A random mathematical model to describe the antibiotic resistance depending on the antibiotic consumption: the Acinetobacter baumannii colistin-resistant case in Valencia, Spain

ABSTRACT

The increase in antibiotic resistance in recent years, mainly due to the non-rational use of antibiotics, is one of the most important global public health threats. In this paper, we propose a mathematical dynamic random model describing the antibiotic resistance evolution of a bacteria and where antibiotic consumption is included is the main driving force in the resistance increase. The random model is solved using the Random Variable Transformation technique and is applied to study the case of Acinetobacter baumannii bacterium resistant to the antibiotic colistin in Valencia, Spain. Using the Multi-Objective Particle Swarm Optimization algorithm, the model has been calibrated with the A. baumannii colistin-resistance and colistin consumption data series. With the optimal model, four possible 7-year future scenarios with different antibiotic consumption trends have been simulated. The model results show how reducing antibiotic consumption does not easily stop the increase in resistance.

KEYWORDS:

• antibiotic resistance
• random models
• probability density function
• random variable Transformation technique
• colistin-resistant Acinetobacter baumannii

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 68W50
• 92D30
• 37H10

Disclosure statement

The authors declare no potential conflict of interests.

Additional information

Funding

This work has been funded by the project SBPLY/21/180225/000062 funded by the Government of Castilla-La Mancha and ERDF A way of making Europe. It is also partially funded by MCIN/AEI/10.13039/501100011033 and “ESF Investing your future” through the projects PID2019-106758GB-C33 and PID2020-115270GB-I00. Additionally, it has been funded by the Universitat Politècnica de València PAID-01-22 program under grant 20230185.