zbMATH — the first resource for mathematics

Epidemic patch models applied to pandemic influenza: contact matrix, stochasticity, robustness of predictions. (English) Zbl 1168.92325
Summary: Due to the recent emergence of the H5N1 virus, the modelling of pandemic influenza has become a relevant issue. We present an SEIR model formulated to simulate a possible outbreak in Italy, analysing its structure and, more generally, the effect of including specific details into a model. These details regard population heterogeneities, such as age and spatial distribution, as well as stochasticity, that regulates the epidemic dynamics when the number of infectives is low. We discuss and motivate the specific modelling choices made when building the model and investigate how the model details influence the predicted dynamics. Our analysis may help in deciding which elements of complexity are worth including in the design of a deterministic model for pandemic influenza, in a balance between, on the one hand, keeping the model computationally efficient and the number of parameters low and, on the other hand, maintaining the necessary realistic features.

92D30 Epidemiology
37N25 Dynamical systems in biology
Full Text: DOI
[1] Li, K.S.; Guan, Y.; Wang, J.; Smith, G.J.D.; Xu, K.M.; Duan, L.; Rahardjo, A.P.; Puthavathana, P.; Buranathai, C.; Nguyen, T.D.; Estoepangestie, A.T.S.; Chaisingh, A.; Auewarakul, P.; Long, H.T.; Hanh, N.T.H.; Webby, R.J.; Poon, L.L.M.; Chen, H.; Shortridge, K.F.; Yuen, K.Y.; Webster, R.G.; Peiris, J.S.M., Genesis of a highly pathogenic and potentially pandemic H5N1 influenza virus in eastern Asia, Nature, 430, 6996, 209, (2004)
[2] World Health Organization, Outbreak news, Avian influenza, Turkey-update, Weekly Epidemiological Record 81, 2006.
[3] World Health Organization, Epidemiology of WHO-confirmed human cases of avian A(H5N1) infection, Weekly Epidemiological Record, vol. 81, 2006.
[4] Monto, A.S., Vaccines and antiviral drugs in pandemic preparedness, Emerg. infect. dis., 12, 55, (2006)
[5] Stephenson, I.; Gust, I.; Kieny, M.P.; Pervikov, Y., Development and evaluation of influenza pandemic vaccines, Lancet infect. dis., 6, 71, (2006)
[6] Influenza team (ECDC), Pandemic preparedness in the European Union – multi-sectoral planning needed, Eurosurveillance 12 (2007).
[7] World Health Organization, WHO global influenza preparedness plan: the role of WHO and recommendations for national measures before and during pandemics, 2005.
[8] Glass, R.J.; Glass, L.M.; Beyeler, W.E.; Min, H.J., Targeted social distancing design for pandemic influenza, Emerg. infect. dis., 12, 1671, (2006)
[9] Chun, B.C., Modelling the impact of pandemic influenza, J. prev. med. public health, 38, 379, (2005)
[10] Doyle, A.; Bonmarin, I.; Levy-Bruhl, D.; Le Strat, Y.L.; Desenclos, J.C., Influenza pandemic preparedness in France: modelling the impact of interventions, J. epidemiol. commun. health, 60, 5, 399, (2006)
[11] EPICO working group, Modelling scenarios of diffusion and control of pandemic influenza, Italy, Eurosurveillance 12(1) (2007) 3105.
