Modelling and calibrating antibiotic resistance dynamics with uncertainty: a particle swarm optimization approach for estimating random parameters distribution

Abstract Nowadays, the rapid growth of antibiotic resistance, mainly due to the non-rational use of antibiotics, is one of the threats to global public health. In this context, mathematical modelling of the dynamics of antibiotic resistance, considering the randomness intrinsic to the biological process, would allow studying the long-term evolution of the resistance. In this work, we present an antibiotic resistance model and we propose a novel method to calibrate and estimate an empirical joint distribution of the model parameters which is representative of a real-world scenario. Unlike other approaches, our method does not assume any a priori family of parameter distributions or independence between them. The model calibration has been carried out using the Particle Swarm Optimization (PSO) evolutionary algorithm. Based on the record of their multiple evaluations, our method consists of taking a sample from the parameter space that represents equidistributedly the different zones of the error function explored by the PSO. The sample selection is carried out first with a k -means clustering, and then with two antagonistic objective functions that choose the set of solutions most representative of the data, i.e. that best fit and best capture their uncertainty within a certain confidence interval. From this final sample, an estimation of the empirical joint distribution is obtained. The method has been successfully applied to the case study: the colistin-resistant Acinetobacter baumannii dynamics in the Valencian Community, Spain. The method has been tested under different calibration conditions by varying the number of PSO iterations. The results show that the parameters distributions are representative of the data and the method has been shown to be robust under all calibration scenarios. In all cases, the model simulations of the final sample adequately fit both the calibration and validation resistance data series and capture a high proportion of randomness (around 70% or more) within the 95% confidence interval. Moreover, the empirical joint PDF has revealed the dependence or correlation between the model parameters. All in all, this contribution demonstrates the applicability of the method to a real problem and, due to its metaheuristic approach, its potential application to other mathematical modelling problems with uncertainty.