caa a22 4500 445330392 CHVBK 20180317142735.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00285-010-0344-x doi (NATIONALLICENCE)springer-10.1007/s00285-010-0344-x Exact epidemic models on graphs using graph-automorphism driven lumping [Elektronische Daten] [Péter Simon, Michael Taylor, Istvan Kiss] The dynamics of disease transmission strongly depends on the properties of the population contact network. Pair-approximation models and individual-based network simulation have been used extensively to model contact networks with non-trivial properties. In this paper, using a continuous time Markov chain, we start from the exact formulation of a simple epidemic model on an arbitrary contact network and rigorously derive and prove some known results that were previously mainly justified based on some biological hypotheses. The main result of the paper is the illustration of the link between graph automorphisms and the process of lumping whereby the number of equations in a system of linear differential equations can be significantly reduced. The main advantage of lumping is that the simplified lumped system is not an approximation of the original system but rather an exact version of this. For a special class of graphs, we show how the lumped system can be obtained by using graph automorphisms. Finally, we discuss the advantages and possible applications of exact epidemic models and lumping. Springer-Verlag, 2010 Network nationallicence Epidemic nationallicence Markov chain nationallicence Lumping nationallicence Graph automorphism nationallicence Simon Péter Institute of Mathematics, Eötvös Loránd University Budapest, Budapest, Hungary aut Taylor Michael Department of Mathematics, University of Sussex, Falmer, BN1 9RF, Brighton, UK aut Kiss Istvan Department of Mathematics, University of Sussex, Falmer, BN1 9RF, Brighton, UK aut Journal of Mathematical Biology Springer-Verlag 62/4(2011-04-01), 479-508 0303-6812 62:4<479 2011 62 285 https://doi.org/10.1007/s00285-010-0344-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0344-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Simon Péter Institute of Mathematics, Eötvös Loránd University Budapest, Budapest, Hungary aut NATIONALLICENCE 700 1- Taylor Michael Department of Mathematics, University of Sussex, Falmer, BN1 9RF, Brighton, UK aut NATIONALLICENCE 700 1- Kiss Istvan Department of Mathematics, University of Sussex, Falmer, BN1 9RF, Brighton, UK aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 62/4(2011-04-01), 479-508 0303-6812 62:4<479 2011 62 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer