Mathematical modeling and intelligent methods in systems biology and medicine applied to complex diseases: An overview.

This article presents a comprehensive analysis of the intersection between mathematical models, classic algorithmic simulations as well as with machine learnig, alongside their applications, in biology, medicine and bioinformatics. From the first models on population growth and competition, we review the evolution of formalizations to present modeling of complex diseases such as diabetes, cancer, aging, and neurodegenerative disorders. Mathematical models are introduced and categorized, alongside the algorithms and computational methods from deterministic models on exponential and logistic growth, predator-prey dynamics, SIR framework, and cellular automata. The stochastic models on reaction-diffusion, Monte Carlo methods, Markov chains, and Bayesian networks. Thermodynamics-based models on phase transitions and cancer growth; as well the close related Ising Hamiltonian-based models on cancer immunoediting, joint to aspects on genetic and phenotype immune response. The role of classic and deep machine learning -hybrid- models for integrating multi-omic data in challenging scenario prediction. It is highlighted through relevant applications on systems and precision medicine.