MATHEMATICAL BIOSCIENCES http://www.mbejournal.org/ AND ENGINEERING Volume 3, Number 4, October 2006 pp. 661–682 MODELLING THE HUMAN IMMUNE RESPONSE MECHANISMS TO MYCOBACTERIUM TUBERCULOSIS INFECTION IN THE LUNGS Gesham Magombedze Department of Applied Mathematics National University of Science and Technology PO Box AC939 Ascot, Bulawayo, Zimbabwe Winston Garira Department of Applied Mathematics National University of Science and Technology PO Box AC939 Ascot, Bulawayo, Zimbabwe Eddie Mwenje Department of Applied Biololgy National University of Science and Technology PO Box AC939 Ascot, Bulawayo, Zimbabwe (Communicated by Sergei S. Pilyugin) Abstract. This work elaborates on the effects of cytotoxic lymphocytes (CTLs) and other immune mechanisms in determining whether a TB-infected individ- ual will develop active or latent TB. It answers one intriguing question: why do individuals infected with Mycobacterium tuberculosis (Mtb) experience dif- ferent clinical outcomes? In addressing this question, we have developed a model that captures the effects of CTLs and the combined effects of CD4+ helper T cells (Th1 and Th2) immune response mechanisms to TB infection. The occurrence of active or latent infection is shown to depend on a number of factors that include effector function and levels of CTLs. We use the model to predict disease progression scenarios, including primary, latency or clearance. Model analysis shows that occurrence of active disease is much attributed to the Mtb pathogen ability to persist outside the intracellular environment and that high levels of CTLs result in latent TB, while low levels of CTLs result in active TB. This is attributed to the CTLs’ ability to directly kill infected macrophages and the bacteria inside the infected macrophages. The study suggests directions for further basic studies and potential new treatment strategies. 1. Introduction. Tuberculosis (TB) remains the single largest infectious disease causing high mortality in humans. The majority of cases occur in developing coun- tries, with sub-Saharan Africa having the highest incidence rate per capita [3]. In South Africa alone, two million people coinfected with Mycobacterium tuberculosis (Mtb) and human immunodeficiency virus (HIV) [3] were reported by the year 2000. Today Mtb remains one of the most ubiquitous pathogens in the world. Estimates are that one third of the world’s population is infected with the bacillus and that it 2000 Mathematics Subject Classification. 92D30. Key words and phrases. Mycobacterium tuberculosis (Mtb), cytotoxic lymphocytes (CTLs). 661