December  2011, 4(6): 1499-1509. doi: 10.3934/dcdss.2011.4.1499

A computational study of avian influenza

1. 

College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

2. 

Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, United States

3. 

Mathematics Department, College of William and Mary, Williamsburg, VA 23187, United States

Received  April 2009 Revised  October 2009 Published  December 2010

We propose a PDE model and conduct numerical simulation to study the temporal and spatial dynamics of the Avian Influenza, and investigate its epidemic and possibly pandemic effects in both the bird and human populations. We present several numerical examples to carefully study the population dynamics with small initial perturbations. Our results show that in the absence of external controls, any small amount of initial infection would lead to an outbreak of the influenza with considerably high death rates in both birds and human beings.
Citation: Shu Liao, Jin Wang, Jianjun Paul Tian. A computational study of avian influenza. Discrete and Continuous Dynamical Systems - S, 2011, 4 (6) : 1499-1509. doi: 10.3934/dcdss.2011.4.1499
References:
[1]

D. A. Anderson, J. C. Tannehill and R. H. Pletcher, "Computational Fluid Mechanics and Heat Transfer," Hemisphere Publishing Corporation, 1984.

[2]

S. Deckelman and J. P. Tian, A case study of disease ecology: Modeling of avian flu, preprint, (2010).

[3]

V. D. Goot et al., Comparison of the transmission characteristics of low and high pathogenicity avian influenza A virus (H5N2), Epidemiological Infections, 131 (2003), 1003-1013. doi: 10.1017/S0950268803001067.

[4]

T. Horimoto and Y. Kawaoka, Pandemic threat posed by avian influenza A viruses, Clinical Microbiology Reviews, Jan., (2001), 129-149. doi: 10.1128/CMR.14.1.129-149.2001.

[5]

T. Ito, et al, Generation of a highly pathogenic avian influenza A virus from an avirulent field isolated by passaging in chickens, The Journal of Virology, (2001), 4439-4443. doi: 10.1128/JVI.75.9.4439-4443.2001.

[6]

M. Lewis, J.Renclawowicz and P. v. d. Driessche, Traveling waves and spread rates for a West Nile virus model, Bulletin of Mathematical Biology, 68 (2006), 3-23. doi: 10.1007/s11538-005-9018-z.

[7]

B. Olsen et al., Global patterns of influenza A virus in wild birds, Science, 312 (2006), 384-388. doi: 10.1126/science.1122438.

[8]

R. R. Rogoes and S. Bonhoeffer, Emergence of drug-resistant influenza virus: Population dynamics considerations, Science, 312 (2006), 389-391. doi: 10.1126/science.1122947.

[9]

J. Shi, J. P. Tian and X. Hou, A model for emergence of high pathogenicity avian influenza virus from outbreaks with low pathogenicity avian influenza virus, preprint, (2010).

[10]

J. P. Tian, Case study of disease ecology: Avian influenza a virus, international symposium on ecology, Evolution and Modeling of Disease Dynamics, Beijing, China, (2007).

[11]

 , World health organization web page: www.who.org.  

[12]

 , Center for disease control and prevention web page: www.cdc.gov.  

show all references

References:
[1]

D. A. Anderson, J. C. Tannehill and R. H. Pletcher, "Computational Fluid Mechanics and Heat Transfer," Hemisphere Publishing Corporation, 1984.

[2]

S. Deckelman and J. P. Tian, A case study of disease ecology: Modeling of avian flu, preprint, (2010).

[3]

V. D. Goot et al., Comparison of the transmission characteristics of low and high pathogenicity avian influenza A virus (H5N2), Epidemiological Infections, 131 (2003), 1003-1013. doi: 10.1017/S0950268803001067.

[4]

T. Horimoto and Y. Kawaoka, Pandemic threat posed by avian influenza A viruses, Clinical Microbiology Reviews, Jan., (2001), 129-149. doi: 10.1128/CMR.14.1.129-149.2001.

[5]

T. Ito, et al, Generation of a highly pathogenic avian influenza A virus from an avirulent field isolated by passaging in chickens, The Journal of Virology, (2001), 4439-4443. doi: 10.1128/JVI.75.9.4439-4443.2001.

[6]

M. Lewis, J.Renclawowicz and P. v. d. Driessche, Traveling waves and spread rates for a West Nile virus model, Bulletin of Mathematical Biology, 68 (2006), 3-23. doi: 10.1007/s11538-005-9018-z.

[7]

B. Olsen et al., Global patterns of influenza A virus in wild birds, Science, 312 (2006), 384-388. doi: 10.1126/science.1122438.

[8]

R. R. Rogoes and S. Bonhoeffer, Emergence of drug-resistant influenza virus: Population dynamics considerations, Science, 312 (2006), 389-391. doi: 10.1126/science.1122947.

[9]

J. Shi, J. P. Tian and X. Hou, A model for emergence of high pathogenicity avian influenza virus from outbreaks with low pathogenicity avian influenza virus, preprint, (2010).

[10]

J. P. Tian, Case study of disease ecology: Avian influenza a virus, international symposium on ecology, Evolution and Modeling of Disease Dynamics, Beijing, China, (2007).

[11]

 , World health organization web page: www.who.org.  

[12]

 , Center for disease control and prevention web page: www.cdc.gov.  

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