The Basic Reproduction Number for Cellular SIR Networks

The basic reproduction number \(R_0\) is the average number of new infections produced by a typical infective individual in the early stage of an infectious disease, following the introduction of few infective individuals in a completely susceptible population. If \(R_0<1\) , then the disease dies, whereas for \(R_0>1\) the infection can invade the host population and persist. This threshold quantity is well studied for SIR compartmental or mean field models based on ordinary differential equations, and a general method for its computation has been proposed by van den Driessche and Watmough. We concentrate here on SIR epidemiological models that take into account the contact network N underlying the transmission of the disease. In this context, it is generally admitted that \(R_{0}\) can be approximated by the average number \(R_{2,3}\) of infective individuals of generation three produced by an infective of generation two. We give here a simple analytic formula of \(R_{2,3}\) for SIR cellular networks. Simulations on two-dimensional cellular networks with von Neumann and Moore neighborhoods show that \(R_{2,3}\) can be used to capture a threshold phenomenon related the dynamics of SIR cellular network and confirm the good quality of the simple approach proposed recently by Aparicio and Pascual for the particular case of Moore neighborhood.     

Basic Reproduction Number for HIV Model Incorporating Commercial Sex and Behavior Change

The basic reproduction number is obtained for an HIV epidemic model incorporating direct and indirect commercial sex as well as behavior change by the female commercial sex workers (CSWs) and their male customers in response to the proliferation of the disease in the community. A recent result by van den Driessche P., and Watmough J. (Math. Biosci. 180:29–48, 2002) is utilized to compute the threshold parameters for the local asymptotic stability of the Disease-Free Equilibrium (DFE), by considering the transfers in and out of the infective classes. Numerical examples are used to describe the uniqueness and global properties of the endemic equilibrium when DFE is unstable. Biological interpretation of the results obtained in this work is discussed, as are the implications of our results for the design of public health policies such as targeting strategy to target intervention and control measures toward specific high-risk population groups in order to reduce infections. We show that targeting any one sector of the commercial sex alone for prevention will be difficult to have a decided effect on eradicating the epidemic. However, if the aim of the targeted intervention policy is not eradication of the epidemic but decrease in HIV incidence of a particular high-risk group, then concentrated targeting strategy could be sufficient, if properly implemented. This work also demonstrates the usefulness of the theorem of van den Driessche and Watmough (Math. Biosci. 180:29–48, 2002) in obtaining threshold parameters for complicated infectious diseases models.     

Periodic Matrix Population Models: Growth Rate,Basic Reproduction Number,and Entropy

This article considers three different aspects of periodic matrix population models. First, a formula for the sensitivity analysis of the growth rate λ is obtained that is simpler than the one obtained by Caswell and Trevisan. Secondly, the formula for the basic reproduction number ℛ₀ in a constant environment is generalized to the case of a periodic environment. Some inequalities between λ and ℛ₀ proved by Cushing and Zhou are also generalized to the periodic case. Finally, we add some remarks on Demetrius’ notion of evolutionary entropy H and its relationship to the growth rate λ in the periodic case.     

Short Term Depression Unmasks the Ghost Frequency

Short Term Plasticity (STP) has been shown to exist extensively in synapses throughout the brain. Its function is more or less clear in the sense that it alters the probability of synaptic transmission at short time scales. However, it is still unclear what effect STP has on the dynamics of neural networks. We show, using a novel dynamic STP model, that Short Term Depression (STD) can affect the phase of frequency coded input such that small networks can perform temporal signal summation and determination with high accuracy. We show that this property of STD can readily solve the problem of the ghost frequency, the perceived pitch of a harmonic complex in absence of the base frequency. Additionally, we demonstrate that this property can explain dynamics in larger networks. By means of two models, one of chopper neurons in the Ventral Cochlear Nucleus and one of a cortical microcircuit with inhibitory Martinotti neurons, it is shown that the dynamics in these microcircuits can reliably be reproduced using STP. Our model of STP gives important insights into the potential roles of STP in self-regulation of cortical activity and long-range afferent input in neuronal microcircuits.     

Effect of the Number of Patches in a Multi-patch SIRS Model with Fast Migration on the Basic Reproduction Rate

We consider a two-patch epidemiological system where individuals can move from one patch to another, and local interactions between the individuals within a patch are governed by the classical SIRS model. When the time-scale associated with migration is much smaller than the time-scale associated with infection, aggregation methods can be used to simplify the initial complete model formulated as a system of ordinary differential equations. Analysis of the aggregated model then shows that the two-patch basic reproduction rate is smaller than the 1 patch one. We extend this result to a linear chain of P patches (P > 2). These results are illustrated by some examples for which numerical integration of the system of ordinary differential equations is performed. Simulations of an individual based model implemented with a multi-agent system are also carried out.     

