Theoretical assessment of the relative incidences of sensitive and resistant tuberculosis epidemic in presence of drug treatment. (English) Zbl 1327.92026
Summary: Despite the availability of effective treatment, tuberculosis (TB) remains a major global cause of mortality. Multidrug-resistant tuberculosis (MDR-TB) is a form of TB that is resistant to at least two drugs used for the treatment of TB, and originally is developed when a case of drug-susceptible TB is improperly or incompletely treated. This work is concerned with a mathematical model to evaluate the effect of MDR-TB on TB epidemic and its control. The model assessing the transmission dynamics of both drug-sensitive and drug-resistant TB includes slow TB (cases that result from endogenous reactivation of susceptible and resistant latent infections). We identify the steady states of the model to analyse their stability. We establish threshold conditions for possible scenarios: elimination of sensitive and resistant strains and coexistence of both. We find that the effective reproductive number is composed of two critical values, relative reproductive number for drug-sensitive and drug-resistant strains. Our results imply that the potential for the spreading of the drug-resistant strain should be evaluated within the context of several others factors. We have also found that even the considerably less fit drug-resistant strains can lead to a high MDR-TB incidence, because the treatment is less effective against them.
References:
| [1] | R. F. Baggaley, Modelling the Impact of Antiretroviral Use in Resource-Poor Settings,, PLoS Medicine, 3 (2006) · doi:10.1371/journal.pmed.0030124 |
| [2] | A. Berman, <em>Nonnegative Matrices in the Mathematical Sciences</em>,, Academic (1979) · Zbl 0484.15016 |
| [3] | C. P. Bhunu, Modeling HIV/AIDS and Tuberculosis coinfection,, Bulletin of Mathematical Biology, 71, 1745 (2009) · Zbl 1173.92018 · doi:10.1007/s11538-009-9423-9 |
| [4] | S. M. Blower, Modeling the emergence of the ’hot zones’: Tuberculosis and the amplification dynamics of drug resistance,, Nature Medicine, 10, 1111 (2004) · doi:10.1038/nm1102 |
| [5] | S. M. Blower, Control strategies for tuberculosis epidemics: New models for old problems,, Science, 273, 497 (1996) · doi:10.1126/science.273.5274.497 |
| [6] | S. M. Blower, The intrinsic transmission dynamics of tuberculosis epidemics,, Nature Medicine, 1, 815 (1995) · doi:10.1038/nm0895-815 |
| [7] | S. M. Blower, Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: A theoretical framework,, Journal of Molecular Medicine, 76, 624 (1998) · doi:10.1007/s001090050260 |
| [8] | M. W. Borgdorff, New measurable indicator for tuberculosis case detection,, Emerging Infectious Diseases, 10, 1523 (2004) · doi:10.3201/eid1009.040349 |
| [9] | S. Borrell, Infectiousness, reproductive fitness and evolution of drug-resistant <em>Mycobacterium tuberculosis</em>,, The International Journal of Tuberculosis and Lung Disease, 13, 1456 (2009) |
| [10] | C. R. Braden, Simultaneous infection with multiple strains of <em>Mycobacterium tuberculosis</em>,, Clinical Infectious Diseases, 33 (2001) · doi:10.1086/322635 |
| [11] | S. Bowong, Modeling and analysis of the transmission dynamics of tuberculosis without and with seasonality,, Nonlinear Dynamics, 67, 2027 (2012) · Zbl 1242.92039 · doi:10.1007/s11071-011-0127-y |
| [12] | CDC., Drug resistant tuberculosis among the homeless Boston,, MMWR, 34, 429 (1985) |
| [13] | T. Cohen, Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness,, Nature Medicine, 10, 1117 (2004) · doi:10.1038/nm1110 |
| [14] | T. Cohen, Are survey-based estimates of the burden of drug resistant TB too low? Insight from a simulation study,, PLos ONE, 3 (2008) · doi:10.1371/journal.pone.0002363 |
| [15] | C. Colijin, Spontaneous emergence of multiple drug resistance in Tuberculosis before and during therapy,, PLos ONE, 6 (2011) · doi:10.1371/journal.pone.0018327 |
| [16] | C. Colijn, Latent coeinfection and the maintenance of strain diversity,, Bulletin of Mathematical Biology, 71, 247 (2009) · Zbl 1169.92035 · doi:10.1007/s11538-008-9361-y |
| [17] | H. D. Costello, Drug resistance among previously treated tuberculosis patients, a brief report., American Review of Respiratory Disease, 121, 313 (1980) |
| [18] | Dickman et al., Detection of multiple strains of <em>Mycobacterium tuberculosis</em> using MIRU-VNTR in patients with pulmonary tuberculosis in Kampala, Uganda., BMC Infectious Diseases, 10, 1471 (2010) |
| [19] | C. Dye, Will tuberculosis become resistant to all antibiotics?, Proceedings of the Royal Society of London B, 268, 45 (2001) · doi:10.1098/rspb.2000.1328 |
| [20] | M. A. Espinal, The global situation of MDR-TB,, Tuberculosis, 83, 44 (2003) · doi:10.1016/S1472-9792(02)00058-6 |
