Mathematical analysis of a model for the transmission dynamics of bovine tuberculosis

Mathematical Methods in the Applied Sciences

Volumn 34, Issue 15, 2011, Pages 1873-1887

  Agusto, Folashade B ^a   Lenhart, Suzanne ^a   Gumel, Abba B ^b   Odoi, Agricola ^a  

^a UNIVERSITY OF TENNESSEE   (United States)

^b UNIVERSITY OF MANITOBA   (Canada)

Author keywords

bovine tuberculosis; equilibria; reproduction number; stability

Indexed keywords

BOVINE TUBERCULOSIS; CATTLE HERD; DETERMINISTIC MODELS; DISEASE-FREE EQUILIBRIUM; ENDEMIC EQUILIBRIUM; EQUILIBRIA; GLOBALLY ASYMPTOTICALLY STABLE; MATHEMATICAL ANALYSIS; REPRODUCTION NUMBER; RIGOROUS ANALYSIS; TRANSMISSION DYNAMICS;

CONVERGENCE OF NUMERICAL METHODS; DYNAMICS;

MAMMALS;

EID: 80053560629     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.1486     Document Type: Article

References (37)

1. CFSPH 2007. Bovine Tuberculosis. Accessed on June 27, 2010.
2. DEFRA. 2008. Bovine TB: What is bovine tuberculosis? Accessed on June 27, 2010
3. Morris RS, Pfeiffer DU, Jackson R,. The epodemiology of Mycobacterium bovis infection. Journal of Veterinary Microbiology 1994; 40: 153-177.
4. Buhr B, McKeever K, Adachi K,. Economic Impact of Bovine Tuberculosis on Minnesota's Cattle and Beef Sector, 2009. Research in agriculture and applied economics. Accessed on July 26, 2010.
5. Sheppard A, Turner M,. An Economic Impact Assessment of Bovine Tuberculosis in South West England. Research in agriculture and applied economics, 2005. Accessed on July 26, 2010.
6. Emerging Disease Issues 2007. Bovine Tuberculosis. Accessed on November 16, 2008.
7. Raviglione MC, Snider DE, Kochi A,. Global epidemiology of tuberculosis. JAMA 1995; 273: 220-226.
8. Bouvet E, Casalino E, Mendoza-Sassi G, Lariven S, Vallee E, Pernet M, et al,. A nosocomial outbreak of multidrug-resistant Mycobacterium bovis among HIV infected patients. A case-control study. AIDS 1993; 7: 1453-1460. (Pubitemid 23333834)
9. Dankner WM, Waecker NJ, Essey MA, Moser K, Thompson M, Davis CH,. Mycobacterium bovis infections in San Diego: a clinicoepidemiologic study of 73 patients and a historical review of a forgotten pathogen. Medicine (Baltimore) 1993; 72: 11-37. (Pubitemid 23047073)
10. Grange JM, Daborn C, Cosivi O,. HIV-related tuberculosis due to Mycobacterium bovis. European Respiratory Journal 1994; 7: 1564-1566. (Pubitemid 24294238)
11. Moda G, Daborn CJ, Grange JM, Cosivi O,. The zoonotic importance of Mycobacterium bovis. Tubercle and Lung Disease 1996; 77: 103-108. (Pubitemid 26139140)
12. Cosivi O, Meslin F-X, Daborn CJ, Grange JM,. The epidemiology of Mycobacterium bovis infection in animals and humans, with particular reference to Africa. Scientific and Technical Review 1995; 14: 733-746.
13. Martin SW,. Livestock Disease Eradication: Evaluation of the Cooperative State-Federal Bovine Tuberculosis Eradication Program. National Academy Press: Washington, 1994.
14. Institute for Animal Health. Disease Facts-Bovine tuberculosis. Accessed on June 27, 2010.
15. Greater Wellington Regional Council, 2004. Accessed on October 28, 2008.
16. Emerging Disease Issues 2007. Caudal-Fold Tuberculin Test(CFT). Accessed on October 7, 2009.
17. Barlow ND, Kean JM, Hickling G, Livingstone PG, Robson AB,. A simulation model for the spread of bovine tuberculosis within New Zealand cattle herds. Preventive Veterinary Medicine 1997; 32: 57-75. (Pubitemid 127399139)
