A nosocomial-pathogens-infections model with impulsive antibiotics treatment on multiple bacteria

Abstract

A nosocomial-pathogens-infections model with impulsive antibiotics treatment on multiple bacteria and time-dependent drug efficacy is proposed in this paper to describe the patients infected by the bacterial populations of both antibiotic-wild-type and antibiotic-resistant strains during the course of combination treatment. The purposes of this paper are to investigate the efficacies of periodic input of antibiotic dosage on bacterial populations with impulsive drug effects and to preserve or restore antibiotic effectiveness. Two antibiotics are used to induce instantaneous antibiotic efficacies at fixed times and antibiotic concentrations decay exponentially. Using the theories of asymptotic periodic systems, uniform persistence theory of discrete dynamical systems and monotone dynamics, sufficient conditions for treatment success as well as for treatment failure are established via the basic reproduction ratio of periodic compartment models. In particular, the results show that if any basic reproduction ratio for the patients infected by wild-type bacteria, resistant bacteria or those infected by both strains is larger than unity, then there will be persistent treatment failure for patients infected by resistant bacteria. This study indicates the significance of exploring a more effective therapeutic regimen for nosocomial infection. Numerical simulations have been performed to verify/extend our analytical results.