Abstract.
We construct a very simple epidemic model for influenza spreading in an age-class-distributed population, by coupling a lattice gas model for the population dynamics with a SIR stochastic model for susceptible, infected and removed/immune individuals. We use as a test case the age-distributed Italian epidemiological data for the novel influenza A(H1N1). The most valuable features of this model are its country-independent and virus-independent structure (few demographic, social and virological data are used to fix some parameters), its large statistic due to a very short run-time machine, and its easy generalizability to include mitigation strategies. In spite of its simplicity, the model presented reproduces the epidemiological Italian data, with sensible predictions for the reproduction number and theoretically interesting results for the generation time distribution.
Similar content being viewed by others
References
J.K. Taubenberger, A.H. Reid, R.M. Lourens, R. Wang, G. Jin, Nature 437, 889 (2005)
N.P. Johnson, J. Mueller, Bull. Hist. Med. Spring 76, 105 (2002)
J.S. Koen, Am. J. Vet. Med. 14, 468 (1919)
P.P. Laidlaw, Lancet 1, 1118 (1935)
W.I.B. Beveridge, New Scientist 23, 790 (1978)
S.E. Lindstrom, N.J. Cox, A. Klimov, Virology 328, 101 (2004)
C. Scholtissek, W. Rohde, V. Von Hoyningen, R. Rott, Virology 87, 13 (1978)
Center for Disease Control, MMWR. 58, 400 (2009)
Center for Disease Control, MMWR. 58, 467 (2009)
V. Trifonov, H. Khiabanian, B. Greenbaum, R. Rabadan, Euro Surveill. 14, 19193 (2009)
C. Scholtissek, Med Princip Prac. 2, 65 (1990)
W.O. Kermack, A.G. McKendrick, Proc. R. Soc. London, Ser. A 115, 700 (1927)
R.M. Anderson, R.M. May, Infectious Diseases of Humans (Oxford University Press, Oxford, UK, 1991)
L.A. Rvachev, I.M. Longini, Math. Biosci. 75, 3 (1985)
L. Hufnagel, D. Brockmann, T. Geisel, Proc. Natl. Acad. Sci. U.S.A. 101, 15124 (2004)
T.C. Germann, K. Kadau, I.M. Longini, C.A. Macken, Proc. Natl. Acad. Sci. U.S.A. 103, 5935 (2006)
N.M. Ferguson, D.A.T. Cummings, S. Cauchemez, C. Fraser, S. Riley, A. Meeyai, S. Iamsirithaworn, D.S. Burke, Nature 437, 209 (2005)
H. Yasuda, K. Suzuki, Euro Surveill. 14, 19385 (2009)
L.R. Elveback, J.P. Fox, E. Ackerman, A. Langworthy, M. Boyd, L. Gatewood, Am. J. Epidemiol. 103, 152 (1976)
S. Merler, M. Ajelli, Proc. R. Soc. B 277, 557 (2010)
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)
M.E. Halloran, I.M. Longini, D.M. Cowart, A Nizam, Vaccine 20, 3254 (2002)
M.E. Halloran, I.M. Longini, A. Nizam, Y. Yang, Science 298, 1428 (2002)
I.M. Longini, M.E. Halloran, A. Nizam, Y. Yang, Am. J. Epidemiol. 159, 623 (2004)
I.M. Longini, A. Nizam, S. Xu, K. Ungchusak, W. Hanshaoworakul, D.A.T. Cummings, M.E. Halloran, Science 309, 1083 (2005)
N.M. Ferguson, D.A.T. Cummings, C. Fraser, J.C. Cajka, P.C. Cooley, D.S. Burke, Nature 442, 448 (2006)
N.E. Basta, D.L. Chao, M.E. Halloran, L. Matrajt, I.M. Longini Jr., Am. J. Epidemiol. 15, 679 (2009)
Y. Yang, J.D. Sugimoto, M.E. Halloran, N.E. Basta, D.L. Chao, L. Matrajt, G. Potter, E. Kenah, I.M. Longini Jr., Science 326, 729 (2009)
F. Odaira, H. Takahashi, T. Toyokawa, Y. Tsuchihashi, T. Kodama, Y. Yahata, T. Sunagawa, K. Taniguchi, N. Okabe, Euro Surveill. 14, 19320 (2009)
A study of the model for different finite dimensions, $d$, of the lattice is in progress. We have performed simulations on regular lattices with $d=2$, 3, 4 and 6 (where each site has $2\cdot d$ nearest-neighbor sites). Preliminary results show that, fixed the total number of sites and the total number of individuals (occupied sites), it is possible to reproduce the maximum of the histogram shown in fig. fig1 with transmission probability, $P_a$, 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
R. Pemantle, Ann. Probabil. 20, 2089 (1992)
S.Y. Del Valle, J.M. Hyman, H.W. Hethcote, S.G. Eubank, Social Networks 29, 539 (2007)
At high values of $\beta$ 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 $\beta$ are not considered at all.
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
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
H. Khiabanian, M.G. Farrell, K.St. George, R. Rabadan, PLoS ONE 4 e6832. doi:10.1371/journal.pone.0006832 (2009)
E. Miller, K. Hoschler, P. Hardelid, E. Stanford, N. Andrews, M. Zambon, Lancet 375, 1100 (2010)
C. Fraser et al., Science 324, 1557 (2009)
J. Wallinga, M. Lipsitch, Proc. R. Soc. B 274, 599 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fierro, A., Liccardo, A. A simple stochastic lattice gas model for H1N1 pandemic. Application to the Italian epidemiological data. Eur. Phys. J. E 34, 11 (2011). https://doi.org/10.1140/epje/i2011-11011-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2011-11011-2