A mathematical model of avian influenza with half-saturated incidence

Theory in Biosciences

Volumn 133, Issue 1, 2014, Pages 23-38

  Chong, Nyuk Sian ^a   Tchuenche, Jean Michel ^b   Smith, Robert J ^a  

^a UNIVERSITY OF OTTAWA   (Canada)

^b UNIVERSITY OF GUELPH   (Canada)

Author keywords

Avian influenza; Half saturated incidence; Isolation; Personal protection; Vaccination

Indexed keywords

AVES; AVIAN INFLUENZA VIRUS;

INFLUENZA VACCINE;

ANIMAL; ARTICLE; AVIAN INFLUENZA; BIRD; COMPUTER SIMULATION; DISEASE TRANSMISSION; EPIDEMIC; HUMAN; INCIDENCE; INFLUENZA; MUTATION; THEORETICAL MODEL; TIME;

ANIMALS; BIRDS; COMPUTER SIMULATION; DISEASE OUTBREAKS; HUMANS; INCIDENCE; INFLUENZA IN BIRDS; INFLUENZA VACCINES; INFLUENZA, HUMAN; MODELS, THEORETICAL; MUTATION; TIME FACTORS;

EID: 84896396950     PISSN: 14317613     EISSN: 16117530     Source Type: Journal    
DOI: 10.1007/s12064-013-0183-6     Document Type: Article

References (44)

