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Modelling and analysis of influenza A (H1N1) on networks - PubMed

  • ️Sat Jan 01 2011

Modelling and analysis of influenza A (H1N1) on networks

Zhen Jin et al. BMC Public Health. 2011.

Abstract

Background: In April 2009, a new strain of H1N1 influenza virus, referred to as pandemic influenza A (H1N1) was first detected in humans in the United States, followed by an outbreak in the state of Veracruz, Mexico. Soon afterwards, this new virus kept spreading worldwide resulting in a global outbreak. In China, the second Circular of the Ministry of Health pointed out that as of December 31, 2009, the country's 31 provinces had reported 120,000 confirmed cases of H1N1.

Methods: We formulate an epidemic model of influenza A based on networks. We calculate the basic reproduction number and study the effects of various immunization schemes. The final size relation is derived for the network epidemic model. The model parameters are estimated via least-squares fitting of the model solution to the observed data in China.

Results: For the network model, we prove that the disease-free equilibrium is globally asymptotically stable when the basic reproduction is less than one. The final size will depend on the vaccination starting time, T, the number of infective cases at time T and immunization schemes to follow. Our theoretical results are confirmed by numerical simulations. Using the parameter estimates based on the observation data of the cumulative number of hospital notifications, we estimate the basic reproduction number R0 to be 1.6809 in China.

Conclusions: Network modelling supplies a useful tool for studying the transmission of H1N1 in China, capturing the main features of the spread of H1N1. While a uniform, mass-immunization strategy helps control the prevalence, a targeted immunization strategy focusing on specific groups with given connectivity may better control the endemic.

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Figures

Figure 1
Figure 1

The data of the Influenza A infection in China. The data of the influenza A infection in China reported by Chinese CDC from June 1 to November 22, 2009.

Figure 2
Figure 2

The model. Flow diagram of the transmission. Individuals may be Susceptible, Exposed, Asymptomatic, Infected or Recovered.

Figure 3
Figure 3

Observed data and model simulation. Observed data and model simulation of the number of infected individuals. The minimum degree is 3 and maximum degree is 100.

Figure 4
Figure 4

R0 as a function of k2 and p. R0 is plotted as a function of k2 and p. Here, k1 = 10, λ1 = λ2 = 0.0104, δ = 0.4, α1 = α2 = 1/7 and P(k) = 2m2k–v (m = 3 and ν = 3.5).

Figure 5
Figure 5

The final sizes for susceptible, recovered and vaccinated population. The final sizes of the susceptible, recovered and vaccinated are plotted as a function of p. We use parameters λ1 = 0.01, λ2 = 0.188, δ = 0.4, α1 = α2 = 0.141, γ = 0.85 and P(k) = 2m2k–ν (m = 3 and ν = 3.5).

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References

    1. WHO. Pandemic (H1N1) 2009 - update 82. http://www.who.int/csr/don/2010 01 08/en/
    1. H1N1 Public Files. http://www.moh.gov.cn/publicfiles/business/htmlfiles/mohwsyjbgs/s7863/20...
    1. Updated Interim Recommendations for the Use of Antiviral Medications in the Treatment and Prevention of Influenza for the 2009-2010 Season. http://www.cdc.gov/h1n1flu/recommendations.htm
    1. Bronze MS. H1N1 Influenza (Swine Flu) http://emedicine.medscape.com/article/1807048-overview
    1. Heffernan JM, Smith RJ, Wahl LM. Perspectives on the basic reproductive ratio. J. R. Soc. Interface. 2005;2(4):281–293. doi: 10.1098/rsif.2005.0042. - DOI - PMC - PubMed

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