MATHEMATICAL MODELS OF TUBERCULOSIS: ACCOMPLISHMENTS AND FUTURE CHALLENGES

Tuberculosis is a leading cause of infectious mortality. Although anti-biotic treatment is available and there is vaccine, tuberculosis levels are rising in many areas of the world. The recent emergence of drug-resistant of TB is alarming, as are the potential effects of HIV on TB epidemics. Mathematical models have been used to study tuberculosis in the past and have influenced policy; there is renewed opportunity for mathematical models to contribute today. Here we review and compare the mathematical models of tuberculosis dynamics in the literature. We present two models of our own: a spatial stochastic individual-based model and a set of delay differential equations encapsulating the same biological assumptions. We compare two different assumptions about partial immunity and explore the effect of preventative treatments. We argue that seemingly subtle differences in model assumptions can have significant effects on biological conclusions.