18. Kao RR, Roberts MG, Ryan TJ,. A model of bovine tuberculosis control in domesticated cattle herds. Proceedings of the Royal Society B: Biological Sciences 1997; 264: 1069-1076. (Pubitemid 27351101)
19. Kleeberg HH,. The tuberculin test in cattle. Journal of the South African Veterinary Medicine Association 1960; 31: 213-225.
20. Blood DC, Radostits OM,. Veterinary medicine: a textbook of the diseases of cattle, sheep, pigs, goats, and horses, 7th edn. Bailliere Tindall Ltd.: London, 1989.
21. Barlow ND, Kean JM, Caldwell NP, Ryan TJ,. Modelling the regional dynamics and management of bovine tuberculosis in New Zealand cattle herds. Preventive Veterinary Medicine 1998; 36: 25-38. (Pubitemid 128417826)
22. Bicknell KB, Wilen JE, Howitt RE,. Public policy and private incentives for livestock disease control. Australian Journal of Agricultural and Resource Economics 1999; 43: 501-521. (Pubitemid 30042334)
23. Kean JM, Barlow ND, Hickling GJ,. Evaluating potential sources of bovine tuberculosis infection in a New Zealand cattle herd. New Zealand Journal of Agricultural Research 1999; 42: 101-106. (Pubitemid 29285135)
24. van den Driessche P,. Some epidemiological models with delays. In Differential equations and applications to biology and industry, M. Martelli, K. Cooke, E. Cumberbatch, et al. (eds). World Scientific: Singapore, 1996; 507-520.
25. van den Driessche P, Wang L, Zou X,. Modeling Diseases with Latency and Relapse. Mathematical Biosciences and Engineering 2007; 4 (2): 205-219. (Pubitemid 47147348)
26. Neill SD, Hanna J, Mackie DP, Bryson TGD,. Isolation of Mycobacterium bovis from the respiratory tracts of skin test negative cattle. Veterinary Record 1992; 13 (1): 45-47.
27. Stoneham G, Johnston J,. Report on the brucellosis and tuberculosis eradication campaign. Paper No. 97, Australian Bureau of Agricultural Economics Occasional, Canberra, 1986.
28. Norby B, Bartlett1 PC, Fitzgerald SD, Granger LM, Bruning-Fann CS, Whipple D L, Payeur JB,. The sensitivity of gross necropsy, caudal fold and comparative cervical tests for the diagnosis of bovine tuberculosis. Journal of Veterinary Diagnostic Investigation 2004; 16: 126-131. (Pubitemid 38377465)
29. Thieme HR,. Mathematics in Population Biology. Princeton University Press: Princeton, NJ, 2003.
30. Agusto FB, Gumel AB,. Theoretical Assessment of Avian Influenza Vaccine. DCDS Series B 2010; 13 (1): 1-25. DOI: 10.3934/dcdsb.2009.13.1.
31. van den Driessche P, Watmough J,. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci 2002; 180: 29-48. (Pubitemid 35304346)
32. Anderson RM, May RM,. Infectious Diseases of Humans. Oxford University Press: Oxford, 1991.
33. 0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology 1990; 28: 503-522.
34. Hethcote HW,. The mathematics of infectious diseases. SIAM Review 2000; 42 (4): 599-653.
35. Hale JK,. Ordinary Differential Equations. John Wiley and Sons: New York, 1969.
36. Barlow ND,. Non-linear transmission and simple models for bovine tuberculosis. Journal of Animal Ecology 2000; 69: 703-713. (Pubitemid 30597764)
37. Whipple DL, Bolin CA, Davis AJ, Jarnagin JL, Johnson DC, Nabors RS, Payeur JB, Saari DA, Wilson AJ, Wolf MM,. Comparison of the sensitivity of the caudal fold skin test and a commercial gamma-interferon assay for diagnosis of bovine tuberculosis. American Journal of Veterinary Research 1995; 56 (4): 415-419.