Simon Péter (ELTE Matematikai Intézet, Alkalmazott Analízis és Számításmatematikai Tanszék)

Epidemic propagation on networks

Abstract:

Networks have become extremely useful in modelling complex systems. Their use has led to rapid progress in the study of spreading processes such as information, rumour and epidemics. The exact mathematical model of a stochastic network process, like epidemic propagation on a graph, can be formulated as a large system of linear differential equations. Despite of the fact, that the mathematical model is relatively simple, the analytical or numerical study of the system gets hard when the number of nodes in the graph is a large number. Hence the approximation of the system by simple non-linear differential equations is one of the most important tools of investigation. In this talk we give an introduction to this rapidly evolving field with emphasis on the mathematical methods introduced so far. Besides considering spreading processes on static networks we will deal with adaptive networks, when the epidemic dynamics on the network is coupled with a network which evolves in time. Moreover, we show how this approach leads to the control of the network process, a mathematical problem attracting significant research interest nowadays.

Reference

• Kiss., I.Z, Miller, J.C., Simon, P.L., Mathematics of Epidemics on Networks; From Exact to Approximate Models, Springer (2017). link

About the lecturer:

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