Consistency of epidemiologic estimates

Background: The epidemiology of a disease describes numbers of people becoming incident, being prevalent, recovering, surviving, and dying from the disease or from other causes. As a matter of accounting principle, the inflow, stock, and outflows must be compatible, and if we could observe completely every person involved, the epidemiologic estimates describing the disease would be consistent. Lack of consistency is an indicator for possible measurement error. Methods: We examined the consistency of estimates of incidence, prevalence, and excess mortality of dementia from the Rotterdam Study. We used the incidence and excess mortality estimates to calculate with a mathematical disease model a predicted prevalence, and compared the predicted to the observed prevalence. Results: Predicted prevalence is in most age groups lower than observed, and the difference between them is significant for some age groups. Conclusions: The observed discrepancy could be due to overestimates of prevalence or excess mortality, or an underestimate of incidence, or a combination of all three. We conclude from an analysis of possible causes that it is not possible to say which contributes most to the discrepancy. Estimating dementia incidence in an aging cohort presents a dilemma: with a short follow-up border-line incident cases are easily missed, and with longer follow-up measurement problems increase due to the associated aging of the cohort. Checking for consistency is a useful strategy to signal possible measurement error, but some sources of error may be impossible to avoid.

A dynamic mathematical model for sequential leach bed anaerobic digestion of organic fraction of municipal solid waste

A mathematical model that describes the operation of a sequential leach bed process for anaerobic digestion of organic fraction of municipal solid waste (MSW) is developed and validated. This model assumes that ultimate mineralisation of the organic component of the waste occurs in three steps, namely solubilisation of particulate matter, fermentation to volatile organic acids (modelled as acetic acid) along with liberation of carbon dioxide and hydrogen, and methanogenesis from acetate and hydrogen. The model incorporates the ionic equilibrium equations arising due to dissolution of carbon dioxide, generation of alkalinity from breakdown of solids and dissociation of acetic acid. Rather than a charge balance, a mass balance on the hydronium and hydroxide ions is used to calculate pH. The flow of liquid through the bed is modelled as occurring through two zones-a permeable zone with high flushing rates and the other more stagnant. Some of the kinetic parameters for the biological processes were obtained from batch MSW digestion experiments. The parameters for flow model were obtained from residence time distribution studies conducted using tritium as a tracer. The model was validated using data from leach bed digestion experiments in which a leachate volume equal to 10% of the fresh waste bed volume was sequenced. The model was then tested, without altering any kinetic or flow parameters, by varying volume of leachate that is sequenced between the beds. Simulations for sequencing/recirculating 5 and 30% of the bed volume are presented and compared with experimental results. (C) 2002 Elsevier Science B.V. All rights reserved.

A mathematical model of integrin-mediated haptotactic cell migration

Haptotactic cell migration, a directed response to gradients of cell—extracellular matrix adhesion, is an important process in a number of biological phenomena such as wound healing and tumour cell invasion. Previously, mathematical models of haptotaxis have been developed on the premise that cells migrate in response to gradients in the density of the extracellular matrix. In this paper, we develop a novel mathematical model of haptotaxis which includes the adhesion receptors known as integrins and a description of their functional activation, local recruitment and protrusion as part of lamellipodia. Through the inclusion of integrins, the modelled cell matter is able to respond to a true gradient of cell–matrix adhesion, represented by functionally active integrins. We also show that previous matrix-mediated models are in fact a subset of the novel integrin-mediated models, characterised by specific choices of diffusion and haptotaxis coefficients in their model equations. Numerical solutions suggest the existence of travelling waves of cell migration that are confirmed via a phase plane analysis of a simplified model.