Mathematical Biosciences and Engineering, 2014, 11(4): 971-993. doi: 10.3934/mbe.2014.11.971.

Primary: 92D30; Secondary: 92C50.

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

1. 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
2. Universidade de Campinas, IMECC, DMA, Praça Sérgio Buarque de Holanda, 651, Campinas, SP
3. Università di Torino, Dipartimento di Matematica "Giuseppe Peano", Via Carlo Alberto 10, 10123 Torino

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 thatis resistant to at least two drugs used for the treatment of TB,and originally is developed when a case of drug-susceptibleTB is improperly or incompletely treated.This work is concerned with a mathematical model to evaluate the effect ofMDR-TB on TB epidemic and its control.The model assessing the transmission dynamics of both drug-sensitive anddrug-resistant TB includes slow TB(cases that result from endogenous reactivation of susceptible andresistant latent infections). We identify the steady states of the model toanalyse 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 iscomposed of two critical values, relative reproductive number for drug-sensitiveand drug-resistant strains.Our results imply that thepotential for the spreading of the drug-resistant strain should be evaluated withinthe context of several others factors.We have also found that even the considerably less fit drug-resistant strainscan lead to a high MDR-TB incidence, because the treatment is less effective against them.
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Keywords MDR-TB; drug resistance; treatment; mathematical models; equilibria.

Citation: Silvia Martorano Raimundo, Hyun Mo Yang, Ezio Venturino. Theoretical assessment of the relative incidences of sensitive andresistant tuberculosis epidemic in presence of drug treatment. Mathematical Biosciences and Engineering, 2014, 11(4): 971-993. doi: 10.3934/mbe.2014.11.971

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