Mathematical Physics and Harmonic Analysis Seminar

Date: December 2, 2022

Time: 09:00AM - 10:00AM

Location: Zoom

Speaker: Hannah Kravitz, Portland State University

Title: An application of PDEs on metric graphs to epidemiology

Abstract: It has been known that a network structure enhances the spread of epidemics since the inception of the field. In the first epidemiological study John Snow (often called the father of epidemiology) determined that cholera was spreading through the 1850s London city water grid. Since then, numerous studies have supported the relationship between network structure and disease spread – parasites may be carried along fluvial networks, the colonial-era railway system in DR Congo may have contributed to the geographic spread of the first HIV outbreak, mosquitoes carrying dengue fever may be carried on trucks along highway systems, and the novel coronavirus spread from country to county first through the international air transport network.

With these examples in mind, a variation of the susceptible-infected-removed (SIR) model is developed that couples travel along a network with spatially diffusive spread in a 2D region. The model begins with a metric graph structure (a network in which a distance coordinate is defined on the edges). The classic well-mixed SIR model is implemented at the vertices of the graph (may be conceived as “cities”) which is coupled to a transport model on the edges (“roads”). This structure is embedded in a 2D region, dividing it into several subregions whose boundaries are made up of the metric graph and outer borders. A diffusive SIR model is implemented in the 2D region. This talk will discuss the development of the model and present some preliminary results.