Mathematical Biosciences and Engineering (MBE)

Theoretical assessment of the relative incidences of sensitive and resistant tuberculosis epidemic in presence of drug treatment

Pages: 971 - 993, Volume 11, Issue 4, August 2014      doi:10.3934/mbe.2014.11.971

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Silvia Martorano Raimundo - Faculdade de Medicina da Universidade de São Paulo, Disciplina de Informática Médica and LIM01-HCFMUSP, Rua Teodoro Sampaio, 115, CEP: 05405-000, São Paulo, SP, Brazil (email)
Hyun Mo Yang - Universidade de Campinas, IMECC, DMA, Praça Sérgio Buarque de Holanda, 651, Campinas, SP, Brazil (email)
Ezio Venturino - Università di Torino, Dipartimento di Matematica "Giuseppe Peano", Via Carlo Alberto 10, 10123 Torino, Italy (email)

Abstract: 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.

Keywords:  MDR-TB, drug resistance, treatment, mathematical models, equilibria.
Mathematics Subject Classification:  Primary: 92D30; Secondary: 92C50.

Received: August 2013;      Accepted: October 2013;      Available Online: March 2014.