| [21] | L. Esteva, Influence of vertical and mechanical transmission on the dynamics of dengue disease,, Math. Biosc., 167, 51 (2000) · Zbl 0970.92011 · doi:10.1016/S0025-5564(00)00024-9 |
| [22] | Z. Feng, A two-strain Tuberculosis model with age of infection,, SIAM Journal on Applied Mathematics, 62, 1634 (2002) · Zbl 1017.35066 · doi:10.1137/S003613990038205X |
| [23] | M. L. Garcia-Garcia et. al., Clinical consequences and transmissibility of drug-resistant tuberculosis in souther Mexico,, Archives of Internal Medicine, 160, 630 (2000) |
| [24] | M. Gomes, The reinfection threshold promotes variability in tuberculosis epidemiology and vaccine efficacy,, Proceedings of the Royal Society B, 271, 617 (2004) · doi:10.1098/rspb.2003.2606 |
| [25] | J. K. Hale, <em>Ordinary Differential Equations</em>,, 2nd Ed. krieger (1980) · Zbl 0433.34003 |
| [26] | W. H. Hethcote, The mathematcs of infectious diseases,, SIAM Review, 42, 599 (2000) · Zbl 0993.92033 · doi:10.1137/S0036144500371907 |
| [27] | M. C. M. Jong, How does transmission of infection depend on population size?, in D. Mollison (Ed.), 5 (1994) · Zbl 0850.92042 |
| [28] | Y. Liu, <em>Modeling Transmission of Tuberculosis with MDR and Undetected Cases</em>,, Discrete Dynamics in Nature and Society (2011) · Zbl 1229.92060 · doi:10.1155/2011/296905 |
| [29] | S. M. Moghadas, Population-wide emergence of antiviral resistance during pandemic influenza,, PLos ONE, 3 (2008) · doi:10.1371/journal.pone.0001839 |
| [30] | E. Nardell, Exogenous reinfection with tuberculosis in a shelter for the homeless,, The New England Journal of Medicine, 315, 1570 (1986) · doi:10.1056/NEJM198612183152502 |
| [31] | D. Okuonghae, Analysis of a mathematical model for tuberculosis: What could be done to increase case detection,, Journal of Theoretical Biology, 269, 31 (2011) · Zbl 1307.92351 · doi:10.1016/j.jtbi.2010.09.044 |
| [32] | D. J. Ordway, Drug-resistant strains of Mycobaterium tuberculosis exhibit a range of virulence for mice,, Infection and Immunity, 63, 741 (1995) |
| [33] | S. M. Raimundo, Modeling the emergence of HIV-1 drug-resistance resulting from antiretroviral therapy: Insights from theoretical and numerical studies,, BioSystems, 108, 1 (2012) · doi:10.1016/j.biosystems.2011.11.009 |
| [34] | S. M. Raimundo, The attracting basins and the assessment of the transmission coefficients for HIV and M. Tuberculosis infections among women inmates,, Journal of Biological Systems, 10, 61 (2002) · Zbl 1099.92039 |
| [35] | S. M. Raimundo, An approach to estimating the transmission coefficients for AIDS and for tuberculosis using mathematical models,, Systems Analysis Modelling Simulation, 43, 423 (2003) · Zbl 1057.92047 · doi:10.1080/02329290290027175 |
| [36] | S. M. Raimundo, Modelling congenital transmission of Chagas’disease,, Biosystems, 99, 215 (2010) · doi:10.1016/j.biosystems.2009.11.005 |
| [37] | H. Rinder, Heteroesistance in <em>Mycobacterium tuberculsosis</em>,, The International Journal of Tuberculosis and Lung Disease, 5, 339 (2001) |
| [38] | P. Rodrigues, Drug resistance in tuberculosis - a reinfection model,, Theoretical Population Biology, 71, 196 (2007) · Zbl 1118.92036 · doi:10.1016/j.tpb.2006.10.004 |
| [39] | R. Sergeev, Models to understand the popualtion-level impact of mixed strain <em>M. tuberculosis</em> infections,, Journal of Theoretical Biology, 280, 88 (2011) · Zbl 1397.92405 · doi:10.1016/j.jtbi.2011.04.011 |
| [40] | O. Sharomi, Dynamical analysis of a multi-strain model of HIV in the presence of antiretroviral drugs,, Journal of Biological Dynamics, 2, 323 (2008) · Zbl 1154.92033 · doi:10.1080/17513750701775599 |
| [41] | P. M. Small, Exogenous reinfection with multidrug-resistant Mycobacterium tuberculosis in patients with advanced HIV infection,, The New England Journal of Medicine, 328, 1137 (1993) · doi:10.1056/NEJM199304223281601 |
| [42] | DE Jr. Snider, Infection and disease among contacts of tuberculosis cases with drug resistant and drug susceptible bacilli,, The American Review of Respiratory Disease, 132, 125 (1985) |
| [43] | I. H. Spicknall, A modeling framework for the evolution and spread of antibiotic resistance: literature review and model categorization,, Am J Epidemiol, 178, 508 (2013) · doi:10.1093/aje/kwt017 |
| [44] | L. Teixeira et al, Infection and disease among household contacts of patients with multidrug-resistant tuberculosis,, The International Journal of Tuberculosis and Lung Disease, 5, 321 (2001) |
| [45] | 2011/2012 Tuberculosis Global Facts, Progress WHO Global Tuberculosis Control Report, 2011,, <a href= (2012) |
| [46] | World Health Organization, Anti-tuberculosis drug resistance in the world. Prevalence and trends,, WHO/CDS/TB/2000/.278 The WHO/IUATLD Global Project on Anti-Tuberculosis Drug Resistance Surveillance. Report 2. World Health Organization (2000) |
| [47] | <a href=, Tuberculosis,, Fact sheet N. 104 (2012) |
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