Differential and Integral Equations

Asymptotic behavior in nosocomial epidemic models with antibiotic resistance

Erika M. C. D'Agata, Pierre Magal, Shigui Ruan, and Glenn Webb

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Abstract

We study a model of an antibiotic resistance in a hospital setting. The model connects two population levels - bacteria and patients. The bacteria population is divided into non-resistant and resistant strains. The bacterial strains satisfy ordinary differential equations describing the recombination and reversion processes producing the two strains within each infected individual. The patient population is divided into susceptibles, infectives infected with the non-resistant bacterial strain, and infectives infected with the resistant bacterial stain. The infective classes satisfy partial differential equations for the infection age densities of the two classes. We establish conditions for the existence of three possible equilibria for this model: (1) extinction of both infective classes, (2) extinction of the resistant infectives and endemicity of the non-resistant infectives, and (3) endemicity of both infective classes. We investigate the asymptotic behavior of the solutions of the model with respect to these equilibria.

Article information

Source
Differential Integral Equations, Volume 19, Number 5 (2006), 573-600.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050443

Mathematical Reviews number (MathSciNet)
MR2235142

Zentralblatt MATH identifier
1212.35229

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35B40: Asymptotic behavior of solutions 35Q80: PDEs in connection with classical thermodynamics and heat transfer 37L30: Attractors and their dimensions, Lyapunov exponents 37N25: Dynamical systems in biology [See mainly 92-XX, but also 91-XX] 92D30: Epidemiology

Citation

D'Agata, Erika M. C.; Magal, Pierre; Ruan, Shigui; Webb, Glenn. Asymptotic behavior in nosocomial epidemic models with antibiotic resistance. Differential Integral Equations 19 (2006), no. 5, 573--600. https://projecteuclid.org/euclid.die/1356050443


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