Bifurcation analysis and global dynamics of a mathematical model of antibiotic resistance in hospitals

Abstract

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 [4, 5] 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 [4, 5]. The invasion reproduction number R ar of antibiotic-resistant bacteria is introduced. We give the relationship of R ar and two control reproduction numbers of sensitive bacteria and resistant bacteria (R sc and R rc ). More importantly, we prove that a backward bifurcation may occur at R ar = 1 when the model includes superinfection which is not mentioned in [5]. That is, there exists a new threshold R c ar , and if R c ar < R ar < 1, then the system can have two interior equilibria and it supports an interesting bistable phenomenon. This provides critical information on controlling the antibiotic-resistance in a hospital.

Number of infections suffered by a focal individual in a two‐strain SIS model with partial cross‐immunity

“…In the context of nosocomial pathogens, we illustrate in Section 4 the approach by describing the spread of sensitive and resistant bacteria among patients within a hospital ward. Unlike the studies of Cen et al 14 and Lipsitch et al 15 where the interest is in deterministic models, we show how Markov chain models can be helpful for understanding the transmission of resistance in hospitals. Our numerical results highlight that the effectiveness of antibiotics is an important but not unique piece of the overall resistance problem, and factors such as the fitness cost also have a strong effect on the numbers of infections.…”

“…This section is devoted to numerical experiments to implement the analytical results we obtained in Section as well as to provide evidences that these results are likely to hold in realistic situations. Specifically, experiments in Figures are related to the compartmental model of Lipsitch et al, which addresses antibiotic resistance in hospitals; for related work, see the papers by Cen et al and Gómez‐Corral and López‐García ,. Section 3.3…”

“…Over the last decades, there have been numerous theoretical studies on the persistence and extinction of multiple pathogen strains in deterministic (see, eg, Ackleh and Allen, Allen et al, Allen and Kirupaharan(, Section 2.1), Kendall and Saunders(, Section 3), Nuño et al, Rowthorn and Walther, Saunders(, Section 2)) and stochastic models (see, eg, Allen and Kirupaharan(, Section 2.2), Amador et al, Ball and Becker, Ball and Britton, Bhattacharyya et al, Gómez‐Corral and López‐García, Kendall and Saunders(, Section 4), Saunders(, Section 3)). These models involving several different strains of a pathogen have been applied to the study of the bacterial resistance to antibiotics() and diseases such as arenavirus and hantavirus, HIV/AIDS, HIV/TB, influenza, myxomatosis in rabbit populations, tuberculosis, and viral respiratory tract diseases, to name a few.…”

Computational Health Engineering Applied to Model Infectious Diseases and Antimicrobial Resistance Spread

“…Most of these models are highly useful to predict and control outbreaks [35]. In addition, dynamics models based on systems instead of compartments [116] are also beneficial to implement in a specific community or region [103]. The stochastic models are the most suitable, when considering variables such as cross-transmission or temporary nursery staff, in the study of outbreaks [117] (Table A1).…”

Multi‐drug antimicrobial resistance model

“…Consequently, the fractional-order formulation is quite relevant. [21][22][23][24] The authors [25][26][27][28] show that the coexistence of drug sensitive and drug resisting strains is an observed phenomena.…”