Abstract

MODELING THE IMPACT OF DRUG RESISTANCE AND SENSITIVITY ON TRANSMISSION DYNAMICS OF TUBERCULOSIS INCORPORATING CASE DETECTION

A. A. Momoh1, A. I. Kura1, N. G. A. Abimbola2 and Ali I. M.3

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Abstract In this paper, an epidemiology model of tuberculosis with case detection is developed and analysed. The total population is compartmentazed into eight (8) classes namely: Vaccinated, Susceptible Latently infected with drug-resistance TB, Latently infected with drug sensitive-TB, Infectious with drug resistance-TB, Infectious with drug sensitive-TB, Recovered with drug resistance-TB and Recovered with drug sensitive-TB. We prove the positivity of the solution and boundedness of the model which shows that the model is mathematically and biologically well posed. The disease free equilibrium, endemic equilibrium, reproduction number where established. The local and global stability analysis were established and found to be stable if 0 R ?1 and otherwise if 0 R ?1. Finally, we solve the model equations numerically to study the impact of case detection, transmission probability, vaccination and treatment of infected individuals on the transmission dynamics of tuberculosis. The results show that the tested parameters are vital if tuberculosis must be brought under control.

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