Simulating Individual-Based Models of Epidemics in Hierarchical Networks

Current mathematical modeling methods for the spreading of infectious diseases are too simplified and do not scale well. We present the Simulator of Epidemic Evolution in Complex Networks (SEECN), an efficient simulator of detailed individual-based models by parameterizing separate dynamics operators, which are iteratively applied to the contact network. We reduce the network generator's computational complexity, improve cache efficiency and parallelize the simulator. To evaluate its running time we experiment with an HIV epidemic model that incorporates up to one million homosexual men in a scale-free network, including hierarchical community structure, social dynamics and multi-stage intranode progression. We find that the running times are feasible, on the order of minutes, and argue that SEECN can be used to study realistic epidemics and its properties experimentally, in contrast to defining and solving ever more complicated mathematical models as is the current practice.

[1]  Y. Saad,et al.  Krylov Subspace Methods on Supercomputers , 1989 .

[2]  A. Grabowski,et al.  Epidemic spreading in a hierarchical social network. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Christos Faloutsos,et al.  Realistic, Mathematically Tractable Graph Generation and Evolution, Using Kronecker Multiplication , 2005, PKDD.

[4]  M. Keeling.  The implications of network structure for epidemic dynamics. , 2005, Theoretical population biology.

[5]  F. Sorrentino.  Effects of the network structural properties on its controllability. , 2007, Chaos.

[6]  Rick Quax,et al.  Modeling and simulating the propagation of infectious diseases using complex networks , 2008 .

[7]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[8]  A. Grabowski,et al.  THE SIS MODEL OF EPIDEMIC SPREADING IN A HIERARCHICAL SOCIAL NETWORK , 2005 .

[9]  J. Kurths,et al.  Hierarchical synchronization in complex networks with heterogeneous degrees. , 2006, Chaos.

[10]  M. Keeling,et al.  Networks and epidemic models , 2005, Journal of The Royal Society Interface.

[11]  Alessandro Vespignani,et al.  Dynamical Patterns of Epidemic Outbreaks in Complex Heterogeneous Networks , 1999 .

[12]  Peter M. A. Sloot,et al.  International Journal of Computer Mathematics Stochastic Simulation of Hiv Population Dynamics through Complex Network Modelling Stochastic Simulation of Hiv Population Dynamics through Complex Network Modelling , 2022 .

[13]  L. da F. Costa,et al.  Characterization of complex networks: A survey of measurements , 2005, cond-mat/0505185.

[14]  Neil M Ferguson,et al.  Space and contact networks: capturing the locality of disease transmission , 2006, Journal of The Royal Society Interface.

[15]  Thomas Petermann,et al.  Role of clustering and gridlike ordering in epidemic spreading. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  M M Telo da Gama,et al.  Recurrent epidemics in small world networks. , 2004, Journal of theoretical biology.

[17]  Aravind Srinivasan,et al.  Modelling disease outbreaks in realistic urban social networks , 2004, Nature.

[18]  Edward Ott,et al.  Characterizing the dynamical importance of network nodes and links. , 2006, Physical review letters.

[19]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Alessandro Vespignani,et al.  The Role of Geography and Traffic in the Structure of Complex Networks , 2007, Adv. Complex Syst..

[21]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Albert-László Barabási,et al.  The Architecture of Biological Networks , 2006 .

[23]  N E Day,et al.  New therapy explains the fall in AIDS incidence with a substantial rise in number of persons on treatment expected. , 1999, AIDS.

[24]  Kamesh Madduri,et al.  A high-performance framework for analyzing massive complex networks , 2008 .

[25]  N. Konno,et al.  Multi-state epidemic processes on complex networks. , 2005, Journal of theoretical biology.

[26]  A. Barabasi,et al.  Network biology: understanding the cell's functional organization , 2004, Nature Reviews Genetics.

[27]  Y. Moreno,et al.  Epidemic outbreaks in complex heterogeneous networks , 2001, cond-mat/0107267.

[28]  Stefan Bornholdt,et al.  Handbook of Graphs and Networks: From the Genome to the Internet , 2003 .

[29]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[30]  Alessandro Vespignani,et al.  Epidemics and immunization in scale‐free networks , 2002, cond-mat/0205260.

[31]  Alessandro Vespignani,et al.  Epidemic dynamics in finite size scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.