Population dynamics models based on the transmission mechanism of MCR-1

• Published in: Physica A 2019-02, Vol.515, p.310-323
• Main Authors: Qu, Leilei, Gao, Xubin, Kang, Baolin, He, Mingfeng, Pan, Qiuhui
• Format: Article
• Language: English
• Subjects: Antibiotic resistance; Mathematic model; Mcr-1; Population dynamics; Stability of equilibrium points
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2018.09.141

Antimicrobial resistance is now considered as one of the most serious global threats to human health in the 21st century. Recently, the discovery of a plasmid-borne colistin resistance gene, mcr-1, in China heralds the emergence of truly pan-drug-resistant bacteria. The gene has been found primarily in Escherichia coli but has also been identified in other members of the Enterobacteriaceae in animal, food, human, and environmental samples on every continent. Until now, the articles published have appeared to fairly use and interpret experimental studies. The aim of our work is to develop mathematic models that quantitatively describe the dynamic of the population of domestic animals and humans. We propose two ordinary differential equation models for the transmission dynamic of mcr-1 gene. The models are analyzed using stability theory of differential equations. Positive equilibrium points of the system are investigated and their stability analyses are carried out. Moreover, the numerical simulations of the proposed model are also represented Our results show that the fraction of animals used for human consumption is the most effective parameters of controlling the spread of mcr-1 gene in comparison with other parameters. •We establish mathematical models based on the transmission mechanic of mcr-1 gene.•The mcr-1 gene cannot be transmitted vertically in the population of animals.•The models are analyzed using stability theory of differential equations and c numerical simulations.•The effect of three important parameters which can be controlled by human are discussed.•Colistin resistance is not as serious as we imagined due to its transmission mechanism.