Practical unidentifiability of a simple vector-borne disease model: implications for parameter estimation and intervention assessment
Authors: Kao Yu-Han , Eisenberg Marisa C. 
Published: July 2017

Background

Mathematical modeling has an extensive history in vector-borne disease epidemiology, and is increasingly used for prediction, intervention design, and understanding mechanisms. Many of these studies rely on parameter estimation to link models and data, and to tailor predictions and counterfactuals to specific settings. However, few studies have formally evaluated whether vector-borne disease models can properly estimate the parameters of interest given the constraints of a particular dataset.

Methodology/Principle Findings

Identifiability methods allow us to examine whether model parameters can be estimated uniquely—a lack of consideration of such issues can result in misleading or incorrect parameter estimates and model predictions. Here, we evaluate both structural (theoretical) and practical identifiability of a commonly used compartmental model of mosquitoborne disease, using 2010 dengue epidemic in Taiwan as a case study. We show that while the model is structurally identifiable, it is practically unidentifiable under a range of human and mosquito time series measurement scenarios. In particular, the transmission parameters form a practically identifiable combination and thus cannot be estimated separately, which can lead to incorrect predictions of the effects of interventions. However, in spite of unidentifiability of the individual parameters, the basic reproduction number was successfully estimated across the unidentifiable parameter ranges. These identifiability issues can be resolved by directly measuring several additional human and mosquito life-cycle parameters both experimentally and in the field.

Conclusions

While we only consider the simplest case for the model, without explicit environmental drivers, we show that a commonly used model of vector-borne disease is unidentifiable from human and mosquito incidence data, making it difficult or impossible to estimate parameters or assess intervention strategies. This work illustrates the importance of examining identifiability when linking models with data to make predictions, and particularly highlights the importance of combining experimental, field, and case data if we are to successfully estimate epidemiological and ecological parameters using models.

Author Summary

Mathematical models have seen increasing use in understanding transmission processes, developing interventions, and predicting disease incidence and prevalence. Vector-borne diseases in particular present both a challenge and an opportunity for modeling, due to the complex interactions between host and vector species. A key step in many of these studies is connecting transmission models with data to infer parameters and make useful predictions, which requires careful consideration of identifiability and uncertainty of the model parameters. Whether due to intrinsic limitations of the model structure, or practical limitations of the data collected, is common that many different parameter values may yield the same or very similar fits to the data, making it impossible to successfully estimate the parameters. This issue of parameter unidentifiability can have broad implications for our ability to draw conclusions from mechanistic models—in some cases making it difficult or impossible to generate specific predictions, forecasts, or parameter estimates from a given model and data. Here, we evaluate these questions for a commonly-used model of vectorborne disease, examining how parameter uncertainty and unidentifiability can affect intervention predictions, estimation of the basic reproduction number, and other public health conclusions drawn from the model.