A simple stochastic lattice gas model for H1N1 pandemic. Application to the Italian epidemiological data

European Physical Journal E

Volumn 34, Issue 2, 2011, Pages

  Fierro, A ^a,b   Liccardo, A ^b,c  

^a CNR   (Italy)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^c INFN SEZIONE DI NAPOLI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL LATTICES; DYNAMIC MODELS; GAS DYNAMICS; POPULATION DYNAMICS; STOCHASTIC SYSTEMS; VIRUSES;

EPIDEMIC MODELING; GENERATION TIME; INFLUENZA A; LATTICE GAS MODEL; MITIGATION STRATEGY; REPRODUCTION NUMBERS; SIMPLE STOCHASTIC; TEST CASE;

STOCHASTIC MODELS;

ADOLESCENT; ADULT; AGE DISTRIBUTION; AGED; ARTICLE; BIOLOGICAL MODEL; CHILD; DIFFUSION; DISEASE TRANSMISSION; GAS; HUMAN; INFANT; INFLUENZA; INFLUENZA VIRUS A H1N1; ITALY; MIDDLE AGED; MONTE CARLO METHOD; NEWBORN; PANDEMIC; PHYSIOLOGY; PRESCHOOL CHILD; REPRODUCIBILITY; STATISTICS; TIME;

ADOLESCENT; ADULT; AGE DISTRIBUTION; AGED; CHILD; CHILD, PRESCHOOL; DIFFUSION; GASES; HUMANS; INFANT; INFANT, NEWBORN; INFLUENZA A VIRUS, H1N1 SUBTYPE; INFLUENZA, HUMAN; ITALY; MIDDLE AGED; MODELS, BIOLOGICAL; MONTE CARLO METHOD; PANDEMICS; REPRODUCIBILITY OF RESULTS; STOCHASTIC PROCESSES; TIME FACTORS; YOUNG ADULT;

EID: 79951974133     PISSN: 12928941     EISSN: 1292895X     Source Type: Journal    
DOI: 10.1140/epje/i2011-11011-2     Document Type: Article

References (39)

