Nonlinear dynamics of avian influenza epidemic models

Mathematical Biosciences

Volumn 283, Issue , 2017, Pages 118-135

  Liu, Sanhong ^a,b   Ruan, Shigui ^b,c   Zhang, Xinan ^b  

^a HUBEI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b CENTRAL CHINA NORMAL UNIVERSITY   (China)

^c University of Miami   (United States)

Author keywords

Allee effect; Avian influenza; Global asymptotical stability; Liapunov function; Periodic solution

Indexed keywords

BIRDS; DYNAMICS; LYAPUNOV FUNCTIONS; POPULATION STATISTICS; VIRUSES;

ALLEE EFFECTS; AVIAN INFLUENZA; GLOBAL ASYMPTOTICAL STABILITY; LIAPUNOV FUNCTION; PERIODIC SOLUTION;

DISEASE CONTROL;

ALLEE EFFECT; AVIAN INFLUENZA; COMPUTER SIMULATION; DISEASE INCIDENCE; DISEASE TRANSMISSION; DISEASE VECTOR; EPIDEMIOLOGY; NONLINEARITY; NUMERICAL MODEL;

ALLEE EFFECT; ARTICLE; AVIAN INFLUENZA; EPIDEMIC; LINEAR SYSTEM; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; NONLINEAR SYSTEM; PREVALENCE; SIMULATION; THEORETICAL STUDY; ZOONOSIS; ANIMAL; BIRD; HUMAN; INFLUENZA; TRANSMISSION;

CHINA;

AVES; INFLUENZA A VIRUS;

ANIMALS; BIRDS; HUMANS; INFLUENZA IN BIRDS; INFLUENZA, HUMAN; NONLINEAR DYNAMICS;

EID: 85002688351     PISSN: 00255564     EISSN: 18793134     Source Type: Journal    
DOI: 10.1016/j.mbs.2016.11.014     Document Type: Article

References (62)

