A Lattice Model for Influenza Spreading

We construct a stochastic SIR model for influenza spreading on a D-dimensional lattice, which represents the dynamic contact network of individuals. An age distributed population is placed on the lattice and moves on it. The displacement from a site to a nearest neighbor empty site, allows individuals to change the number and identities of their contacts. The dynamics on the lattice is governed by an attractive interaction between individuals belonging to the same age-class. The parameters, which regulate the pattern dynamics, are fixed fitting the data on the age-dependent daily contact numbers, furnished by the Polymod survey. A simple SIR transmission model with a nearest neighbors interaction and some very basic adaptive mobility restrictions complete the model. The model is validated against the age-distributed Italian epidemiological data for the influenza A(H1N1) during the season, with sensible predictions for the epidemiological parameters. For an appropriate topology of the lattice, we find that, whenever the accordance between the contact patterns of the model and the Polymod data is satisfactory, there is a good agreement between the numerical and the experimental epidemiological data. This result shows how rich is the information encoded in the average contact patterns of individuals, with respect to the analysis of the epidemic spreading of an infectious disease.

[1]  Emilio Zagheni,et al.  What types of contacts are important for the spread of infections?: using contact survey data to explore European mixing patterns. , 2011, Epidemics.

[2]  L. Meyers,et al.  Susceptible–infected–recovered epidemics in dynamic contact networks , 2007, Proceedings of the Royal Society B: Biological Sciences.

[3]  Alessandro Vespignani,et al.  The GLEaMviz computational tool, a publicly available software to explore realistic epidemic spreading scenarios at the global scale , 2011, BMC infectious diseases.

[4]  Matt J Keeling,et al.  Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[5]  M. Lipsitch,et al.  How generation intervals shape the relationship between growth rates and reproductive numbers , 2007, Proceedings of the Royal Society B: Biological Sciences.

[6]  K. Aihara,et al.  Transmission of severe acute respiratory syndrome in dynamical small-world networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  D. Morineau,et al.  Phase separation of a binary liquid in anodic aluminium oxide templates , 2011, The European physical journal. E, Soft matter.

[8]  E. Zagheni,et al.  Using time-use data to parameterize models for the spread of close-contact infectious diseases. , 2008, American journal of epidemiology.

[9]  W. Edmunds,et al.  Delaying the International Spread of Pandemic Influenza , 2006, PLoS medicine.

[10]  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.

[11]  Raul Rabadan,et al.  Differences in Patient Age Distribution between Influenza A Subtypes , 2009, PloS one.

[12]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[13]  Chen-Ping Zhu,et al.  Scaling of directed dynamical small-world networks with random responses. , 2003, Physical review letters.

[14]  A L Lloyd,et al.  Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics. , 2001, Theoretical population biology.

[15]  Thilo Gross,et al.  Epidemic dynamics on an adaptive network. , 2005, Physical review letters.

[16]  M. Newman.  Spread of epidemic disease on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  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.

[18]  F. Y. Wu.  The Potts model , 1982 .

[19]  M E J Newman,et al.  Predicting epidemics on directed contact networks. , 2006, Journal of theoretical biology.

[20]  N. Andrews,et al.  Incidence of 2009 pandemic influenza A H1N1 infection in England: a cross-sectional serological study , 2010, The Lancet.

[21]  C. Macken,et al.  Mitigation strategies for pandemic influenza in the United States. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Matteo Chinazzi,et al.  Little Italy: An Agent-Based Approach to the Estimation of Contact Patterns- Fitting Predicted Matrices to Serological Data , 2010, PLoS Comput. Biol..

[23]  S. Merler,et al.  The role of population heterogeneity and human mobility in the spread of pandemic influenza , 2010, Proceedings of the Royal Society B: Biological Sciences.

[24]  R. Mikolajczyk,et al.  Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases , 2008, PLoS medicine.

[25]  Jari Saramäki,et al.  Modelling development of epidemics with dynamic small-world networks. , 2005, Journal of theoretical biology.

[26]  Herbert W. Hethcote,et al.  Mixing patterns between age groups in social networks , 2007, Soc. Networks.

[27]  Alessandro Vespignani,et al.  Towards a Characterization of Behavior-Disease Models , 2011, PloS one.

[28]  C. Furlanello,et al.  Mitigation Measures for Pandemic Influenza in Italy: An Individual Based Model Considering Different Scenarios , 2008, PloS one.

[29]  V. Jansen,et al.  Modelling the influence of human behaviour on the spread of infectious diseases: a review , 2010, Journal of The Royal Society Interface.

[30]  Jeremi K. Ochab,et al.  Shift of percolation thresholds for epidemic spread between static and dynamic small-world networks , 2010, 1011.2985.

[31]  David R. de Souza,et al.  Stochastic lattice gas model describing the dynamics of the SIRS epidemic process , 2009, 0908.1296.

[32]  M. Newman,et al.  Epidemics and percolation in small-world networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[33]  M. Newman,et al.  Scaling and percolation in the small-world network model. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[35]  D. Watts,et al.  Multiscale, resurgent epidemics in a hierarchical metapopulation model. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Leticia F. Cugliandolo,et al.  Topics in coarsening phenomena , 2009, 0911.0771.

[37]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[38]  A. Fierro,et al.  A simple stochastic lattice gas model for H1N1 pandemic. Application to the Italian epidemiological data , 2011, The European physical journal. E, Soft matter.

[39]  Joshua M. Epstein,et al.  Controlling Pandemic Flu: The Value of International Air Travel Restrictions , 2007, PloS one.

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

[41]  Berg,et al.  Multicanonical ensemble: A new approach to simulate first-order phase transitions. , 1992, Physical review letters.

[42]  E. Lyons,et al.  Pandemic Potential of a Strain of Influenza A (H1N1): Early Findings , 2009, Science.

[43]  D. Cummings,et al.  Strategies for containing an emerging influenza pandemic in Southeast Asia , 2005, Nature.

[44]  M. Kretzschmar,et al.  Using data on social contacts to estimate age-specific transmission parameters for respiratory-spread infectious agents. , 2006, American journal of epidemiology.

[45]  Alessandro Vespignani,et al.  Modeling the Worldwide Spread of Pandemic Influenza: Baseline Case and Containment Interventions , 2007, PLoS medicine.

[46]  Alessandro Vespignani,et al.  Comparing large-scale computational approaches to epidemic modeling: Agent-based versus structured metapopulation models , 2010, BMC infectious diseases.

[47]  Gail E. Potter,et al.  The Transmissibility and Control of Pandemic Influenza A (H1N1) Virus , 2009, Science.

[48]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .