Published: Oct. 27, 2023

Sebin Gracy, Rice Academy of Fellows, Rice University

Spreading processes over networks

The talk focuses on mathematical epidemiology, or, more broadly, on spreading processes. Spreading processes are observed in several settings. Prominent examples include the spread of viruses, in particular, pandemics such as COVID-19, Spanish flu; spread of opinions on social media; adoption of products in a market; and propagation of species in an ecological environment. While there are several models available in the literature, we focus on the SIS (susceptible-infected-susceptible) model. From an analysis point of view, we are interested in questions such as what are the various equilibria of the aforementioned model? When do they exist? When are they stable? We first discuss the case where there is only one virus spreading in a network. Thereafter, we will look at the (more general) case where multiple viruses are simultaneously circulating in the population; this can be subdivided into settings where the viruses are in competition with each other, or where they cooperate with each other.

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