PDE and Applied Mathematics Seminar[ Edit ]
Moderator: Itay Shafrir
Mathematical epidemiology uses modelling to study the spread of contagious diseases in a population, in order to understand the underlying mechanisms and aid public health planning. In recent years there is growing interest in applying similar models to the study of `social contagion': the spread of ideas and behaviors. It is of great interest is to consider the ways in which social contagion differs from biological contagion at the individual level, and to use mathematical modelling to understand the population-level consequences of these differences. In this talk I will present simple `two-stage' contagion models motivated by social-science literature, and study their dynamics. It turns out that these models give rise to some interesting and non-intuitive nonlinear phenomena which do not arise in the `classical' models of mathematical epidemiology, and which might have relevance to understanding some real-world observations.
The Boltzmann equation without angular cutoff is considered when the initial data is a perturbation of a global Maxwellian with algebraic decay in the velocity variable. Global solution is proved by combining the analysis in moment propagation, spectrum of the linearized operator and the smoothing effect of the linearized operator when initial data in Sobolev space with negative index.
This is a joint work with Ricardo Alonso, Yoshinori Morimoto and Weiran Sun.