Epidemic modeling in complex realities.

In our global world, the increasing complexity of social relations and transport infrastructures are key factors in the spread of epidemics. In recent years, the increasing availability of computer power has enabled both to obtain reliable data allowing one to quantify the complexity of the networks on which epidemics may propagate and to envision computational tools able to tackle the analysis of such propagation phenomena. These advances have put in evidence the limits of homogeneous assumptions and simple spatial diffusion approaches, and stimulated the inclusion of complex features and heterogeneities relevant in the description of epidemic diffusion. In this paper, we review recent progresses that integrate complex systems and networks analysis with epidemic modelling and focus on the impact of the various complex features of real systems on the dynamics of epidemic spreading.

[1]  B Grenfell,et al.  Space, persistence and dynamics of measles epidemics. , 1995, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[2]  Alessandro Vespignani,et al.  Velocity and hierarchical spread of epidemic outbreaks in scale-free networks. , 2003, Physical review letters.

[3]  A. L.,et al.  Spatial Heterogeneity in Epidemic Models , 2022 .

[4]  A. Vespignani,et al.  The Modeling of Global Epidemics: Stochastic Dynamics and Predictability , 2006, Bulletin of mathematical biology.

[5]  P. E. Kopp,et al.  Superspreading and the effect of individual variation on disease emergence , 2005, Nature.

[6]  Alessandro Vespignani,et al.  The role of the airline transportation network in the prediction and predictability of global epidemics , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[8]  J. Hyman,et al.  Scaling laws for the movement of people between locations in a large city. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  A. Roddam Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation O Diekmann and JAP Heesterbeek, 2000, Chichester: John Wiley pp. 303, £39.95. ISBN 0-471-49241-8 , 2001 .

[10]  H. Hethcote,et al.  An immunization model for a heterogeneous population. , 1978, Theoretical population biology.

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

[12]  Catherine H Mercer,et al.  Scale-Free Networks and Sexually Transmitted Diseases: A Description of Observed Patterns of Sexual Contacts in Britain and Zimbabwe , 2004, Sexually transmitted diseases.

[13]  Alessandro Vespignani,et al.  EPIDEMIC SPREADING IN SCALEFREE NETWORKS , 2001 .

[14]  Simon Cauchemez,et al.  Strategies for containing an emerging influenza pandemic in SE Asia. Supplementary Information , 2005 .

[15]  L. A. Rvachev,et al.  A mathematical model for the global spread of influenza , 1985 .

[16]  David Bawden,et al.  Book Review: Evolution and Structure of the Internet: A Statistical Physics Approach. , 2006 .

[17]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[18]  L. Amaral,et al.  The web of human sexual contacts , 2001, Nature.

[19]  Reuven Cohen,et al.  Efficient immunization strategies for computer networks and populations. , 2002, Physical review letters.

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

[21]  R. May,et al.  How Viruses Spread Among Computers and People , 2001, Science.

[22]  Robert M. May,et al.  Stability and Complexity in Model Ecosystems , 2019, IEEE Transactions on Systems, Man, and Cybernetics.

[23]  N. Ferguson,et al.  Planning for smallpox outbreaks , 2003, Nature.

[24]  M. Guinchard,et al.  L'International Air Transport Association , 1956 .

[25]  T. Geisel,et al.  Forecast and control of epidemics in a globalized world. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[26]  A. Flahault,et al.  A method for assessing the global spread of HIV-1 infection based on air travel. , 1992, Mathematical population studies.

[27]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[28]  O. Diekmann,et al.  Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation , 2000 .

[29]  R. May,et al.  Dimensions of superspreading , 2005, Nature.

[30]  R M May,et al.  Spatial, temporal, and genetic heterogeneity in host populations and the design of immunization programmes. , 1984, IMA journal of mathematics applied in medicine and biology.

[31]  B. Bolker,et al.  Chaos and biological complexity in measles dynamics , 1993, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[32]  G. Glass,et al.  Assessing the impact of airline travel on the geographic spread of pandemic influenza , 2003 .

[33]  B. M. Fulk MATH , 1992 .

[34]  I. Longini A mathematical model for predicting the geographic spread of new infectious agents , 1988 .

[35]  J. H. Ellis,et al.  Modeling the Spread of Annual Influenza Epidemics in the U.S.: The Potential Role of Air Travel , 2004, Health care management science.

[36]  J. Yorke,et al.  Gonorrhea Transmission Dynamics and Control , 1984 .

[37]  A. Danchin,et al.  The Severe Acute Respiratory Syndrome , 2003 .

[38]  Alessandro Vespignani,et al.  Immunization of complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  R. Guimerà,et al.  The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[40]  Y. Guan,et al.  The severe acute respiratory syndrome. , 2003, The New England journal of medicine.

[41]  Alessandro Vespignani,et al.  The Structure of Interurban Traffic: A Weighted Network Analysis , 2005, physics/0507106.

[42]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[43]  M. Keeling Models of foot-and-mouth disease , 2005, Proceedings of the Royal Society B: Biological Sciences.

[44]  Roy M. Anderson,et al.  Spatial heterogeneity and the design of immunization programs , 1984 .

[45]  S. Cornell,et al.  Dynamics of the 2001 UK Foot and Mouth Epidemic: Stochastic Dispersal in a Heterogeneous Landscape , 2001, Science.

[46]  M. Keeling,et al.  Estimating spatial coupling in epidemiological systems: a mechanistic approach , 2002 .

[47]  A. Nizam,et al.  Containing Pandemic Influenza at the Source , 2005, Science.

[48]  Arthur Massey,et al.  Epidemiology in Relation to Air Travel , 1933, The Indian Medical Gazette.

[49]  M. Elizabeth Halloran,et al.  Containing Pandemic Influenza at the Source , 2005, Science.

[50]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[51]  Grenfell,et al.  Cities and villages: infection hierarchies in a measles metapopulation , 1998 .