Abstract: This work uses mathematical models to study human behavior changes' effects on infectious disease transmission dynamics. It centers on two main topics. The first concerns how behavior response evolves during epidemics and the effects of adaptive precaution behavior on epidemics. The second topic is how to build general framework models incorporating human behavior response in epidemiological modelling.

Abstract: Discrete homotopy theory is a relatively new area of mathematics, concerned with applying methods from homotopy theory in topology to the category of graphs. In order to do this, a notion of a product between graphs is required. Classically two products have been considered, the box product and the categorical product. These products lead to two different homotopy theories, namely A-theory and X-theory, respectively. This leads us to the question of why these two products are considered, and if one can define other products to study discrete homotopy theory with instead. In this talk, we will answer this question by fully characterizing all closed symmetric monoidal products on the category of graphs. 

This talk will be based on joint work with C. Kapulkin (arxiv:2310.00493).