[12] Ferguson, N.M.; Cummings, D.A.T.; Fraser, C.; Cajka, J.C.; Cooley, P.C.; Burke, D.S., Strategies for mitigating an influenza pandemic, Pnas, 103, 5935, (2006)
[13] Germann, T.; Kadau, K.; Longini, I.M.; Macken, C.A., Mitigation strategies for pandemic influenza in the united states, Pnas, 103, 5935, (2006)
[14] Hak, E.; Meijboom, M.J.; Buskens, E., Modelling the health – economic impact of the next influenza pandemic in The Netherlands, Vaccine, 24, 6756, (2006)
[15] Longini, I.M.; Halloran, M.E.; Nizam, A.; Yang, Y., Containing pandemic influenza with antiviral agents, Am. J. epidemiol., 159, 623, (2004)
[16] Longini, I.M.; Nizam, A.; Xu, S.; Ungchusak, K.; Hanshaoworakul, W.; Cummings, D.A.T.; Halloran, M.E., Containing pandemic influenza at the source, Science, 309, 1083, (2005)
[17] Patel, R.; Longini, I.M.; Halloran, M.E., Finding optimal vaccination strategies for pandemic influenza using genetic algorithms, J. theor. biol., 234, 201, (2005)
[18] Wu, J.T.; Riley, S.; Fraser, C.; Leung, G.M., Reducing the impact of the next influenza pandemic using household-based public health interventions, Plos med., 3, 1532, (2006)
[19] Ciofi degli Atti, M.L.; Merler, S.; Rizzo, C.; Ajelli, M.; Massari, M.; Manfredi, P.; Furlanello, C.; Scalia Tomba, G.; Iannelli, M., Mitigation measures for pandemic influenza in Italy: an individual based model considering different scenariosinfluenza, Plos one, 3, 3, e1790, (2008)
[20] Arino, J.; Brauer, F.; van den Driessche, P.; Watmough, J.; Wu, J.R., Simple models for containment of a pandemic, J. roy. soc. interface, 3, 453, (2006)
[21] Gani, R.; Hughes, H.; Fleming, D.; Griffin, T.; Medlock, J.; Leach, S., Potential impact of antiviral drug use during influenza pandemic, Emerg. infect. dis., 11, 9, 1355, (2005)
[22] Roberts, M.G.; Baker, M.; Jennings, L.C.; Sertsou, G.; Wilson, N., A model for the spread and control of pandemic influenza in an isolated geographical region, J. roy. soc. interface, 4, 325, (2007)
[23] Flahault, A.; Vergu, E.; Coudeville, L.; Grais, R.F., Strategies for containing a global influenza pandemic, Vaccine, 24, 6751, (2006)
[24] Grais, R.F.; Ellis, J.H.; Glass, G.E., Assessing the impact of airline travel on the geographic spread of pandemic influenza, Eur. J. epidemiol., 18, 1065, (2003)
[25] Colizza, V.; Barrat, A.; Barthelemy, M.; Valleron, A.; Vespignani, A., Modeling the worldwide spread of pandemic influenza: baseline case and containment interventions, Plos med., 4, 95, (2007)
[26] Cooper, B.S.; Pitman, R.J.; Edmunds, W.J.; Gay, N.J., Delaying the international spread of pandemic influenza, Plos med., 3, 845, (2006)
[27] Rizzo, C.; Lunelli, A.; Pugliese, A.; Bella, A.; Manfredi, P.; Scalia Tomba, G.P.; Iannelli, M.; Ciofi degli Atti, M.L., Scenarios of diffusion and control of an influenza pandemic in Italy, Epidemiol. infect., 136, 1650, (2008)
[28] Fleming, D.M.; Elliot, A.J., Lessons from 40 years’ surveillance of influenza in england and wales, Epidemiol. infect., 136, 866, (2008)
[29] Ministero della Salute, Piano nazionale di preparazione e risposta ad una pandemia influenzale. <http://www.ministerosalute.it/imgs/C_17_pubblicazioni_511_allegato.pdf>, 2006.
[30] Ferguson, N.M.; Cummings, D.A.T.; Cauchemez, S.; Fraser, C.; Riley, S.; Meeyai, A.; Iamsirithaworn, S.; Burke, D.S., Strategies for containing an emerging influenza pandemic in southeast Asia, Nature, 437, 209, (2005)
[31] Cauchemez, S.; Carrat, F.; Viboud, C.; Valleron, A.J.; Boelle, P.Y., A Bayesian MCMC approach to study transmission of influenza: application to household longitudinal data, Stat. med., 23, 3469, (2004)
[32] J.M. Hyman, T. LaForce, Bioterrorism: mathematical modeling applications in Homeland security, Frontiers in Applied Mathematics, SIAM, 2003, pp. 215-240 (Chapter 10).
