network models, predictions using cyclical behaviors, etc.-) for solving equations arising from models (some existing and others I have created) of the growth of several types of epidemics; where besides I integrate technical analysis (correlative models) with fundamental analysis (explanatory models), and apply inverse problem methods (both existing ones and others I have developed) to fit parameters in the equations. It is worth mentioning that I achieve good and interesting results in all the above mentioned.
Finally, I conduct a comparative analysis of the different models and synthesize them in order to develop more accurate forecasts of the growth of these epidemics, as said models correct each other. Through this synthesis of methods, I manage to achieve some improvement in forecasting the progression of epidemics, at least in the short term, and a slight improvement in the medium term. It remains for future research to develop and refine all these procedures.
Keywords: Epidemiological models; differential equations; deterministic models; stochastic models; new epidemiological models; new approximate methods; comparative analysis
14-15 Sep 2026 
Singapore 
