A two strain tuberculosis transmission model with therapy and quarantine

Abstract

A two strain tuberculosis model with treatment which allows TB patients with the drug sensitive of strain Mycobacterium tuberculosis to be cured is presented. The model is further extended to incorporate quarantine for active TB cases with multi‐drug resistant TB strains. The model assumes that latently infected individuals develop active disease as a result of endogenous activation and exogenous reinfection. Qualitative analysis of the model including positivity, boundedness and persistence of solutions are presented. The thresholds and equilibria quantities for the models are determined and stability of the solution is analyzed. From the study we conclude that quarantine of the multi‐drug resistant tuberculosis cases reduces the multi‐drug resistant tuberculosis induced reproduction number to values below unit, thus this intervention strategy can control the development of multi‐drug resistant tuberculosis epidemic. Also effective chemoprophylaxis and treatment of infectives result in a reduction of multi‐drug resistant tuberculosis cases since most multi‐drug resistant tuberculosis cases are a result of inappropriate treatment.

First published online: 14 Oct 2010