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Modeling Adaptive Behavior in Influenza Transmission

Published online by Cambridge University Press:  06 June 2012

W. Wang
W. Wang*
Affiliation:
Key Laboratory of Eco-environments in Three Gorges Reservoir Region, School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P. R. China
*
⋆ Corresponding author. E-mail: wendi@swu.edu.cn
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Abstract

Contact behavior plays an important role in influenza transmission. In the progression of influenza spread, human population reduces mobility to decrease infection risks. In this paper, a mathematical model is proposed to include adaptive mobility. It is shown that the mobility response does not affect the basic reproduction number that characterizes the invasion threshold, but reduces dramatically infection peaks, or removes the peaks. Numerical calculations indicate that the mobility response can provide a very good protection to susceptible individuals, and a combination of mobility response and treatment is an effective way to control influenza outbreak.

Keywords

mobilityresponsepatternstability
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 3: Epidemiology , 2012 , pp. 253 - 262
Copyright
© EDP Sciences, 2012

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References

M. Balinska, C. Rizzo. Behavioural responses to influenza pandemics : what do we know ? PLoS. Curr., (2009), p. RRN1037.
Capasso, V., Serio, G.. Ageneralization of the Kermack-McKendrick deterministic epidemic model. Math. Biosci., 42 (1978), 43-61. CrossRefGoogle Scholar
Cui, J., Sun, Y., Zhu, H.. The impact of media on the control of infectious diseases. J. Dynam. Differential Equations, 20 (2008), 31-53. CrossRefGoogle Scholar
Derrick, W. R., van den Driessche, P.. A disease transmision model in a nonconstant population. J. Math. Biol., 31 (1993), 495-512. CrossRefGoogle Scholar
d’Onofrio, A., Manfredi, P.. Information-related changes in contact patterns may trigger oscillations in the endemic prevalence of infectious diseases. J. Theor. Biol., 256 (2009), 473-478. CrossRefGoogle ScholarPubMed
Epstein, J. M., Parker, J., Cummings, D., Hammond, R. A.. Coupled contagion dynamics of fear and disease : mathematical and computational explorations. PLoS One, 3 (2008), e3955. CrossRefGoogle ScholarPubMed
Funk, S., Gilad, E., Jansen, V. A. A.. Endemic disease, awareness, and local behavioural response. J. Theor. Biol., 264 (2010), 501-509. CrossRefGoogle ScholarPubMed
Gao, D., Ruan, S.. An SIS patch model with variable transmission coefficients. Mathematical Biosciences, 232 (2011), 110-115. CrossRefGoogle ScholarPubMed
Kiss, I. Z., Cassell, J., Recker, M., Simon, P. L.. The impact of information transmission on epidemic outbreaks. Math. Biosci., 225 (2010), 1-10. CrossRefGoogle ScholarPubMed
J.P. LaSalle, S. Lefschetz. Stability by Lyapunov’s Direct Method. Academic Press, New York, 1961.
Liu, W. M., Hethcote, H. W., Levin, S. A.. Dynamical behavior of epidemiological models with nonlinear incidence rates. J. Math. Biol., 25 (1987), 359-380. CrossRefGoogle ScholarPubMed
Liu, W. M., Levin, S. A., Iwasa, Y.. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J. Math. Biol., 23 (1986), 187-204. CrossRefGoogle ScholarPubMed
Poletti, P., Caprile, B., Ajelli, M. Pugliese, A., Merler, S.. Spontaneous behavioural changes in response to epidemics. J. Theor. Biol., 260 (2009), 31-40. CrossRefGoogle Scholar
Qiu, Z., Feng, Z.. Transmission dynamics of an influenza model with vaccination and antiviral treatment. Bull. Math. Biol., 72 (2010), 1-33. CrossRefGoogle ScholarPubMed
Ruan, S., Wang, W.. Dynamical behavior of an epidemic model with a nonlinear incidence rate. J. Differential Equations, 188 (2003), 135-163. CrossRefGoogle Scholar
Ruan, S., Wang, W., Levin, S.. The effect of global travel on the spread of SARS. Mathematical Biosciences and Engineering, 3 (2006), 205-218. CrossRefGoogle ScholarPubMed
Sattenspiel, L., Herring, D. A.. Simulating the effect of quarantine on spread of the 1918-19 flue in central Canada. Bull. Math. Biol., 65 (2003), 1-26. CrossRefGoogle Scholar
Sun, C., Yang, W., Arino, J., Khan, K.. Effect of media-induced social distancing on disease transmission in a two patch setting. Math. Biosci., 230 (2011), 87-95. CrossRefGoogle Scholar
Tanaka, M. M., Kumm, J., Feldman, M. W.. Coevolution of pathogens and cultural practices : a new look at behavioral heterogeneity in epidemics. Theor. Popul. Biol., 62 (2002), 111-119. CrossRefGoogle Scholar
Tang, S., Xiao, Y., Yang, Y., Zhou, Y., Wu, J., Ma, Z.. Community-based measures for mitigating the 2009 H1N1 pandemic in China. PLoS One. 5 (2010), e10911. CrossRefGoogle Scholar
van den Driessche, P., Watmough, J.. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci., 180 (2002), 29-48. CrossRefGoogle ScholarPubMed
Wang, W.. Epidemic models with nonlinear infection forces. Mathematical Biosciences and Engineering, 3 (2006), 267-279. CrossRefGoogle ScholarPubMed
Wang, W., Ruan, S.. Simulating the SARS outbreak in Beijing with limited data. J. Theor. Biol., 227 (2004), 369-379. CrossRefGoogle ScholarPubMed
Xiao, D., Ruan, S.. Global analysis of an epidemic model with nonmonotone incidence rate. Math. Biosci., 208 (2007), 419-429. CrossRefGoogle ScholarPubMed