Modelling challenges in context: Lessons from malaria, HIV, and tuberculosis

• Malaria, HIV, and TB prompt mathematical challenges in infectious disease modelling.
• There exist many critical knowledge gaps to accurately parameterise models.
• Complex within-host dynamics leads to variation in infectiousness among individuals.
• Pathogen genetic diversity alters prevalence and transmission of pathogens.
• Heterogeneous behaviour influences exposure and treatment effectiveness.

Malaria, HIV, and tuberculosis (TB) collectively account for several million deaths each year, with all three ranking among the top ten killers in low-income countries. Despite being caused by very different organisms, malaria, HIV, and TB present a suite of challenges for mathematical modellers that are particularly pronounced in these infections, but represent general problems in infectious disease modelling, and highlight many of the challenges described throughout this issue. Here, we describe some of the unifying challenges that arise in modelling malaria, HIV, and TB, including variation in dynamics within the host, diversity in the pathogen, and heterogeneity in human contact networks and behaviour. Through the lens of these three pathogens, we provide specific examples of the other challenges in this issue and discuss their implications for informing public health efforts.