Parameter Scaling for Epidemic Size in a Spatial Epidemic Model with Mobile Individuals

In recent years, serious infectious diseases tend to transcend national borders and widely spread in a global scale. The incidence and prevalence of epidemics are highly influenced not only by pathogen-dependent disease characteristics such as the force of infection, the latent period, and the infectious period, but also by human mobility and contact patterns. However, the effect of heterogeneous mobility of individuals on epidemic outcomes is not fully understood. Here, we aim to elucidate how spatial mobility of individuals contributes to the final epidemic size in a spatial susceptible-exposed-infectious-recovered (SEIR) model with mobile individuals in a square lattice. After illustrating the interplay between the mobility parameters and the other parameters on the spatial epidemic spreading, we propose an index as a function of system parameters, which largely governs the final epidemic size. The main contribution of this study is to show that the proposed index is useful for estimating how parameter scaling affects the final epidemic size. To demonstrate the effectiveness of the proposed index, we show that there is a positive correlation between the proposed index computed with the real data of human airline travels and the actual number of positive incident cases of influenza B in the entire world, implying that the growing incidence of influenza B is attributed to increased human mobility.

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

[2]  Romualdo Pastor-Satorras,et al.  Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  N. Boccara,et al.  Automata network SIR models for the spread of infectious diseases in populations of moving individuals , 1992 .

[4]  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.

[5]  Alessandro Vespignani,et al.  Human Mobility Networks, Travel Restrictions, and the Global Spread of 2009 H1N1 Pandemic , 2011, PloS one.

[6]  Churn-Jung Liau,et al.  Efficient Simulation of the Spatial Transmission Dynamics of Influenza , 2010, PloS one.

[7]  R. Anderson,et al.  Epidemic thresholds and vaccination in a lattice model of disease spread. , 1997, Theoretical population biology.

[8]  Ming Tang,et al.  Epidemic spreading by objective traveling , 2009 .

[9]  Alessandro Vespignani,et al.  Reaction–diffusion processes and metapopulation models in heterogeneous networks , 2007, cond-mat/0703129.

[10]  Ming Tang,et al.  Numerical identification of epidemic thresholds for susceptible-infected-recovered model on finite-size networks , 2015, Chaos.

[11]  Alessandro Vespignani,et al.  Multiscale mobility networks and the spatial spreading of infectious diseases , 2009, Proceedings of the National Academy of Sciences.

[12]  Neil M. Ferguson,et al.  Evaluating the Adequacy of Gravity Models as a Description of Human Mobility for Epidemic Modelling , 2012, PLoS Comput. Biol..

[13]  Harriet L. Mills,et al.  The Spatial Resolution of Epidemic Peaks , 2014, PLoS Comput. Biol..

[14]  Denis Mollison,et al.  Spatial Contact Models for Ecological and Epidemic Spread , 1977 .

[15]  B Grenfell,et al.  Empirical determinants of measles metapopulation dynamics in England and Wales , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

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

[17]  Masaya M. Saito,et al.  Enhancement of Collective Immunity in Tokyo Metropolitan Area by Selective Vaccination against an Emerging Influenza Pandemic , 2013, PloS one.

[18]  Anna T. Lawniczak,et al.  Individual-based lattice model for spatial spread of epidemics , 2002, nlin/0207048.

[19]  Alessandro Vespignani,et al.  Modeling the spatial spread of infectious diseases: The GLobal Epidemic and Mobility computational model , 2010, J. Comput. Sci..

[20]  Alessandro Vespignani,et al.  Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: theory and simulations. , 2007, Journal of theoretical biology.

[21]  Gouhei Tanaka,et al.  Random and Targeted Interventions for Epidemic Control in Metapopulation Models , 2014, Scientific Reports.

[22]  Alessandro Vespignani,et al.  Invasion threshold in heterogeneous metapopulation networks. , 2007, Physical review letters.

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

[24]  Zhongyuan Ruan,et al.  Epidemic spreading with information-driven vaccination. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Ian M. Hall,et al.  Comparison of smallpox outbreak control strategies using a spatial metapopulation model , 2007, Epidemiology and Infection.

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

[27]  R. Anderson,et al.  Persistence and dynamics in lattice models of epidemic spread. , 1996, Journal of theoretical biology.

[28]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[29]  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.

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

[31]  M. Keeling,et al.  Modeling Infectious Diseases in Humans and Animals , 2007 .

[32]  KARL PEARSON,et al.  The Problem of the Random Walk , 1905, Nature.

[33]  Laura M. Glass,et al.  Targeted Social Distancing Designs for Pandemic Influenza , 2006, Emerging infectious diseases.

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

[35]  Keiji Fukuda,et al.  Nonpharmaceutical Interventions for Pandemic Influenza, International Measures , 2006, Emerging infectious diseases.

[36]  J. H. Ellis,et al.  Erratum: Assessing the Impact of Airline Travel on the Geographic Spread of Pandemic Influenza , 2004, European Journal of Epidemiology.

[37]  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.

[38]  P. Grassberger On the critical behavior of the general epidemic process and dynamical percolation , 1983 .

[39]  Ángel Martín del Rey,et al.  Modeling epidemics using cellular automata , 2006, Applied Mathematics and Computation.

[40]  S. Riley Large-Scale Spatial-Transmission Models of Infectious Disease , 2007, Science.

[41]  David J. Philp,et al.  Quantifying social distancing arising from pandemic influenza , 2007, Journal of The Royal Society Interface.

[42]  Ming Tang,et al.  Recovery rate affects the effective epidemic threshold with synchronous updating , 2016, Chaos.

[43]  Y. Xia,et al.  Measles Metapopulation Dynamics: A Gravity Model for Epidemiological Coupling and Dynamics , 2004, The American Naturalist.