LEADER 04396nam 22007335 450 001 9910254279903321 005 20251006160438.0 010 $a3-319-50806-7 024 7 $a10.1007/978-3-319-50806-1 035 $a(CKB)4340000000062030 035 $a(DE-He213)978-3-319-50806-1 035 $a(MiAaPQ)EBC6315016 035 $a(MiAaPQ)EBC5595895 035 $a(Au-PeEL)EBL5595895 035 $a(OCoLC)990142270 035 $a(PPN)202987922 035 $a(Au-PeEL)EBL6315016 035 $a(EXLCZ)994340000000062030 100 $a20170608d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematics of Epidemics on Networks $eFrom Exact to Approximate Models /$fby István Z. Kiss, Joel C. Miller, Péter L. Simon 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (xviii, 413 pages)$cillustrations 225 1 $aInterdisciplinary Applied Mathematics,$x2196-9973 ;$v46 300 $aIncludes index. 327 $aPreface -- Introduction to Networks and Diseases -- Exact Propagation Models: Top Down -- Exact Propagation Models: Bottom-Up -- Mean-Field Approximations for Heterogeneous Networks -- Percolation-Based Approaches for Disease Modelling -- Hierarchies of SIR Models -- Dynamic and Adaptive Networks -- Non-Markovian Epidemics -- PDE Limits for Large Networks -- Disease Spread in Networks with Large-scale structure -- Appendix: Stochastic Simulation -- Index. 330 $aThis textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate students, as well as doctoral students, postdoctoral researchers and academic experts who are engaged in modeling stochastic processes on networks; Providing software that can solve the differential equation models or directly simulate epidemics in networks. Replete with numerous diagrams, examples, instructive exercises, and online access to simulation algorithms and readily usable code, this book will appeal to a wide spectrum of readers from different backgrounds and academic levels. Appropriate for students with or without a strong background in mathematics, this textbook can form the basis of an advanced undergraduate or graduate course in both mathematics and biology departments alike. . 410 0$aInterdisciplinary Applied Mathematics,$x2196-9973 ;$v46 606 $aBiomathematics 606 $aDynamics 606 $aGraph theory 606 $aEpidemiology 606 $aProbabilities 606 $aMathematical and Computational Biology 606 $aDynamical Systems 606 $aGraph Theory 606 $aEpidemiology 606 $aProbability Theory 615 0$aBiomathematics. 615 0$aDynamics. 615 0$aGraph theory. 615 0$aEpidemiology. 615 0$aProbabilities. 615 14$aMathematical and Computational Biology. 615 24$aDynamical Systems. 615 24$aGraph Theory. 615 24$aEpidemiology. 615 24$aProbability Theory. 676 $a614.4 700 $aKiss$b István Z$0759617 702 $aMiller$b Joel C 702 $aSimon$b Péter L 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254279903321 996 $aMathematics of epidemics on networks$92039118 997 $aUNINA