A nosocomial epidemic model with infection of patients due to contaminated rooms

Browne, Cameron J.; Webb, Glenn

doi:10.3934/mbe.2015.12.761

Cited by 12 publications

(5 citation statements)

References 17 publications

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“…Transmission of MRSA from environmental surfaces to gloves or hands of HCWs has been documented by several investigators (Boyce 27 ). Though there are some studies in modeling the impact of environmental contaminations in nosocomial infections (see, for example, McBryde and McElwain 28 , Hall et al 29 , Wang 30 , Wang et al 31 , Browne and Webb 32 ), little is known about the role of environmental infection in the transmission dynamics of MRSA, and this provides the motivation of our research.…”

Section: Introductionmentioning

confidence: 99%

Modeling Nosocomial Infections of Methicillin-Resistant Staphylococcus aureus with Environment Contamination*

Wang

Ruan

2017

Sci Rep

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In this work, we investigate the role of environmental contamination on the clinical epidemiology of antibiotic-resistant bacteria in hospitals. Methicillin-resistant Staphylococcus aureus (MRSA) is a bacterium that causes infections in different parts of the body. It is tougher to treat than most strains of Staphylococcus aureus or staph, because it is resistant to some commonly used antibiotics. Both deterministic and stochastic models are constructed to describe the transmission characteristics of MRSA in hospital setting. The deterministic epidemic model includes five compartments: colonized and uncolonized patients, contaminated and uncontaminated health care workers (HCWs), and bacterial load in environment. The basic reproduction number R 0 is calculated, and its numerical and sensitivity analysis has been performed to study the asymptotic behavior of the model, and to help identify factors responsible for observed patterns of infections. A stochastic epidemic model with stochastic simulations is also presented to supply a comprehensive analysis of its behavior. Data collected from Beijing Tongren Hospital will be used in the numerical simulations of our model. The results can be used to provide theoretical guidance for designing efficient control measures, such as increasing the hand hygiene compliance of HCWs and disinfection rate of environment, and decreasing the transmission rate between environment and patients and HCWs.

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Section: Introductionmentioning

confidence: 99%

Modeling Nosocomial Infections of Methicillin-Resistant Staphylococcus aureus with Environment Contamination*

Wang

Ruan

2017

Sci Rep

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“…The dynamic of the H7N9 virus transmission is similar to that of a nosocomial bacteria infection [5], from which was the modeling idea originated. Figure 1 shows the dynamics of H7N9 transmission from live poultry to human and among live poultry.…”

Section: Background and Methodsmentioning

confidence: 99%

A mathematical model about human infections of H7N9 influenza in China with the intervention of live poultry markets closing

Xi¹

2014

Preprint

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This paper develops a deterministic differential equations model that captures the H7N9 virus transmission from live poultry to human via poultryhuman contacts in live poultry markets (LPMs). The virus circulation among live poultry, which happens but is hard to be detected (since contaminated live poultry appear to be asymptomatic), is also incorporated in the model. The time-dependent contact rate between human and live poultry based on LPMs closing information can be estimated. From data of LPMs closing news, the contact rate function can be easily estimated. This model could serve as a rational basis for public health authorities to evaluate the effectiveness of LPM closing, as well as other interventions according to simple modifications. Without data about daily cases, I also provide suggestions for some of the basic parameters that would be a useful fitness parameter set for future simulation.

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“…For example in case of an epidemiological model different splittings of A may yield different formulas for the basic reproduction number R 0 , some of which may be easier to compute due for example to the availability of different types of patient data. See for example the recent paper [8] in this direction.…”

Section: (Re)formulation Of a Nonlinear Problemmentioning

confidence: 99%

Net reproduction functions for nonlinear structured population models

Farkas

2018

Math. Model. Nat. Phenom.

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The goal of this note is to present a general approach to define the net reproduction function for a large class of nonlinear physiologically structured population models. In particular, we are going to show that this can be achieved in a natural way by reformulating a nonlinear problem as a family of linear ones; each of the linear problems describing the evolution of the population in a different, but constant environment. The reformulation of a nonlinear population model as a family of linear ones is a new approach, and provides an elegant way to study qualitative questions, for example the existence of positive steady states. To define the net reproduction number for any fixed (constant) environment, i.e. for the linear models, we use a fairly recent spectral theoretic result, which characterizes the connection between the spectral bound of an unbounded operator and the spectral radius of a corresponding bounded operator. For nonlinear models, varying the environment naturally leads to a net reproduction function. ProloguePhysiologically structured population models have been developed and studied extensively in the past decades, see for example the monographs [18,35,38,45] for an in-depth introduction and review of the topic. Our general research agenda, to relate the stability of steady states of physiologically structured population models to biologically meaningful quantities, allowed us to obtain a number of interesting results, see e.g. [27,29,30,31,32]. In particular, as we have seen for example in [1,27,29,30,31,32], the existence and stability of steady states of nonlinear structured population models can often be characterised using an appropriately defined net reproduction function. In fact we note that stability questions of nonlinear matrix population models were already investigated in the same spirit, see for example the paper [46]. However, we would like to emphasize that previously net reproduction functions were defined for concrete nonlinear models on an 'ad hoc' basis, but typically via analysing the corresponding steady state equations, see e.g. [1,27,28,29,30,31,32] for more details. It is our goal in this paper to present a general framework, which is applicable to different classes of nonlinear models.The existence of positive steady states is an important and interesting question, when studying nonlinear population models; and to establish the existence of non-trivial steady states is often challenging. This is especially the case for models formulated as infinite dimensional dynamical systems, for example delay equations, partial differential equations or integro-differential equations, see e.g. [33,34]. To overcome some of the difficulties, we have developed a very general framework to treat steady state problems of some classes of nonlinear partial differential or partial integro-differential equations, see [10,11,12]. The power of the method we developed becomes apparent for models with so-called infinite dimensional nonlinearities, when in fact the existence 1991 Mathematics Subj...

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A nosocomial epidemic model with infection of patients due to contaminated rooms

Cited by 12 publications

References 17 publications

Modeling Nosocomial Infections of Methicillin-Resistant Staphylococcus aureus with Environment Contamination*

Modeling Nosocomial Infections of Methicillin-Resistant Staphylococcus aureus with Environment Contamination*

A mathematical model about human infections of H7N9 influenza in China with the intervention of live poultry markets closing

Net reproduction functions for nonlinear structured population models

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