1. J.K. Taubenberger A.H. Reid R.M. Lourens R. Wang G. Jin 2005 Nature 437 889 10.1038/nature04230 2005Natur.437..889T (Pubitemid 41486764)
2. N.P. Johnson J. Mueller 2002 Bull. Hist. Med. Spring 76 105 10.1353/bhm.2002.0022
3. J.S. Koen 1919 Am. J. Vet. Med. 14 468
4. P.P. Laidlaw 1935 Lancet 1 1118 10.1016/S0140-6736(01)19376-1
5. W.I.B. Beveridge 1978 New Scientist 23 790
6. S.E. Lindstrom N.J. Cox A. Klimov 2004 Virology 328 101 10.1016/j.virol.2004.06.009 (Pubitemid 39221916)
7. C. Scholtissek W. Rohde V. Von Hoyningen R. Rott 1978 Virology 87 13 10.1016/0042-6822(78)90153-8
8. Center for Disease Control 2009 MMWR. 58 400
9. Center for Disease Control 2009 MMWR. 58 467
10. V. Trifonov H. Khiabanian B. Greenbaum R. Rabadan 2009 Euro Surveill. 14 19193
11. C. Scholtissek 1990 Med Princip Prac. 2 65
12. W.O. Kermack A.G. McKendrick 1927 Proc. R. Soc. London, Ser. A 115 700 10.1098/rspa.1927.0118 1927RSPSA.115..700K
13. R.M. Anderson, R.M. May, Infectious Diseases of Humans (Oxford University Press, Oxford, UK, 1991)
14. L.A. Rvachev I.M. Longini 1985 Math. Biosci. 75 3 0567.92017 10.1016/0025-5564(85)90064-1 800965 (Pubitemid 16243275)
15. L. Hufnagel D. Brockmann T. Geisel 2004 Proc. Natl. Acad. Sci. U.S.A. 101 15124 10.1073/pnas.0308344101 2004PNAS..10115124H (Pubitemid 39391729)
16. T.C. Germann K. Kadau I.M. Longini C.A. Macken 2006 Proc. Natl. Acad. Sci. U.S.A. 103 5935 10.1073/pnas.0601266103 2006PNAS..103.5935G
17. N.M. Ferguson D.A.T. Cummings S. Cauchemez C. Fraser S. Riley A. Meeyai S. Iamsirithaworn D.S. Burke 2005 Nature 437 209 10.1038/nature04017 2005Natur.437..209F (Pubitemid 41294478)
18. H. Yasuda K. Suzuki 2009 Euro Surveill. 14 19385
19. L.R. Elveback J.P. Fox E. Ackerman A. Langworthy M. Boyd L. Gatewood 1976 Am. J. Epidemiol. 103 152
20. S. Merler M. Ajelli 2010 Proc. R. Soc. B 277 557 10.1098/rspb.2009.1605
21. M.L. Ciofi degli Atti, S. Merler, C. Rizzo, M. Ajelli, M. Massari, P. Manfredi, C. Furlanello, G. Scalia Tomba, M. Iannelli, PLoS ONE 3 e1790. doi: 10.1371/journal.pone.0001790 (2008) (Pubitemid 351917325)
22. M.E. Halloran I.M. Longini D.M. Cowart A Nizam 2002 Vaccine 20 3254 10.1016/S0264-410X(02)00316-X (Pubitemid 35245809)
23. M.E. Halloran I.M. Longini A. Nizam Y. Yang 2002 Science 298 1428 10.1126/science.1074674 2002Sci...298.1428H (Pubitemid 35346144)
24. I.M. Longini M.E. Halloran A. Nizam Y. Yang 2004 Am. J. Epidemiol. 159 623 10.1093/aje/kwh092 (Pubitemid 38405377)
25. I.M. Longini A. Nizam S. Xu K. Ungchusak W. Hanshaoworakul D.A.T. Cummings M.E. Halloran 2005 Science 309 1083 10.1126/science.1115717 2005Sci...309.1083L (Pubitemid 41134467)
26. N.M. Ferguson D.A.T. Cummings C. Fraser J.C. Cajka P.C. Cooley D.S. Burke 2006 Nature 442 448 10.1038/nature04795 2006Natur.442..448F (Pubitemid 44264793)
27. N.E. Basta D.L. Chao M.E. Halloran L. Matrajt I.M. Longini Jr. 2009 Am. J. Epidemiol. 15 679 10.1093/aje/kwp237
28. Y. Yang J.D. Sugimoto M.E. Halloran N.E. Basta D.L. Chao L. Matrajt G. Potter E. Kenah I.M. Longini Jr. 2009 Science 326 729 10.1126/science.1177373 2009Sci...326..729Y
29. F. Odaira H. Takahashi T. Toyokawa Y. Tsuchihashi T. Kodama Y. Yahata T. Sunagawa K. Taniguchi N. Okabe 2009 Euro Surveill. 14 19320
30. a, decreasing with increasing d. However we are not able to reproduce the overall histogram for each value of the dimension. In particular we find that the width of the simulated curve decreases increasing d, and the best agreement is found for d=3 and d=4. Instead, the width of the curve obtained with d=2 is larger than the experimental one, which corresponds to a diffusion of the epidemic slower than in the real case. For d=6, we find a curve with a smaller width, corresponding to a faster diffusion of the epidemic. This means that the population is well represented by individuals having a maximum of 6 or 8 simultaneous contacts, while a maximum of 4 (as in 2d lattice) or 12 (as in 6d) are, respectively, unrealistic underestimate and overestimate of the contact number
31. R. Pemantle 1992 Ann. Probabil. 20 2089 0762.60098 10.1214/aop/1176989541 1188054
32. S.Y. Del Valle J.M. Hyman H.W. Hethcote S.G. Eubank 2007 Social Networks 29 539 10.1016/j.socnet.2007.04.005
33. At high values of β the stationary state is not homogeneous: a sort of phase separation occurs where individuals aggregate to form high-density clusters. In the present paper we are not interested in such a case then high values of β are not considered at all.
34. We start with 65 initial infected individuals distributed among the various age classes according to the age-distributed ILI cases registered by the Italian surveillance in the 43rd week, with a reduction factor of 0.015
35. In our simulations the time unit is the Monte Carlo step, which corresponds to the interval when all particles have attempted to move on average one time. The collapse of the numerical data onto the experimental ones is obtained introducing an a priori arbitrary time scale, in particular we put one week equal to 250 Monte Carlo steps
36. H. Khiabanian, M.G. Farrell, K.St. George, R. Rabadan, PLoS ONE 4 e6832. doi: 10.1371/journal.pone.0006832 (2009)
37. E. Miller K. Hoschler P. Hardelid E. Stanford N. Andrews M. Zambon 2010 Lancet 375 1100 10.1016/S0140-6736(09)62126-7
38. C. Fraser 2009 Science 324 1557 10.1126/science.1176062 2009Sci...324.1557F
39. J. Wallinga M. Lipsitch 2007 Proc. R. Soc. B 274 599 10.1098/rspb.2006. 3754 (Pubitemid 47055535)