Mary Ann Horn

Modeling the Invasion of Community-Acquired Methicillin-Resistant Staphylococcus aureus into Hospitals

BACKGROUNDnMethicillin-resistant Staphylococcus aureus (MRSA) has traditionally been associated with infections in hospitals. Recently, a new strain of MRSA has emerged and rapidly spread in the community, causing serious infections among young, healthy individuals. Preliminary reports imply that a particular clone (USA300) of a community-acquired MRSA (CA-MRSA) strain is infiltrating hospitals and replacing the traditional hospital-acquired MRSA strains. If true, this event would have serious consequences, because CA-MRSA infections in hospitals would occur among a more debilitated, older patient population.nnnMETHODSnA deterministic mathematical model was developed to characterize the factors contributing to the replacement of hospital-acquired MRSA with CA-MRSA and to quantify the effectiveness of interventions aimed at limiting the spread of CA-MRSA in health care settings.nnnRESULTSnThe model strongly suggests that CA-MRSA will become the dominant MRSA strain in hospitals and health care facilities. This reversal of dominant strain will occur as a result of the documented expanding community reservoir and increasing influx into the hospital of individuals who harbor CA-MRSA. Competitive exclusion of hospital-acquired MRSA by CA-MRSA will occur, with increased severity of CA-MRSA infections resulting in longer hospitalizations and a larger in-hospital reservoir of CA-MRSA.nnnCONCLUSIONSnImproving compliance with hand hygiene and screening for and decolonization of CA-MRSA carriers are effective strategies. However, hand hygiene has the greatest return of benefits and, if compliance is optimized, other strategies may have minimal added benefit.

The Impact of Persistent Gastrointestinal Colonization on the Transmission Dynamics of Vancomycin-Resistant Enterococci

The transmission dynamics of vancomycin-resistant enterococci (VRE) and factors contributing to their dissemination are complex. Mathematical modeling was used to simulate patterns of dissemination among patients and health care workers (HCWs) and to quantify the contribution of specific factors and infection control interventions on the endemic prevalence (EP) of VRE in a long-term hemodialysis unit. The model predicted that (1) an EP of 12% would be reached over time, regardless of the number of patients initially colonized, (2) endemicity would be sustained by the constant influx of newly colonized patients discharged from the hospital, (3) duration of VRE gastrointestinal colonization would have the most impact on the number of secondary cases, increasing the EP to a maximum of 70%, and (4) decreasing the patient:HCW ratio or improving hand hygiene would decrease the EP to 3%. Decreasing the duration of colonization, limiting hospital acquisition of VRE, and improving compliance with hand hygiene in the hemodialysis unit may decrease the rapidly rising rates of VRE in the patient population.

Efficacy of infection control interventions in reducing the spread of multidrug-resistant organisms in the hospital setting

Multidrug-resistant organisms (MDRO) continue to spread in hospitals globally, but the population-level impact of recommended preventive strategies and the relative benefit of individual strategies targeting all MDRO in the hospital setting are unclear. To explore the dynamics of MDRO transmission in the hospital, we develop a model extending data from clinical individual-level studies to quantify the impact of hand hygiene, contact precautions, reducing antimicrobial exposure and screening surveillance cultures in decreasing the prevalence of MDRO colonization and infection. The effect of an ongoing increase in the influx of patients colonized with MDRO into the hospital setting is also quantified. We find that most recommended strategies have substantial effect in decreasing the prevalence of MDRO over time. However, screening for asymptomatic MDRO colonization among patients who are not receiving antimicrobials is of minimal value in reducing the spread of MDRO.

