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Estimating model parameters is a crucial step in mathematical modelling andtypically involves minimizing the disagreement between model predictions andexperimental data. This calibration data can change throughout a study,particularly if modelling is performed simultaneously with the calibrationexperiments, or during an on-going public health crisis as in the case of theCOVID-19 pandemic. Consequently, the optimal parameter set, or maximallikelihood estimator (MLE), is a function of the experimental data set. Here,we develop a numerical technique to predict the evolution of the MLE as afunction of the experimental data. We show that, when considering perturbationsfrom an initial data set, our approach is significantly more computationallyefficient that re-fitting model parameters while resulting in acceptable modelfits to the updated data. We use the continuation technique to develop anexplicit functional relationship between fit model parameters and experimentaldata that can be used to measure the sensitivity of the MLE to experimentaldata. We then leverage this inverse sensitivity analysis to select betweenmodel fits with similar information criteria, \textit{a priori} determine theexperimental measurements to which the MLE is most sensitive, and suggestadditional experiment measurements that can resolve parameter uncertainty.

A continuation technique for maximum likelihood estimators in biological models