Sensitivity analysis (SA) can aid in identifying influential model parameters and optimizing model structure, yet infectious disease modelling has yet to adopt advanced SA techniques that are capable of providing considerable insights over traditional methods. We investigate five global SA methods-scatter plots, the Morris and Sobol' methods, Latin hypercube sampling-partial rank correlation coefficient and the sensitivity heat map method-and detail their relative merits and pitfalls when applied to a microparasite (cholera) and macroparasite (schistosomaisis) transmission model. The methods investigated yielded similar results with respect to identifying influential parameters, but offered specific insights that vary by method. The classical methods differed in their ability to provide information on the quantitative relationship between parameters and model output, particularly over time. The heat map approach provides information about the group sensitivity of all model state variables, and the parameter sensitivity spectrum obtained using this method reveals the sensitivity of all state variables to each parameter over the course of the simulation period, especially valuable for expressing the dynamic sensitivity of a microparasite epidemic model to its parameters. A summary comparison is presented to aid infectious disease modellers in selecting appropriate methods, with the goal of improving model performance and design.