Simple models for containment of a pandemic
Abstract
Stochastic simulations of network models have become the standard approach to studying epidemics. We show that many of the predictions of these models can also be obtained from simple classical deterministic compartmental models. We suggest that simple models may be a better way to plan for a threatening pandemic with location and parameters as yet unknown, reserving more detailed network models for disease outbreaks already underway in localities where the social networks are well identified.
We formulate compartmental models to describe outbreaks of influenza and attempt to manage a disease outbreak by vaccination or antiviral treatment. The models give an important prediction that may not have been noticed in other models, namely that the number of doses of antiviral treatment required is extremely sensitive to the number of initial infectives. This suggests that the actual number of doses needed cannot be estimated with any degree of reliability. The model is applicable to pre-epidemic vaccination, such as annual vaccination programs in anticipation of an ‘ordinary’ influenza outbreak with limited drift, and as a combination of treatment both before and during an epidemic.
References
-
Balicer R.D, Huerta M, Davidovitch N& Grotto I . 2005 Cost-benefit of stockpiling drugs for influenza pandemic. Emerg. Infect. Dis 11, 1280–1282. Crossref, PubMed, Web of Science, Google Scholar -
Brauer F . 2006 Some simple epidemic models. Math. Biosci. Eng 3, 1–15. Crossref, PubMed, Web of Science, Google Scholar -
Diekmann O& Heesterbeek J.A.P . 2000 Mathematical epidemiology of infectious diseases. Chichester:Wiley. Google Scholar -
Ferguson N.M, Cummings D.A.T, Cauchemez S, Fraser C, Riley S, Meeyai A, Iamsirithaworn S& Burke D.S . 2005 Strategies for containing an emerging influenza pandemic in Southeast Asia. Nature 437, 209–214.doi:10.1038/nature04017. Crossref, PubMed, Web of Science, Google Scholar -
Gani R, Hughes H, Griffin T, Medlock J& Leach S . 2005 Potential impact of antiviral use on hospitalizations during influenza pandemic. Emerg. Infect. Dis 11, 1355–1362. Crossref, PubMed, Web of Science, Google Scholar -
Gumel A, 2004 Modelling strategies for controlling SARS outbreaks. Proc. R. Soc. B 271, 2223–2232.doi:10.1098/rspb.2004.2800. Link, Web of Science, Google Scholar -
Longini I.M, Halloran M.E, Nizam A& Yang Y . 2004 Containing pandemic influenza with antiviral agents. Am. J. Epidemiol 159, 623–633.doi:10.1093/aje/kwh092. Crossref, PubMed, Web of Science, Google Scholar -
Longini I.M, Nizam A, Xu S, Ungchusak K, Hanshaoworakul W, Cummings D.A.T& Halloran M.E . 2005 Containing pandemic influenza at the source. Science 309, 1083–1087.doi:10.1126/science.1115717. Crossref, PubMed, Web of Science, Google Scholar -
van den Driessche P& Watmough J . 2002 Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission. Math. Biosci 180, 29–48.doi:10.1016/S0025-5564(02)00108-6. Crossref, PubMed, Web of Science, Google Scholar