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

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

Treating cofactors can reverse the expansion of a primary disease epidemic

<p>Abstract</p> <p>Background</p> <p>Cofactors, "nuisance" conditions or pathogens that affect the spread of a primary disease, are likely to be the norm rather than the exception in disease dynamics. Here we present a "simplest possible" demographic model that incorporates two distinct effects of cofactors: that on the transmission of the primary disease from an infected host bearing the cofactor, and that on the acquisition of the primary disease by an individual that is not infected with the primary disease but carries the cofactor.</p> <p>Methods</p> <p>We constructed and analyzed a four-patch compartment model that accommodates a cofactor. We applied the model to HIV spread in the presence of the causal agent of genital schistosomiasis, <it>Schistosoma hematobium</it>, a pathogen commonly co-occurring with HIV in sub-Saharan Africa.</p> <p>Results</p> <p>We found that cofactors can have a range of effects on primary disease dynamics, including shifting the primary disease from non-endemic to endemic, increasing the prevalence of the primary disease, and reversing demographic growth when the host population bears only the primary disease to demographic decline. We show that under parameter values based on the biology of the HIV/<it>S. haematobium </it>system, reduction of the schistosome-bearing subpopulations (e.g. through periodic use of antihelminths) can slow and even reverse the spread of HIV through the host population.</p> <p>Conclusions</p> <p>Typical single-disease models provide estimates of future conditions and guidance for direct intervention efforts relating only to the modeled primary disease. Our results suggest that, in circumstances under which a cofactor affects the disease dynamics, the most effective intervention effort might not be one focused on direct treatment of the primary disease alone. The cofactor model presented here can be used to estimate the impact of the cofactor in a particular disease/cofactor system without requiring the development of a more complicated model which incorporates many other specific aspects of the chosen disease/cofactor pair. Simulation results for the HIV/<it>S. haematobium </it>system have profound implications for disease management in developing areas, in that they provide evidence that in some cases treating cofactors may be the most successful and cost-effective way to slow the spread of primary diseases.</p

Pros and cons of estimating the reproduction number from early epidemic growth rate of influenza A (H1N1) 2009

<p>Abstract</p> <p>Background</p> <p>In many parts of the world, the exponential growth rate of infections during the initial epidemic phase has been used to make statistical inferences on the reproduction number, <it>R</it>, a summary measure of the transmission potential for the novel influenza A (H1N1) 2009. The growth rate at the initial stage of the epidemic in Japan led to estimates for <it>R </it>in the range 2.0 to 2.6, capturing the intensity of the initial outbreak among school-age children in May 2009.</p> <p>Methods</p> <p>An updated estimate of <it>R </it>that takes into account the epidemic data from 29 May to 14 July is provided. An age-structured renewal process is employed to capture the age-dependent transmission dynamics, jointly estimating the reproduction number, the age-dependent susceptibility and the relative contribution of imported cases to secondary transmission. Pitfalls in estimating epidemic growth rates are identified and used for scrutinizing and re-assessing the results of our earlier estimate of <it>R</it>.</p> <p>Results</p> <p>Maximum likelihood estimates of <it>R </it>using the data from 29 May to 14 July ranged from 1.21 to 1.35. The next-generation matrix, based on our age-structured model, predicts that only 17.5% of the population will experience infection by the end of the first pandemic wave. Our earlier estimate of <it>R </it>did not fully capture the population-wide epidemic in quantifying the next-generation matrix from the estimated growth rate during the initial stage of the pandemic in Japan.</p> <p>Conclusions</p> <p>In order to quantify <it>R </it>from the growth rate of cases, it is essential that the selected model captures the underlying transmission dynamics embedded in the data. Exploring additional epidemiological information will be useful for assessing the temporal dynamics. Although the simple concept of <it>R </it>is more easily grasped by the general public than that of the next-generation matrix, the matrix incorporating detailed information (e.g., age-specificity) is essential for reducing the levels of uncertainty in predictions and for assisting public health policymaking. Model-based prediction and policymaking are best described by sharing fundamental notions of heterogeneous risks of infection and death with non-experts to avoid potential confusion and/or possible misuse of modelling results.</p

Precise magnesium isotope measurements in core top planktic and benthic foraminifera

This study presents a new methodology to obtain highly precise measurements (±0.1‰) of magnesium isotope ratios in very small samples of foraminiferal carbonate (40–50 μg). Here this technique is used to examine Mg isotopic variation among different species of core top foraminifera over a range of different ambient conditions. Despite the high degree of temperature control on the abundance of elemental Mg incorporated into foraminiferal tests, analyses of surface dwelling Globigerinoides ruber and G. sacculifer from five cores, with associated sea surface temperatures ranging from 20 to 31°C, show no significant temperature-dependent variations in their Mg isotope ratios. Analyses of different size fractions of G. sacculifer show an increase in Mg/Ca with test size but no variation of Mg isotope ratio. In all, nine planktic and benthic species were analyzed; all show identical Mg isotope ratios with a mean of δ26Mg = −4.72‰, apart from small differences in three species, namely O. universa, G. sacculifer (which are both ∼0.4‰ lighter than the average), and P. obliquiloculata (which is ∼0.4‰ heavier). These results highlight the constancy of foraminiferal Mg isotope ratios, despite changing environmental conditions which dominate Mg/Ca variation and arguably affect Ca isotope fractionation. This is an important observation which needs to be included in any model of foraminiferal calcification. The insusceptibility of δ26Mg values to external parameters makes Mg isotopes ideally suited to constraining past variations in the Mg isotope budget of the oceans and the information this carries about the history of oceanic dolomitization, continental weathering, and hydrothermal behavior

Computational Approaches and Analysis for a Spatio-Structural-Temporal Invasive Carcinoma Model

Spatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the urokinase plasminogen activator (uPA) wherein uPA binds uPA receptors on the cancer cell surface, allowing plasminogen to be cleaved into plasmin, which degrades the extracellular matrix and this way leads to enhanced cancer cell migration. In this paper, we develop a novel numerical approach and associated analysis for spatio-structuro-temporal modelling of the uPA system for up to two-spatial and two-structural dimensions. This is accompanied by analytical exploration of the numerical techniques used in simulating this system, with special consideration being given to the proof of stability within numerical regimes encapsulating a central differences approach to approximating numerical gradients. The stability analysis performed here reveals instabilities induced by the coupling of the structural binding and proliferative processes. The numerical results expound how the uPA system aids the tumour in invading the local stroma, whilst the inhibitor to this system may impede this behaviour and encourage a more sporadic pattern of invasion.PostprintPeer reviewe

Structured models of cell migration incorporating molecular binding processes

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with two examples arising from cancer invasion