Incorporating age and delay into models for biophysical systems.

In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have been used widely. However, some biophysical processes such as gene transcription and translation are known to have a significant gap between the initiation and the completion of the processes, which renders the usual assumption of exponential distribution untenable. In this paper, we consider relaxing this assumption by incorporating age-dependent random time delays (distributed according to a given probability distribution) into the system dynamics. We do so by constructing a measure-valued Markov process on a more abstract state space, which allows us to keep track of the 'ages' of molecules participating in a chemical reaction. We study the large-volume limit of such age-structured systems. We show that, when appropriately scaled, the stochastic system can be approximated by a system of partial differential equations (PDEs) in the large-volume limit, as opposed to ordinary differential equations (ODEs) in the classical theory. We show how the limiting PDE system can be used for the purpose of further model reductions and for devising efficient simulation algorithms. In order to describe the ideas, we use a simple transcription process as a running example. We, however, note that the methods developed in this paper apply to a wide class of biophysical systems.

Visceral leishmaniasis: consequences of a neglected disease in a Bangladeshi community.

Visceral leishmaniasis, or kala azar (KA), affects the rural poor, causing significant morbidity and mortality. We examined the epidemiologic, social, and economic impact of KA in a village in Bangladesh. A population-based survey among 2,348 people demonstrated a KA incidence of 2% per year from 2000 to 2002, with a case-fatality rate of 19% among adult women, compared with 6-8% among other demographic groups. Kala azar cases were geographically clustered in certain sections of the village. Anti-leishmanial drug shortages and the high cost of diagnosis and treatment caused substantial emotional and economic hardship for affected families. Communities wanted to learn more about KA, and were willing to take collective action to confront the problems it causes. To decrease the KA burden in endemic areas, community efforts should be supplemented with effective treatment programs to ensure access to appropriate and affordable diagnosis and case management.