1. [1] Altizer, S., Bartel, R., Han, B.A., Animal migration and infectious disease risk. Science 331 (2011), 296–302.
2. [2] Allee, W.C., Animal Aggregation: A Study in General Sociology. 1931, University of Chicago Press, Chicago.
3. [3] Anderson, R.M., May, R.M., Infectious Diseases of Humans: Dynamics and Control. 1991, Oxford University Press, Oxford.
4. [4] Bao, C., Cui, L., Zhou, M., Hong, L., Wang, H., et al. Live-animal markets and influenza A (H7N9) virus infection. New Eng. J. Med. 368 (2013), 2337–2339.
5. [5] Bourouiba, L., Gourley, S.A., Liu, R., Wu, J., The interaction of migratory birds and domestic poultry and its role in sustaining avian influenza. SIAM J. Appl. Math. 71 (2011), 487–516.
6. [6] Burrows, R., Hofer, H., East, M.L., Population dynamics, intervention and survival in African wild dogs (Lycaon pictus). Proc. R. Soc. B 262 (1995), 235–245.
7. [7] Cai, L., Chen, G., Xiao, D., Multiparametric bifurcations of an epidemiological model with strong Allee effect. J. Math. Biol. 67 (2013), 185–215.
8. [8] Centers for Disease Control and Prevention (CDC), Types of influenza virus, Retrieved January 15, 2014. http://www.cdc.gov/flu/about/viruses/types.htm.
9. [9] Center for Infectious Disease Research and Policy (CIDRAP), China reports three H7N9 infections, two fatal (April 1, 2013). http://www.cidrap.umn.edu/news-perspective/2013/04/china-reports-three-h7n9-infections-two-fatal.
10. [10] Chen, E., Chen, Y., Fu, L., Chen, Z., Gong, Z., et al. Human infection with avian influenza a(H7N9) virus re-emerges in China in winter 2013. Euro Surveill., 18, 2013, 43.
11. [11] Chen, Y., Liang, W., Yang, S., Wu, N., Gao, H., et al. Human infections with the emerging avian influenza a h7n9 virus from wet market poultry: clinical analysis and characterisation of viral genome. Lancet 381 (2013), 1916–1925.
12. [12] Chong, N.S., Smith, R.J., Modeling avian influenza using filippov systems to determine culling of infected birds and quarantine. Nonlinear Anal. Real World Appl. 24 (2015), 196–218.
13. [13] Clifford, D.L., Mazet, J.A.K., Dubovi, E.J., Garcelon, D.K., Coonan, T.J., et al. Pathogen exposure in endangered island fox (Urocyon littoralis) populations: implications for conservation management. Biol. Conserv. 131 (2006), 230–243.
14. [14] Coddington, E.A., Levinson, N., Theory of Ordinary Differential Equations. 1955, McGraw-Hill, New York.
15. [15] Coppel, W.A., Quadratic systems with a degenerate critical point. Bull. Austral. Math. Soc. 38 (1988), 1–10.
16. [16] Coppel, W.A., A new class of quadratic systems. J. Differ. Equ. 92 (1991), 360–372.
17. [17] Coppel, W.A., Stability of Asymptotic Behavior of Differential Equations. 1965, Heath, Boston.
18. [18] de Castro, F., Bolker, B., Mechanisms of disease induced extinction. Ecol. Lett. 8 (2005), 117–126.
19. [19] Diekmann, O., Heesterbeek, J.A.P., Roberts, M.G., The construction of next generation matrices for compartmental epidemic models. J. R. Soc. Interface 7 (2000), 873–885.
20. [20] Friedman, A., Yakubu, A.-A., Fatal disease and demographic Allee effect: population persistence and extinction. J. Biol. Dyn. 6 (2012), 495–508.
21. [21] Friedman, A., Yakubu, A.-A., Host demographicAllee effect, fatal disease, and migration: persistence or extinction. SIAM J. Appl. Math. 72 (2012), 1644–1666.
22. [22] Gourley, S.A., Liu, R., Wu, J., Spatiotemporal distributions of migratory birds: patchy models with delay. SIAM J. Appl. Dyn. Syst. 9 (2010), 589–610.
23. [23] Guckenheimer, J., Holmes, P., Nonlinear Oscillation, Dynamical Systems and Bifurcation of Vector Fields. 1983, Springer-Verlag, New York.
24. [24] Gumel, A.B., Global dynamics of a two-strain avian influenza model. Intl. J. Comput. Math. 86 (2009), 85–108.
25. [25] Hale, J.K., Ordinary Differential Equations. 1969, Wiley, New York.
26. [26] Hilker, F.M., Langlais, M., Malchow, H., The Allee effect and infectious diseases: extinction, multistability and the (dis-)appearance of oscillations. Am. Nat. 173 (2009), 72–88.
27. [27] Hilker, F.M., Langlais, M., Petrovskii, S.V., Malchow, H., A diffusive SI model with Allee effect and application to FLV. Math. Biosci. 206 (2007), 61–80.
28. [28] Iwami, S., Takeuchi, Y., Liu, X., Avian-human influenza epidemic model. Math. Biosci. 207 (2007), 1–25.
29. [29] Iwami, S., Takeuchi, Y., Liu, X., Avian flu pandemic: can we prevent it?. J. Theor. Biol. 257 (2009), 181–190.
30. [30] Iwami, S., Takeuchi, Y., Liu, X., Nakaoka, S., A geographical spread of vaccine-resistance in avian influenza epidemics. J. Theor. Biol. 259 (2009), 219–228.
31. [31] Jones, J.C., Sonnberg, S., Kocer, Z.A., Shanmuganatham, K., Seiler, P., et al. Possible role of songbirds and parakeets in transmission of influenza a(H7N9) virus to humans. Emerg. Infect. Dis. 20 (2014), 380–385.
32. [32] Jones, J.C., Sonnberg, S., Webby, R.J., Webster, R.G., Influenza a (H7N9) virus transmission between finches and poultry. Emerg. Infect. Dis. 21 (2015), 619–628.
33. [33] Jung, E., Iwami, S., Takeuchi, Y., Jo, T.-C., Optimal control strategy for prevention of avian influenza pandemic. J. Theor. Biol. 260 (2009), 220–229.
