2016/09/27 by Xiuli Cen, Zhilan Feng, Cen, Xiuli +5
Medicine · #Classical Analysis and ODEs (math.CA) #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.1610.01446
openalex publication_date 2016/09/27 · openalex created_date 2016/10/14 · openalex updated_date 2026/07/28
Antibiotic-resistant bacteria has posed a grave threat to public health by causing a number of nosocomial infections in hospitals. Mathematical models have been used to study the transmission of antibiotic-resistant bacteria within a hospital and the measures to control antibiotic resistance in nosocomial pathogens. Studies presented in \citeLBL,LB have shown great value in understanding the transmission of antibiotic-resistant bacteria in a hospital. However, their results are limited to numerical simulations of a few different scenarios without analytical analysis of the models in all biologically feasible parameter regions. Bifurcation analysis and identification of the global stability conditions are necessary to assess the interventions which are proposed to limit nosocomial infection and stem the spread of antibiotic-resistant bacteria. In this paper we study the global dynamics of the mathematical model of antibiotic resistance in hospitals in \citeLBL,LB. The invasion reproduction number \mathcal Rar of antibiotic-resistant bacteria is introduced. We give the relationship of \mathcal Rar and two control reproduction numbers of sensitive bacteria and resistant bacteria (\mathcal Rsc and \mathcal Rrc). More importantly, we prove that a backward bifurcation may occur at \mathcal Rar=1 when the model includes superinfection which is not mentioned in \citeLB. That is, there exists a new threshold \mathcal Rarc, and if \mathcal Rarc