Progression from latent infection to active disease in dynamic tuberculosis transmission models: a systematic review of the validity of modelling assumptions

Mathematical modelling is commonly used to evaluate infectious disease control policy and is influential in shaping policy and budgets. Mathematical models necessarily make assumptions about disease natural history and, if these assumptions are not valid, the results of these studies can be biased. We did a systematic review of published tuberculosis transmission models to assess the validity of assumptions about progression to active disease after initial infection (PROSPERO ID CRD42016030009). We searched PubMed, Web of Science, Embase, Biosis, and Cochrane Library, and included studies from the earliest available date (Jan 1, 1962) to Aug 31, 2017. We identified 312 studies that met inclusion criteria. Predicted tuberculosis incidence varied widely across studies for each risk factor investigated. For population groups with no individual risk factors, annual incidence varied by several orders of magnitude, and 20-year cumulative incidence ranged from close to 0% to 100%. A substantial proportion of modelled results were inconsistent with empirical evidence: for 10-year cumulative incidence, 40% of modelled results were more than double or less than half the empirical estimates. These results demonstrate substantial disagreement between modelling studies on a central feature of tuberculosis natural history. Greater attention to reproducing known features of epidemiology would strengthen future tuberculosis modelling studies, and readers of modelling studies are recommended to assess how well those studies demonstrate their validity

Dynamic of a TB-HIV Coinfection Epidemic Model with Latent Age

A coepidemic arises when the spread of one infectious disease stimulates the spread of another infectious disease. Recently, this has happened with human immunodeficiency virus (HIV) and tuberculosis (TB). The density of individuals infected with latent tuberculosis is structured by age since latency. The host population is divided into five subclasses of susceptibles, latent TB, active TB (without HIV), HIV infectives (without TB), and coinfection class (infected by both TB and HIV). The model exhibits three boundary equilibria, namely, disease free equilibrium, TB dominated equilibrium, and HIV dominated equilibrium. We discuss the local or global stabilities of boundary equilibria. We prove the persistence of our model. Our simple model of two synergistic infectious disease epidemics illustrates the importance of including the effects of each disease on the transmission and progression of the other disease. We simulate the dynamic behaviors of our model and give medicine explanations