34. [34] Kang, Y., Castillo-Chavez, C., A simple epidemiological model for populations in the wild with Allee effects and disease-modified fitness. Discrete Contin. Dyn. Syst. B 19 (2014), 89–130.
35. [35] Kang, Y., Castillo-Chavez, C., Dynamics of SI models with both horizontal and vertical transmissions as well as Allee effects. Math. Biosci. 248 (2014), 97–116.
36. [36] Keeling, M.J., Rohani, P., Modeling Infectious Diseases in Humans and Animals. 2008, Princeton University Press, Princeton.
37. [37] Koopmans, M., De Jong, M.D., Avian influenza a h7n9 in Zhejiang, China. Lancet 381 (2013), 1882–1883.
38. [38] Lakshmikantham, V., Leela, S., Martynyuk, A.A., Stability Analysis of Nonlinear Systems. 1989, Marcel Dekker Inc., New York/Basel.
39. [39] Li, Q., Zhou, L., Zhou, M., Chen, Z., Li, F., et al. Epidemiology of human infections with avian influenza a (H7N9) virus in China. New Eng. J. Med. 370 (2014), 520–532.
40. [40] Liu, D., Shi, W., Shi, Y., Wang, D., Xiao, H., et al. Origin and diversity of novel avian influenza a H7N9 viruses causing human infection: phylogenetic, structural, and coalescent analyses. Lancet 381 (2013), 1926–1932.
41. [41] Liu, S., Pang, L., Ruan, S., Zhang, X., Global dynamics of avian influenza epidemic models with psychological effect. Comput. Math. Methods Med., 2015 Article ID 913726, 12 pages. http://dx.doi.org/10.1155/2015/913726.
42. [42] Liu, S., Ruan, S., Zhang, X., On avian influenza epidemic models with time delay. Theory Biosci. 134 (2015), 75–82.
43. [43] Lucchetti, J., Roy, M., Martcheva, M., An Avian Influenza Model and Its Fit to Human Avian Influenza Cases. Tchuenche, J.M., Mukandavire, Z., (eds.) Advances in Disease Epidemiology, 2009, Nova Science Publishers, New York, 1–30.
44. [44] Ma, X., Wang, W., A discrete model of avian influenza with seasonal reproduction and transmission. J. Biol. Dyn. 4 (2010), 296–314.
45. [45] National Health and Family Planning Commission of China (NHFPC), National Notifiable Disease Situation, http://en.nhfpc.gov.cn/diseases.html (in English); http://www.nhfpc.gov.cn/zhuzhan/yqxx/lists.shtml (in Chinese).
46. [46] Pantin-Jackwood, M.J., Miller, P.J., Spackman, E., Swayne, D.E., Susta, L., Costa-Hurtado, M., Suarez, D.L., Role of poultry in the spread of novel h7n9 influenza virus in China. J. Virol. 88 (2014), 5381–5390.
47. [47] Rappole, J.H., Hubalek, Z., Migratory birds and west nile virus. J. Appl. Microbiol. 94 (2003), 47S–58S.
48. [48] Senar, J.C., Conroy, M.J., Multi-state analysis of the impacts of avian pox on a population of serins (Serinus serinus): the importance of estimating recapture rates. Anim. Biodivers. Conserv. 27 (2004), 1–15.
49. [49] Serrano, D., Oro, D., Urua, E., Tella, J., Colony size selection and determines adult survival and dispersal preference: allee effect in a colonial birds. Am. Nat. 166:2 (2005), E22–E31.
50. [50] Skagen, S.K., Yackel, A.A.A., Potential misuse of avian density as a conservation metric. Conserv. Biol. 25 (2011), 48–55.
51. [51] Thieme, H.R., Dhirasakdanon, T., Han, Z., Trevino, R., Species decline and extinction: synergy of infectious disease and Allee effect?. J Biol. Dyn. 3 (2009), 305–323.
52. [52] Tuncer, N., Martcheva, M., Modeling seasonality in avian influenza H5N1. J. Biol. Syst., 21(4), 2013, 1340004 1–30.
53. [53] Vaidya, N.K., Wahl, L.M., Avian influenza dynamics under periodic environmental conditions. SIAM J. Appl. Math. 75:2 (2015), 443–467.
54. [54] 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.
55. [55] Wang, X.-S., Wu, J., Periodic systems of delay differential equations and avian influenza dynamics. J. Math. Sci. 201 (2014), 693–704.
56. [56] Wikelski, M., Foufopoulos, J., Vargas, H., Snell, H., Galápagos birds and diseases: invasive pathogens as threats for island species. Ecol. Soc., 9, 2004, 5.
57. [57] Wilcove, D.S., Rothstein, D., Dubow, J., Phillips, A., Losos, E., Quantifying threats to imperiled species in the United States. Bioscience 48 (1998), 607–615.
58. [58] World Health Organization (WHO), Human infection with avian influenza A(H7N9) virus-update (February 24, 2014). http://www.who.int/csr/don/2014_-02_-24/en/.
59. [59] World Organization for Animal Health (OIE), OIE expert mission finds live bird markets play a key role in poultry and human infections with influenza A (H7N9). Paris (April 30, 2013). http://www.oie.int/en/for-the-media/press-releases/detail/article/oie-expert-mission-finds-live-bird-markets-play-a-key-role-in-poultry-and-human-infections-with-infl/.
60. [60] Zhang, J., Feng, B., The Geometric Theory and Bifurcation Problems of Ordinary Differential Equations. 1997, Peking University Press, Beijing (in Chinese).
61. [61] Zhang, Z., Ding, T., Huang, W., Dong, Z., Qualitative Theory of Differential Equations. 1985, Science Press, Beijing (in Chinese). English Ed., Transl. Math. Monographs Vol. 101, Amer. Math. Soc., Providence, RI, 1992.
62. [62] Zhang, J., Jin, Z., Sun, G., Sun, X., Wang, Y., Huang, B., Determination of original infection source of H7N9 avian influenza by dynamical model. Sci. Rep. 4 (2014), 1–16.