Tuberculosis with relapse: a model. (English) Zbl 1409.92259
Summary: In a model of tuberculosis with relapse, the basic reproduction number \(R_0\) includes new and relapse infections. Lyapunov functions help to prove that the global dynamic is completely determined by \(R_0\). Replicated Latin hypercube sampling shows that early diagnosis and treatment are more efficient when relapse cases are considered.
Keywords:
basic reproduction number; equilibrium; global stability; partial rank correlation coefficient; sensitivity analysis; tuberculosisReferences:
| [1] | Blower, S. M. and Dowlatabadi, H. (1994). Sensitivity and uncertainty analysis of complex models of disease transmission: An HIV model, as an example. International Statistical Review/Revue internationale de statistique, 62(2): 229-243. · Zbl 0825.62860 |
| [2] | Blower, S. M., Mclean, A. R., Porco, T. C., et al. (1995). The intrinsic transmission dynamics of tuberculosis epidemics. Nature Medicine, 1(8): 815-821. |
| [3] | Borgdorff, M. W. (2004). New measurable indicator for tuberculosis case detection. Emerging Infectious Diseases, 10(10): 1523-1528. |
| [4] | Castillo-Chavez, C. and Song, B. (2004). Dynamical models of tuberculosis and their applications. Mathematical Biosciences and Engineering, 1(12): 361-404. · Zbl 1060.92041 |
| [5] | Diekmann, O., Heesterbeek, J. A. P., and Metz, J. A. (1990). On the definition and the computation of the basic reproduction ratio R_0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology, 28(4): 365-382. · Zbl 0726.92018 |
| [6] | Dye, C. and Williams, B. G. (2010). The population dynamics and control of tuberculosis. Science, 328(5980): 856-861. |
| [7] | LaSalle, J. P. and Artstein, Z. (1976). The stability of dynamical systems. Regional Conference Series in Applied Mathematics, SIAM, 25: 1-76. · Zbl 0364.93002 |
| [8] | McKay, M. D., Beckman, R. J., and Conover, W. J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2): 239-245. · Zbl 0415.62011 |
| [9] | Neyrolles, O., Hernandez-Pando, R., Pietri-Rouxel, F., et al. (2006). Is adipose tissue a place for Mycobacterium tuberculosis persistence?PLoS One, 1(1): e43. |
| [10] | Rodrigues, P., Gomes, M. G. M., and Rebelo, C. (2007). Drug resistance in tuberculosisa reinfection model. Theoretical Population Biology, 71(2): 196-212. · Zbl 1118.92036 |
| [11] | Roeger, L. I. W., Feng, Z., and Castillo-Chavez, C. (2009). Modeling TB and HIV co-infections. Mathematical Biosciences and Engineering, 6(6): 815-837. · Zbl 1194.92054 |
| [12] | Sanchez, M. A. and Blower, S. M. (1997). Uncertainty and sensitivity analysis of the basic reproductive rate: Tuberculosis as an example. American Journal of Epidemiology, 145(12): 1127-1137. |
| [13] | Ted, C. and Megan, M. (2004). Modeling epidemics of multidrug-resistant M.tuberculosis of heterogeneous fitness. Nature Medicine, 10(10): 1117-1121. |
| [14] | Tewa, J. J., Bowong, S., Mewoli, B., et al. (2011). Two-patch transmission of tuberculosis. Mathematical Population Studies, 18(3): 189-205. · Zbl 1223.92036 |
| [15] | van den Driessche, P., Wang, L., and Zou, X. (2007). Modeling diseases with latency and relapse. Mathematical Biosciences and Engineering, 4(2): 205-219. · Zbl 1123.92018 |
| [16] | van den Driessche, P. and Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1-2): 29-48. · Zbl 1015.92036 |
| [17] | World Health Organization (WHO). (2008). Global Tuberculosis Control 2008; Surveillance, Planningy Financing: WHO Report 2008. Geneva, Switzerland: WHO Press. |
| [18] | World Health Organization (WHO). (2009). Global Tuberculosis Control: a Short Update to the 2009 Report. Geneva, Switzerland: WHO Press. |
| [19] | World Health Organization (WHO). (2011). Global Tuberculosis Control: WHO Report 2011. Geneva, Switzerland: WHO Press. |
| [20] | Yang, Y., Li, J., and Zhou, Y. C. (2012). Global stability of two tuberculosis models with treatment and self-cure. Rocky Mountain Journal of Mathematics, 42(4): 1367-1386. · Zbl 1251.92024 |
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