# Modelling and analysis of influenza A (H1N1) on networks

Zhen Jin1, Juping Zhang1, Li-Peng Song1, Gui-Quan Sun1, Jianli Kan2 and Huaiping Zhu3*

Author Affiliations

1 Department of Mathematics, North University of China, Taiyuan 030051, China

2 Chinese Center for Disease Control and Prevention, Beijing 10050, China

3 Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Canada, M3J 1P3

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BMC Public Health 2011, 11(Suppl 1):S9  doi:10.1186/1471-2458-11-S1-S9

Published: 25 February 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.