Competition of hospital-acquired and community-acquired methicillin-resistant Staphylococcus aureus strains in hospitals

Recently, we [E.M.C. DAgata, G.F. Webb, M.A. Horn, R.C. Moellering Jr., and S. Ruan, Modelling the invasion of community-acquired methicillin-resistant Staphylococcus aureus into the hospital setting, Clin. Infect. Dis. 48 (2009), pp. 274–284] proposed a deterministic mathematical model to characterize the factors contributing to the replacement of hospital-acquired methicillin-resistant Staphylococcus aureus (HA-MRSA) with the community-acquired MRSA (CA-MRSA) and to quantify the effectiveness of interventions aimed at limiting the spread of CA-MRSA in the hospital setting. Numerical simulations of the model strongly suggest that CA-MRSA will become the dominant MRSA strain in the hospital setting. In this companion paper, we provide steady-state analysis and more numerical simulations of the model. It is shown that when no colonized or infected patients enter the hospital, competitive exclusion of HA-MRSA by CA-MRSA will occur with increased severity of CA-MRSA infections resulting in longer hospitalizations and a larger in-hospital reservoir of CA-MRSA. Improving compliance with hand hygiene and decolonization of CA-MRSA carriers are effective control strategies.

Modeling species-specific diacylglycerol dynamics in the RAW 264.7 macrophage

A mathematical model of the G protein signaling pathway in RAW 264.7 macrophages downstream of P2Y(6) receptors activated by the ubiquitous signaling nucleotide uridine 5-diphosphate is developed. The model, which is based on time-course measurements of inositol trisphosphate, cytosolic calcium, and diacylglycerol, focuses particularly on differential dynamics of multiple chemical species of diacylglycerol. When using the canonical pathway representation, the model predicted that key interactions were missing from the current network structure. Indeed, the model suggested that accurate depiction of experimental observations required an additional branch to the signaling pathway. An intracellular pool of diacylglycerol is immediately phosphorylated upon stimulation of an extracellular receptor for uridine 5-diphosphate and subsequently used to aid replenishment of phosphatidylinositol. As a result of sensitivity analysis of the model parameters, key predictions can be made regarding which of these parameters are the most sensitive to perturbations and are therefore most responsible for output uncertainty.

Local smoothing properties of a Schrödinger equation with nonconstant principal part

A Schrodinger equation with continuous, nonconstant coefficients appearing in the principal part of the differential operator is considered. Through the use of Littman and Taylor’s general technique for proving boundary controllability of evolution equations, a simple proof of exact boundary controllability for the Schrodinger equation is obtained. Proof of the necessary regularity for the solution relies on an approximation argument and the spectral results for elliptic operators of Birman and Solomyak.

Mathematical modelling and analysis of cellular signalling in macrophages

Cell signalling pathways play a crucial role in proper cell development and behaviour, with implications to survival, chemotaxis, proliferation, and even programmed cell death known as apoptosis. In this article, we outline a mathematical model of the G-protein signalling pathway in a particular cell line of macrophages, focusing on activation of a particular G-protein-coupled receptor, P2Y6. The model is based on the kinetics of P2Y6 surface receptors, inositol trisphosphate, cytosolic calcium, and differential dynamics of multiple species of diacylglycerol. Insight into the dynamics of the system is given through recently available experimental results and incorporated into the model. Mathematical analysis of the model, including establishment of global existence, uniqueness, positivity, and boundedness of solutions, and global stability of a unique steady-state solution is discussed.

Stabilization of the Dynamic System of Elasticity by Nonlinear Boundary Feedback

Uniform stabilization for the system of isotropic linear elasticity is established using nonlinear velocity feedback via traction forces on the boundary. Through the use of sharp trace regularity results and a nonlinear compactness/uniqueness argument, a proof is derived without imposition of strong geometric restrictions on the controlled portion of the boundary, thus extending the original work of Lagnese [8].

Effects of Thickness on Sharp Trace Regularity for a Kirchhoff Plate with Free Boundary Conditions

Sharp trace regularity estimates for a Kirchhoff plate with free boundary conditions are established with the primary goal of tracking the effects of thickness in the estimates. Microlocal analysis is used in the proof with an alternative localization to the one seen in the earlier work of Lasiecka and Triggiani. Knowledge of how thickness appears in the estimates has important implications in uniform stability for more complex systems which involve the Kirchhoff plate equation.