Modelling the Role of Diagnosis, Treatment, and Health Education on Multidrug-Resistant Tuberculosis Dynamics

Tuberculosis, an airborne disease affecting almost a third of the world’s population remains one of the major public health burdens globally, and the resurgence of multidrug-resistant tuberculosis in some parts of sub-Saharan Africa calls for concern. To gain insight into its qualitative dynamics at the population level, mathematical modeling which require as inputs key demographic and epidemiological information can fill in gaps where field and lab data are not readily available. A deterministic model for the transmission dynamics of multi-drug resistant tuberculosis to assess the impact of diagnosis, treatment, and health education is formulated. The model assumes that exposed individuals develop active tuberculosis due to endogenous activation and exogenous re-infection. Treatment is offered to all infected individuals except those latently infected with multi-drug resistant tuberculosis. Qualitative analysis using the theory of dynamical systems shows that, in addition to the disease-free equilibrium, there exists a unique dominant locally asymptotically stable equilibrium corresponding to each strain. Numerical simulations suggest that, at the current level of control strategies (with Malawi as a case study), the drug-sensitive tuberculosis can be completely eliminated from the population, thereby reducing multi-drug resistant tuberculosis. 1. Introduction Tuberculosis (TB) is a bacterial infection that is fatal if untreated timely [1]. It is an airborne disease caused by the mycobacterium tuberculosis and primarily affects the lungs (it can also affect the central nervous system, the lymphatic system, the brain, spine, and the kidneys). Approximately one-third of the world’s population is affected [2]. In 1993, concerned with the rising cases of deaths and the new infection rate which were occurring at one per second, the World Health Organization (WHO) declared TB as a global emergency. This resurgence has been closely linked with environmental and social changes that compromised people’s immune system [3]. Out of the 1.7 billion people estimated to be infected with TB, 1.3 billion lived in developing countries [2]. Active TB individuals can infect on average 10–15 other people per year if left untreated [12]. TB progression from inactive (latent) infection to active infection varies from one person to another. People suffering from AIDS have a greater risk of developing active TB with about 50% chance of developing active TB within 2 months and a 5 to 10% chance of developing active TB each year thereafter [1]. TB is treatable and curable if it