Mathematical Biosciences and Engineering (MBE)

Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers
Pages: 813 - 840, Issue 4, August 2016

doi:10.3934/mbe.2016019      Abstract        References        Full text (555.7K)           Related Articles

Martin Luther Mann Manyombe - Department of Mathematics, Faculty of Science, University of Yaounde 1, P.O. Box 812 Yaounde, Cameroon (email)
Joseph Mbang - Department of Mathematics, Faculty of Science, University of Yaounde 1, P.O. Box 812 Yaounde, Cameroon (email)
Jean Lubuma - Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa (email)
Berge Tsanou - Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa (email)

1 H. Abboubakar, J. C. Kamgang, L. N. Nkamba, D. Tieudjo and L. Emini, Modeling the dynamics of arboviral diseases with vaccination perspective, Biomath, 4 (2015), 1507241, 30pp.       
2 R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, 1991.
3 J. Arino, C. C. MCCluskey and P. Van Den Driessche, Global results for an epidemic model with vaccination that exhibits backward bifurcation, SIAM J. Appl. Math., 64 (2003), 260-276.       
4 F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, New York, 2001.       
5 C. Castillo-Chavez and B. Song, Dynamical model of tuberclosis and their applications, Math.Biosci.Eng, 1 (2004), 361-404.       
6 P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.       
7 C. P. Farrington, On vaccine efficacy and reproduction numbers, Math. Biosci., 185 (2003), 89-109.       
8 G. Francois, M. Kew, P. Van Damme, M. J. Mphahlele and A. Meheus, Mutant hepatitis B viruses: A matter of academic interest only or a problem with far-reaching implications, Vaccine, 19 (2001), 3799-3815.
9 M. Ghosh, P. Chandra, P. Sinha and J. B. Shukla, Modelling the spread of carrier-dependent infectious diseases with environmental effect, Appl. Math. Comput., 152 (2004), 385-402.       
10 J. Gjorgjieva, K. Smith, G. Chowell, F. Sanchez, J. Snyder and C. Castillo-Chavez, The role of vaccination in the control of SARS, Math. Biosci. Eng., 2 (2005), 753-769.       
11 S. Goldstein, F. Zhou, S. C. Hadler, B. P. Bell, E. E. Mast and H. S. Margolis, A mathematical model to estimate global hepatitis B disease burden and vaccination impact, Int. J. Epidemiol., 34 (2005), 1329-1339.
12 B. Gomero, Latin Hypercube Sampling and Partial Rank Correlation Coefficient Analysis Applied to an Optimal Control Problem, Master Thesis, University of Tennessee, Knoxville, 2012.
13 A. B. Gumel and S. M. Moghadas, A qualitative study of a vaccination model with non-linear incidence, Appl. Math. Comp, 143 (2003), 409-419.       
14 H. Guo and M. Y. Li, Global dynamics of a staged progression model for infectious diseases, Math. Biosci. Eng., 3 (2006), 513-525.       
15 J. M. Hyman and J. Li, Differential susceptibility and infectivity epidemic models, Math. Biosci. Eng., 3 (2006), 89-100.       
16 D. Kalajdzievska and M. Y. Li, Modeling the effects of carriers on the transmission dynamics of infectious diseases, Math. Biosci. Eng., 8 (2011), 711-722.       
17 J. T. Kemper, The effects of asymptotic attacks on the spread of infectious disease: A deterministic model, Bull. Math. Bio., 40 (1978), 707-718.       
18 A. Korobeinikov, Global properties of sir and seir epidemic models with multiple parallel infectious stages, Bull. Math. Bio., 71 (2009), 75-83.       
19 J. P. LaSalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976.       
20 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), 178-196.       
21 G. F. Medley, N. A. Lindop, W. J. Edmunds and D. J. Nokes, Hepatitis-B virus edemicity: Heterogeneity, catastrophic dynamics and control, Nat. Med., 7 (2001), 617-624.
22 R. Naresh, S. Pandey and A. K. Misra, Analysis of a vaccination model for carrier dependent infectious diseases with environmental effects, Nonlinear Analysis: Modelling and Control, 13 (2008), 331-350.       
23 M. M. Riggs, A. K. Sethi, T. F. Zabarsky, E. C. Eckstein, R. L. Jump and C. J. Donskey, Asymptomatic carriers are a potential source for transmission of epidemic and nonepidemic Clostridium diffcile strains among long-term care facility residents, Clin. Infect. Dis., 45 (2007), 992-998.
24 P. Roumagnac, et al., Evolutionary history of Salmonella typhi, Science, 314 (2006), 1301-1304.
25 C. L. Trotter, N. J. Gay and W. J. Edmunds, Dynamic models of meningococcal carriage, disease, and the impact of serogroup C conjugate vaccination, Am. J. Epidemiol., 162 (2005), 89-100.
26 S. Zhao, Z. Xu and Y. Lu, A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in China, Int. J. Epidemiol., 29 (2000), 744-752.
27 L. Zou, W. Zhang and S. Ruan, Modeling the transmission dynamics and control of hepatitis B virus in China, J. Theor. Biol., 262 (2010), 330-338.       
28 "The ABCs of Hepatitis", Center for Disease Control and Prevention (CDC), 2015. Available from: http://www.cdc.gov/hepatitis/Resources/Professionals/PDFs/ABCTable.pdf
29 WHO, "Fact Sheet N$^o$ 204 on Hepatitis B", July 2015. Available from: http://www.who.int/mediacentre/factsheets/fs204/en/

Go to top