Sumários
Lesson 24 - MMB, Other topics in biomathemedical modeling (online class)
9 dezembro 2020, 14:00 • Jorge Tiago
In the second part, the lectures focused on specific applications of mathematics in biomedicine: vaccination models, cancer dynamics and therapies, immunology and infection, antibiotic resistance and treatment, and multi-strain epidemiological models. The aim was to familiarize the students with classical motifs in dynamic models (nonlinearities, mass-action, Holling-type II functional response, heterogeneity, intervention effects, singular perturbation approaches), and to make them able to read, interpret, and begin to analyze and extend such models. Specific basic codes in R for numerical simulation of simple dynamical systems were also explained. More advanced topics and materials for further reading were suggested.(invited lecturer Erida Gjini).
Lesson 23 - MMB, Introduction with examples from mathematical epidemiology (online class)
9 dezembro 2020, 11:00 • Jorge Tiago
In this first part, the students were presented with an overview of the diferent approaches in mathematical modeling in biology, where central themes were ordinary differential equations, dynamical systems, asymptotic analysis and numerical integration. They were introduced to one-dimensional models like the exponential and logistic population growth, as well as to basic two dimensional models like the Lotka-Volterra competition and predator-prey models. The three classical models of mathematical epidemiology (SI, SIS, SIR) were also briefly discussed, with emphasis on equilibrium analysis and bifurcations mediated bythe basic reproduction number R0. (invited lecturer Erida Gjini)
Lesson 22 - Reduced models for the artery wall
2 dezembro 2020, 14:00 • Jorge Tiago
Several types of order reduction when coupling blood with artery wall dynamics. The independent ring's assumption. The generalized string model. Derivation of an energy estimate.