[33] Anderson, R.M.; May, R.M., Infectious diseases of humans: dynamics and control, (1991), Oxford University Oxford
[34] Manfredi, P.; Williams, J.R., Realistic population dynamics in epidemiological models: the impact of population decline on the dynamics of childhood infectious diseases. measles as an example, Math. biosci., 192, 153, (2004) · Zbl 1073.92046
[35] Mossong, J.; Hens, N.; Jit, M.; Beutels, P.; Auranen, K.; Mikolajczyk, R.; Massari, M.; Salmaso, S.; Scalia Tomba, G.; Wallinga, J.; Heijne, J.; Sadkowska-Todys, M.; Rosinska, M.; Edmunds, W.J., Social contacts and mixing patterns relevant to the spread of infectious diseases, Plos med., 5, 381, (2008)
[36] Diekmann, O.; Heesterbeek, J., Mathematical epidemiology of infectious diseases, Chichester, (2000), Wiley New York · Zbl 0997.92505
[37] Diekmann, O.; Heesterbeek, J.A.P.; Metz, J.A.J., On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. math. biol., 28, 365, (1990) · Zbl 0726.92018
[38] Chowell, G.; Ammon, C.E.; Hengartner, N.W.; Hyman, J.M., Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: assessing the effects of hypothetical interventions, J. theor. biol., 241, 193, (2006)
[39] Chowell, G.; Nishiura, H.; Bettencourt, L.M., Comparative estimation of the reproduction number for pandemic influenza from daily case notification data, J. roy. soc. interface, 4, 155, (2007)
[40] Longini, I.M., A mathematical model for predicting the geographic spread of new infectious agents, Math. biosci., 90, 367, (1987) · Zbl 0651.92016
[41] Mills, C.E.; Robins, J.M.; Lipsitch, M., Transmissibility of 1918 pandemic influenza, Nature, 432, 904, (2004)
[42] Rvachev, L.A.; Longini, I.M., A mathematical model for the global spread of influenza, Math. biosci., 75, 3, (1985) · Zbl 0567.92017
[43] Aparicio, J.P.; Solari, H.G., Population dynamics: Poisson approximation and its relation to the Langevin process, Phys. rev. lett., 86, 4183, (2001)
[44] Gustafsson, L., Poisson simulation – a method for generating stochastic variations in continuous system simulation, Simulation, 74, 5, 264, (2000) · Zbl 1039.68800
[45] Gustafsson, L.; Sternad, M., Bringing consistency to simulation of population models - Poisson simulation as a bridge between micro and macro simulation, Math. biosci., 209, 361, (2007) · Zbl 1126.92040
[46] Solari, H.G.; Natiello, M.A., Stochastic population dynamics: the Poisson approximation, Phys. rev. E, 67, 031918, (2003) · Zbl 1318.60084
[47] Nuño, M.; Reichert, T.A.; Chowell, G.; Gumel, A.B., Protecting residential care facilities from pandemic influenza, Proc. natl. acad. sci., 105, 30, 10625, (2008)
[48] Gillespie, D.T., Exact stochastic simulation of coupled chemical reactions, J. phys. chem., 81, 25, 2340, (1977)
[49] Andersson, H.; Britton, T., Stochastic epidemic models and their statistical analysis, (2000), Springer · Zbl 0951.92021
[50] Débarre, F.; Bonhoeffer, S.; Regoes, R.R., The effect of population structure on the emergence of drug resistance during influenza pandemics, J. roy. soc. interface, 4, 16, 893, (2007)
[51] Daems, R.; Del Giudice, G.; Rappuoli, R., Anticipating crisis: towards a pandemic flu vaccination strategy through alignment of public health and industrial policy, Vaccine, 23, 5732, (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.