A mathematical model of tuberculosis transmission with heterogeneity in disease susceptibility and progression under a treatment regime for infectious cases

Abstract

The effect of difference in susceptibility on the dynamics of tuberculosis is an ongoing study. Several genes in TB co-receptors (e.g. HLA and non-HLA) have been correlated with susceptibility and resistance to tuberculosis and rate of progression to active TB. In this paper, we present a novel mathematical model that distinguishes between susceptibility amongst the population. The model classifies the susceptibles as having no, partial or full natural resistance to tuberculosis and the latently infecteds as rapid, normal or very slow (or no) progressors to active TB depending on the genes. The goal of this paper is to investigate the impact of such heterogeneity on the spread of tuberculosis and to identify key parameters that could be used in understanding these heterogeneities more fully. We derived the reproduction number RT for the model and examine the relative contributions to RT from the three latently infected classes as well as the infectious classes. The effect of treatment under the heterogeneity is also examined.