1. Alexander ME, Bowman C, Moghadas SM, Summers R, Gumel AB, Sahai BM (2004) A vaccination model for transmission dynamics of influenza. SIAM J Appl Dyn Syst 3:503-524
2. Alexander ME, Moghadas SM, Wu J (2008) A delay differential model for pandemic influenza with antiviral treatment. Bull Math Biol 70:382-397
3. Bowman C, Gumel AB, van den Driessche P, Wu J, Zhu H (2005) A mathematical model for assessing control strategies against West Nile virus. Bull Math Biol 67:1107-1133
4. Capasso V, Serio G (1978) A generalization of the Kermack-McKendrick deterministic epidemic model. Math Biosci 42:43-61
5. Centers for Disease Control and Prevention (2007) CDC avian influenza: current H5N1 situation. http://www.cdc.gov/flu/avian/outbreaks/current.htm (Accessed 28 Jan 2013)
6. Centers for Disease Control and Prevention (2010) Key facts about avian influenza (bird flu) and highly pathogenic avian influenza A (H5N1) virus. http://www.cdc.gov/flu/avian/gen-info/facts.htm (Accessed 28 Jan 2013)
7. Centers for Disease Control and Prevention (2012) Human infection with avian influenza A (H5N1) virus: advice for travelers. http://wwwnc.cdc.gov/ travel/page/human-infection-avian-flu-h5n1-advice-for-travelers-current- situation.htm (Accessed 28 Jan 2013)
8. Chan YJ, Lee CL, Hwang SJ et al (2010) Seroprevalence of antibodies to pandemic (H1N1) 2009 influenza virus among hospital staff in a medical center in Taiwan. J Chin Med Assoc 73:62-66
9. Chowell G, Ammon CE, Hengartner NW, Hyman JM (2005) Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: assessing the effects of hypothetical interventions. J Theor Biol 241:193-204
10. Doyle A, Bonmarin I, Lévy-Bruhl D, Le Strat Y, Desenclos J (2006) Influenza pandemic preparedness in France: modelling the impact of interventions. J Epidemiol Commun Health 60:399-404
11. Du Y, Xu R (2010) A delayed SIR epidemic model with nonlinear incidence rate and pulse vaccination. J Appl Math Inform 28:1089-1099
12. Fisher D, Hui D, Zhancheng G, Lee C et al (2011) Pandemic Response Lessons from Influenza H1N1 2009 in Asia Respirol 16:876-882
13. Food and Agriculture Organization of the United Nations (2004) FAO recommendations on the prevention, control and eradication of highly pathogenic avian influenza (HPAI) in Asia (proposed with the support of the OIE). http://www.fao.org/ag/againfo/programmes/en/programmes.htm (Accessed 30 Jan 2013)
14. Food and Agriculture Organization of the United Nations (2008) Possible modes of transmission of avian viruses to people: studies in experimental models. http://www.fao.org/docs/eims/upload//250678/aj155e00.pdf (Accessed 30 Jan 2013)
15. Gao S, Chen L, Nieto JJ, Torres A (2006) Analysis of a delayed epidemic model with pulse vaccination and saturation incidence. Vaccine 24:6037-6045
16. Government of Ontario (2006) Avian influenza: a guide to personal protective clothing and equipment for workers and employers working with or around poultry or wild birds. http://www.health.gov.on.ca/en/pro/programs/emb/ avian/docs/avian-ppe-guide.pdf (Accessed 30 Jan 2013)
17. Gumel AB (2009) Global dynamics of a two-strain avian influenza model. Int J Comput Math 86:85-108
18. Hospital Influenza Working Group (2009) Management of novel influenza epidemics in Singapore: consensus recommendations from the hospital influenza (Singapore). Singapore Med J 50:567-580
19. Iwami S, Takeuchi Y, Liu X (2007) Avian-human influenza epidemic model. Math Biosci 207:1-25
20. Iwami S, Suzuki T, Takeuchi Y (2009) Paradox of vaccination: is vaccination really effective against avian flu epidemics? PLoS One 4:e4915
21. Kaddar A (2009) On the dynamics of a delayed SIR epidemic model with a modified saturated incidence rate. Electr J Differ Equ 133:1-7
22. Kaddar A (2010) Stability analysis in a delayed SIR epidemic model with a saturated incidence rate. Nonlinear Anal Model Control 15(3):299-306
23. Kilbourne ED (2006) Influenza pandemics of the 20th century. Emerg Infect Dis 12:9-14
24. 0. Comput Math Methods Med 2011:527610
25. Lipsitch M, Cohen T, Murray M, Levin BR (2007) Antiviral resistance and the control of pandemic influenza. PLoS Med 4:e15
26. Liu X, Yang L (2012) Stability analysis of an SEIQV epidemic model with saturated incidence rate. Nonlinear Anal Real World Applic 13:2671-2679
27. Longini IM, Halloran ME, Nizam A, Yang Y (2004) Containing pandemic influenza with antiviral agents. Am J Epidemiol 159:623-633
28. Marangon S, Cecchinato M, Capua I (2008) Use of vaccination in avian influenza control and eradication. Zoonoses Public Health 55:65-72
29. May RM, Anderson RM (1978) Regulation and stability of host-parasite population interactions: II. Destabilizing processes. J Anim Ecol 47:249-267
30. Nuño M, Chowell G, Gumel AB (2006) Assessing the role of basic control measures, antivirals and vaccine in curtailing pandemic influenza: scenarios for the US, UK and the Netherlands. J R Soc Interface 4:505-521
31. Perko L (2001) Differential equations and dynamical systems, 3rd edn. Springer, New York
32. Ruan S, Wang W (2003) Dynamical bahavior of an epidemic model with a nonlinear incidence rate. J Differ Equ 188:135-163
33. Stuart-Harris C (1979) Epidemiology of influenza in man. Br Med Bull 35:3-8
34. Tchuenche JM, Dube N, Bhunu CP, Smith? RJ, Bauch CT (2011) The impact of media coverage on the transmission dynamics of human influenza. BMC Public Health 11(Suppl 1):S5
35. van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180:29-48
36. Wei C, Chen L (2008) A delayed epidemic model with pulse vaccination. Discrete Dyn Nat Soc 2008:746951
37. World Health Organization (2006) Avian influenza, including influenza A (H5N1), in humans: WHO interim infection control guideline for health care facilities. https://www.premierinc.com/quality-safety/tools-services/safety/ topics/influenza/downloads/07-who-ai-inf-control-guide05-10-07.pdf (Accessed 30 Jan 2013)
38. World Health Organization (2007) Options for the use of human H5N1 influenza vaccines and the WHO H5N1 vaccine stockpile. http://www.who.int/csr/ resources/publications/WHO-HSE-EPR-GIP-2008-1d.pdf (Accessed 30 Jan 2013)
39. World Health Organization (2011) New: WHO comment on the importance of global monitoring of variant influenza viruses. http://www.who.int/influenza/ human-animal-interface/avian-influenza/h5n1-2011-12-19/en/index.html (Accessed 30 Jan 2013)
40. World Health Organization (2012) H5N1 avian influenza: timeline of major events. http://www.who.int/influenza/human-animal-interface/avian-influenza/ H5N1-avian-influenza-update.pdf (Accessed 30 Jan 2013)
41. Yang J, Zhang F, Wang X (2007) A class of SIR epidemic model with saturation incidence and age of infection. Ninth ACIS international conference on software engineering, artificial intelligence, networking, and parallel/distributed computing, vol 1, pp 146-149
42. Yang Y, Sugimoto JD, Halloran ME, Basta NE et al (2009) The transmissibility and control of pandemic influenza A (H1N1) virus. Sci Agric 326:729-733
43. Zhang F, Li Z-Z, Zhang F (2008) Global stability of an SIR epidemic model with constant infectious period. Appl Math Comput 199:285-291
44. Zhou Y, Liu H (2003) Stability of periodic solutions for an SIS model with pulse vaccination. Math Comput Model 38:299-308