Migration paths saturations in meta-epidemic systems

In this paper we consider a simple two-patch model in which a population affected by a disease can freely move. We assume that the capacity of the interconnected paths is limited, and thereby influencing the migration rates. Possible habitat disruptions due to human activities or natural events are accounted for. The demographic assumptions prevent the ecosystem to be wiped out, and the disease remains endemic in both populated patches at a stable equilibrium, but possibly also with an oscillatory behavior in the case of unidirectional migrations. Interestingly, if infected cannot migrate, it is possible that one patch becomes disease-free. This fact could be exploited to keep disease-free at least part of the population

Dynamics of precipitation pattern formation at geothermal hot springs

We formulate and model the dynamics of spatial patterns arising during the precipitation of calcium carbonate from a supersaturated shallow water flow. The model describes the formation of travertine deposits at geothermal hot springs and rimstone dams of calcite in caves. We find explicit solutions for travertine domes at low flow rates, identify the linear instabilities which generate dam and pond formation on sloped substrates, and present simulations of statistical landscape evolution

Interaction, Pair Formation and Force of Infection Terms in Sexually Transmitted Diseases

15 pages, 1 article*Interaction, Pair Formation and Force of Infection Terms in Sexually Transmitted Diseases* (Busenberg, Stavros; Castillo-Chavez, Carlos) 15 page

Molecular diffusion of CF\u3csub\u3e3\u3c/sub\u3eSF\u3csub\u3e5\u3c/sub\u3e in pure water and artificial seawater

We have experimentally determined the diffusion coefficient for trifluoromethyl sulfur pentafluoride (CF3SF5) in pure water and artificial seawater over a temperature range of − 2.0 °C to 30.0 °C. A working gas standard containing known concentrations of CF3SF5 and sulfur hexafluoride (SF6) was prepared. The working standard was allowed to diffuse across a water barrier, stabilized with agar gel, and the diffused gas was swept into a gas chromatograph with an electron-capture detector to measure the resulting gas mixing ratio. The mixing ratios for both CF3SF5 and SF6 were measured to determine the diffusivity for each species. The diffusion coefficient for SF6 was determined during these experiments as a check against existing literature values and to validate our experimental setup. The experimental data were fit to the Arrhenius equation to yield the following equations DCF3SF5 = 0.0015 exp (-12.9/RT) and DSF6 = 0.037 exp (-19.8/RT), where R is the gas constant in units of kilojoules per mole per kelvin and T is the temperature in kelvin. At the mean temperature of the ocean, 18 °C, DCF3SF5 = 7.02 × 10-6 ± 9.9% and DSF6 = 1.03 × 10-5 ± 13.8 % cm2/s. The diffusion coefficients for SF6 matched the literature data within 4.3% for all temperatures

Pair Formation in Structured Populations

This issue was undated. The date given is an estimate.26 pages, 1 article*Pair Formation in Structured Populations* (Castillo-Chavez, Carlos; Busenberg, Stavros; Gerow, Ken) 26 page

Convergence to equilibrium in degenerate parabolic equations with delay

© 2012 Elsevier Ltd In [11], Busenberg & Huang (1996) showed that small positive equilibria can undergo supercritical Hopf bifurcation in a delay-logistic reaction–diffusion equation with Dirichlet boundary conditions. Consequently, stable spatially inhomogeneous time-periodic solutions exist. Previously in [12] Badii, Diaz & Tesei (1987) considered a similar logistic-type delay-diffusion equation, but differing in two important respects: firstly by the inclusion of nonlinear degenerate diffusion of so-called porous medium type, and secondly by the inclusion of an additional ‘dominating instantaneous negative feedback’ (where terms local in time majorize the delay terms, in some sense). Sufficient conditions were given ensuring convergence of non-negative solutions to a unique positive equilibrium. A natural question to ask, and one which motivated the present work, is: can one still ensure convergence to equilibrium in delay-logistic diffusion equations in the presence of nonlinear degenerate diffusion, but in the absence of dominating instantaneous negative feedback? The present paper considers this question and provides sufficient conditions to answer in the affirmative. In fact the results are much stronger, establishing global convergence for a much wider class of problems which generalize the porous medium diffusion and delay-logistic terms to larger classes of nonlinearities. Furthermore the results obtained are independent of the size of the delay

Flow and geochemistry of groundwater beneath a back-barrier lagoon : the subterranean estuary at Chincoteague Bay, Maryland, USA

This paper is not subject to U.S. copyright. The definitive version was published in Marine Chemistry 113 (2009): 78-92, doi:10.1016/j.marchem.2009.01.004.To better understand large-scale interactions between fresh and saline groundwater beneath an Atlantic coastal estuary, an offshore drilling and sampling study was performed in a large barrier-bounded lagoon, Chincoteague Bay, Maryland, USA. Groundwater that was significantly fresher than overlying bay water was found in shallow plumes up to 8 m thick extending more than 1700 m offshore. Groundwater saltier than bay surface water was found locally beneath the lagoon and the barrier island, indicating recharge by saline water concentrated by evaporation prior to infiltration. Steep salinity and nutrient gradients occur within a few meters of the sediment surface in most locations studied, with buried peats and estuarine muds acting as confining units. Groundwater ages were generally more than 50 years in both fresh and brackish waters as deep as 23 m below the bay bottom. Water chemistry and isotopic data indicate that freshened plumes beneath the estuary are mixtures of water originally recharged on land and varying amounts of estuarine surface water that circulated through the bay floor, possibly at some distance from the sampling location. Ammonium is the dominant fixed nitrogen species in saline groundwater beneath the estuary at the locations sampled. Isotopic and dissolved-gas data from one location indicate that denitrification within the subsurface flow system removed terrestrial nitrate from fresh groundwater prior to discharge along the western side of the estuary. Similar situations, with one or more shallow semi-confined flow systems where groundwater geochemistry is strongly influenced by circulation of surface estuary water through organic-rich sediments, may be common on the Atlantic margin and elsewhere.Primary funding was provided by USGS (Coastal and Marine Geology Program and National Research Program in Water Resources) with additional material support from the National Park Service (C. Zimmerman) and the University of Toledo