Dinamiche sociali ed equazioni alle derivate parziali in ambito epidemiologico

In this short survey, we will discuss the importance of social dynamics in epidemiology and their mathematical modeling using partial differential equations. We will initiallypresent models of interactions between individuals in which social characteristics, such as the age of individuals, the number of social contacts, and their economic wealth, playa keyrole in the spread of an epidemic. Next, we will outline models that also account for additional characteristics such as viral load and the individual's immune defenses. Finally, we will analyze some partial differential models for describing the mobilityof individuals, both at urban and extra-urban scales, and highlight how movement dynamics playa keyrole in the progress of the epidemic.