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Biomedical subjects

Glenn F Webb

Publications and source records attributed to Glenn F Webb.

7 recordsLinked to original sources
PubMed2006

Stabilization of telomeres in nonlinear models of proliferating cell lines.

We analyse an age-structured model of telomere loss in a proliferating cell population. The cell population is divided into telomere classes, which shorten each round of division. The model consists of a nonlinear system of partial differential equations for the telomere classes. We prove that if the highest telomere class is exempted from mortality, then all the classes stabilize to a nontrivial equilibrium dependent on the initial state of cells in the highest telomere class.

Animals↗
PubMed2006

A mathematical analysis of the dynamics of prion proliferation.

How do the normal prion protein (PrP(C)) and infectious prion protein (PrP(Sc)) populations interact in an infected host? To answer this question, we analyse the behavior of the two populations by studying a system of differential equations. The system is constructed under the assumption that PrP(Sc) proliferates using the mechanism of nucleated polymerization. We prove that with parameter input consistent with experimentally determined values, we obtain the persistence of PrP(Sc). We also prove local stability results for the disease steady state, and a global stability result for the disease free steady state. Finally, we give numerical simulations, which are confirmed by experimental data.

Amino Acid Substitution↗
PubMed2005

Asymptotic behaviour of solutions to abstract logistic equations.

We analyze the asymptotic behaviour of solutions of the abstract differential equation u'(t)=Au(t)-F(u(t))u(t)+f. Our results are applicable to models of structured population dynamics in which the state space consists of population densities with respect to the structure variables. In the equation the linear term A corresponds to internal processes independent of crowding, the nonlinear logistic term F corresponds to the influence of crowding, and the source term f corresponds to external effects. We analyze three separate cases and show that for each case the solutions stabilize in a way governed by the linear term. We illustrate the results with examples of models of structured population dynamics -- a model for the proliferation of cell lines with telomere shortening, a model of proliferating and quiescent cell populations, and a model for the growth of tumour cord cell populations.

Algorithms↗
PubMed2005

A model of antibiotic-resistant bacterial epidemics in hospitals.

The emergence of drug-resistant strains of bacteria is an increasing threat to society, especially in hospital settings. Many antibiotics that were formerly effective in combating bacterial infections in hospital patients are no longer effective because of the evolution of resistant strains, which compromises medical care worldwide. In this article, we formulate a two-level population model to quantify key elements in nosocomial (hospital-acquired) infections. At the bacteria level, patients infected with these strains generate both nonresistant and resistant bacteria. At the patient level, susceptible patients are infected by infected patients at rates proportional to the total bacteria load of each strain present in the hospital. The objectives of this paper are to analyze the dynamic elements of nonresistant and resistant bacteria strains in epidemic populations in hospital environments and to provide understanding of measures to avoid the endemicity of resistant antibiotic strains.

Bacterial Infections↗
PubMed2002

Mailborne transmission of anthrax: Modeling and implications.

A mathematical model is developed to analyze the transmission of inhalational anthrax through the postal system by cross-contamination of mail. The model consists of state vectors describing the numbers of cross-contaminated letters generated, the numbers of anthrax spores on these letters, the numbers of resulting infections in recipients, and matrices of transition probabilities acting on these vectors. The model simulates the recent outbreak in the United States, and provides a general framework to investigate the potential impact of possible future outbreaks.

Anthrax↗
PubMed2002

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.

Cross Infection↗