tdsa: An R package for time-dependent sensitivity analysis

Sensitivity analysis of ecological and epidemiological models is often used to identify the best targets of opportunity for control or management, for example, which subpopulations should be prioritised for vaccination or protection. However, effectiveness of a management action depends not just on which system component is targeted but also on when an action is taken. Traditional methods of model sensitivity analysis apply to time-invariant parameter perturbations, which limits their ability to address questions about the timing of management interventions. A semianalytic method for performing time-dependent sensitivity analysis (TDSA) has been recently introduced to address this need (Ng et al., in press). However, some of the steps typically require substantial time and effort.We have developed an R package, tdsa, that automates all steps required for TDSA by using numerical rather than analytic differentiation of model terms to evaluate the sensitivity equations. By avoiding analytic differentiation, the package substantially reduces user effort and risk of human error and increases the generality of TDSA by making it possible to analyse nonparametric or equation-free models.The results of TDSA may be sensitive to assumptions of the system model. By reducing the effort needed to perform TDSA, the tdsa package facilitates comparison of results under different model assumptions, hence allowing for more robust conclusions. We illustrate this using an example involving the transmission of Morogoro virus in the Natal multimammate mouse, under different assumptions about how the contact rate depends on mouse population density.By automating most of the mathematical and programming steps of the semianalytical approach, the tdsa package makes TDSA accessible to a wide range of users with varying quantitative expertise.