5,432
Views
23
CrossRef citations to date
0
Altmetric
Articles

Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis

ORCID Icon, , &
Pages 26-42 | Received 03 May 2018, Accepted 18 Dec 2018, Published online: 09 Jan 2019

References

  • E. Beretta and Y. Takeuchi, Global asymptotic stability of Lotka–Volterra diffusion models with continuous time delay, SIAM J. Appl. Math. 48(3) (1988), pp. 627–651. doi: 10.1137/0148035
  • T. Berge, S. Bowong, J. Lubuma, and M.L.M. Manyombe, Modeling Ebola virus disease transmissions with reservoir in a complex virus life ecology, Math. Biosci. Eng. 15(1) (2018), pp. 21–56. doi: 10.3934/mbe.2018002
  • S.M. Blower, A.R. McLean, T.C. Porco, P.M. Small, P.C. Hopwell, M.A. Sanchez, and A.R. Ross, The intrinsic transmission dynamics of tuberculosis epidemics, nature medicine, Histoire de l'Acad. Roy. Sci. (Paris) avec Mém. des Math. et Phys. and Mé.
  • T.F. Brewer, S.J. Heymann, A.A. Colditz, M.E. Wilson, K. Auerbach, D. Kane, and H.V. Fineberg, Evaluation of tuberculosis control policies using computer simulation, JAMA 276(23) (1996), pp. 1898–1903. doi: 10.1001/jama.1996.03540230048034
  • Centers for Disease Control and Prevention (CDC) and others, The Pink Book: Epidemiology and Prevention of Vaccine Preventable Diseases, 10th ed.
  • G.A. Colditz, T.F. Brewer, C.S. Berkey, M.E. Wilson, E. Burdick, H.V. Fineberg, and F. Mosteller, Efficacy of BCG vaccine in the prevention of tuberculosis: Meta-analysis of the published literature, JAMA 271(9) (1994), pp. 698–702. doi: 10.1001/jama.1994.03510330076038
  • O. Diekmann, J.A.P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Vol. 5, John Wiley & Sons, west sussex, 2000.
  • R. Diel, D. Goletti, G. Ferrara, G. Bothamley, D. Cirillo, B. Kampmann, C. Lange, M. Losi, R. Markova, G.B. Migliori, A. Nienhaus, M. Ruhwald, D. Wagner, J.P. Zellweger, E. Huitric, A. Sandgren, and D. Manissero, Interferon-gamma release assays for the diagnosis of latent mycobacterium tuberculosis infection: A systematic review and meta-analysis, Eur. Respir. J. 37 (2011), pp. 88–99. doi: 10.1183/09031936.00115110
  • H. Guo and M.Y. Li, Global stability in a mathematical model of tuberculosis, Canad. Appl. Math. Quart. 14 (2006), pp. 185–197.
  • J.M. Hyman and J. Li, Differential susceptibility epidemic models, J. Math. Biol. 50(6) (2005), pp. 626–644. doi: 10.1007/s00285-004-0301-7
  • M.L.M. Manyombe, J. Mbang, J. Lubuma, and B. Tsanou, Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers, Math. Biosci. Eng. 13(4) (2016), pp. 813–840. doi: 10.3934/mbe.2016019
  • S. Marino, I.B. Hogue, C.J. Ray, and D.E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol. 254 (2008), pp. 178–196. doi: 10.1016/j.jtbi.2008.04.011
  • D.P. Moualeu, S. Bowong, J. Kurths, Parameter estimation of a tuberculosismodel in a patch environment: Case of Cameroon, Proc. Int. Sym. Math. Comput. Biol. 5 (2013), pp. 352–373.
  • J.P. Narain, M.C. Raviglione, and A. Kochi, HIV-associated tuberculosis in developing countries: Epidemiology and strategies for prevention, Tuber. Lung Dis. 73(6) (1992), pp. 311–321. doi: 10.1016/0962-8479(92)90033-G
  • National Institute of Statistics, Evolution des systèmes statistiques nationaux – Cameron, 2007.
  • National Institute of Statistics, Rapport sur la présentation des résultats définitifs. Technical report, Bureau Central des Recensements et des Etudes de Population, 2010.
  • A.J. Rubel and L.C. Garro, Social and cultural factors in the successful control of tuberculosis, Public Health Rep. 107(6) (1992), p. 626.
  • R.W. West and J.R. Thompson, Modeling the impact of HIV on the spread of tuberculosis in the united states, Math. Biosci. 143(1) (1997), pp. 35–60. doi: 10.1016/S0025-5564(97)00001-1
  • World Health Organization, Media centre: Poliomyelitis, fact sheet, Updated April 2016. Available at http://www.who.int/mediacentre/factsheets/fs114/en/#.
  • World Health Organization et al., Global Tuberculosis Report, 2016.