Model for Short Term Movements in Stapelia variegata Linn

Recently it was demonstrated that holographic interferometry could be used to quantify minute displacements of a mature Stapelia variegata Linn. The previously unobtainable measurements revealed that the short term response of the stapelia was regular enough so that the dynamics could be evaluated through the use of a highly damped mass, spring, dashpot model. Such a model is derived explicitly and the relationship between movements of the entire plant and the dynamics of individual cells or groups of cells is shown.     

A Short Term Quality Control Tool for Biodegradable Microspheres

Accelerated in vitro release testing methodology has been developed as an indicator of product performance to be used as a discriminatory quality control (QC) technique for the release of clinical and commercial batches of biodegradable microspheres. While product performance of biodegradable microspheres can be verified by in vivo and/or in vitro experiments, such evaluation can be particularly challenging because of slow polymer degradation, resulting in extended study times, labor, and expense. Three batches of Leuprolide poly(lactic-co-glycolic acid) (PLGA) microspheres having varying morphology (process variants having different particle size and specific surface area) were manufactured by the solvent extraction/evaporation technique. Tests involving in vitro release, polymer degradation and hydration of the microspheres were performed on the three batches at 55°C. In vitro peptide release at 55°C was analyzed using a previously derived modification of the Weibull function termed the modified Weibull equation (MWE). Experimental observations and data analysis confirm excellent reproducibility studies within and between batches of the microsphere formulations demonstrating the predictability of the accelerated experiments at 55°C. The accelerated test method was also successfully able to distinguish the in vitro product performance between the three batches having varying morphology (process variants), indicating that it is a suitable QC tool to discriminate product or process variants in clinical or commercial batches of microspheres. Additionally, data analysis utilized the MWE to further quantify the differences obtained from the accelerated in vitro product performance test between process variants, thereby enhancing the discriminatory power of the accelerated methodology at 55°C.     

Short Term Preservation of Hide Using Vacuum: Influence on Properties of Hide and of Processed Leather

The objective of this work was to investigate vacuum influence on hide preservation time and how it affects hide structure. It was established that vacuum prolongs the storage time without hide tissue putrefaction up to 21 days when the storage temperature is 4°C. The microorganisms act for all storage times, but the action is weak and has no observable influence on the quality of hide during the time period mentioned. The hide shrinkage temperature decrease is negligible, which shows that breaking of intermolecular bonds does not occur. Optical microscopy, infrared spectroscopy and differential scanning calorimetry also did not show any structural changes which can influence the quality of leather produced from such hide. The qualitative indexes of wet blue processed under laboratory conditions and of leather produced during industrial trials are presented. Indexes such as chromium compounds exhaustion, content of chromium in leather, content of soluble matter in dichloromethane, strength properties, and shrinkage temperature were determined. Properties of the leather produced from vacuumed hide under industrial conditions conformed to the requirements of shoe upper leather.     

Assessment of Nitrification Potential in Ground Water Using Short Term, Single-Well Injection Experiments

Nitrification was measured within a sand and gravel aquifer on Cape Cod, MA, using a series of single-well injection tests. The aquifer contained a wastewater-derived contaminant plume, the core of which was anoxic and contained ammonium. The study was conducted near the downgradient end of the ammonium zone, which was characterized by inversely trending vertical gradients of oxygen (270 to 0 μM) and ammonium (19 to 625 μM) and appeared to be a potentially active zone for nitrification. The tests were conducted by injecting a tracer solution (ambient ground water + added constituents) into selected locations within the gradients using multilevel samplers. After injection, the tracers moved by natural ground water flow and were sampled with time from the injection port. Rates of nitrification were determined from changes in nitrate and nitrite concentration relative to bromide. Initial tests were conducted with ¹⁵N-enriched ammonium; subsequent tests examined the effect of adding ammonium, nitrite, or oxygen above background concentrations and of adding difluoromethane, a nitrification inhibitor. In situ net nitrate production exceeded net nitrite production by 3- to 6- fold and production rates of both decreased in the presence of difluoromethane. Nitrification rates were 0.02–0.28 μmol (L aquifer)⁻¹ h⁻¹ with in situ oxygen concentrations and up to 0.81 μmol (L aquifer)⁻¹ h⁻¹ with non-limiting substrate concentrations. Geochemical considerations indicate that the rates derived from single-well injection tests yielded overestimates of in situ rates, possibly because the injections promoted small-scale mixing within a transport-limited reaction zone. Nonetheless, these tests were useful for characterizing ground water nitrification in situ and for comparing potential rates of activity when the tracer cloud included non-limiting ammonium and oxygen concentrations.     

On the Reproduction Number of a Gut Microbiota Model

A spatially structured linear model of the growth of intestinal bacteria is analysed from two generational viewpoints. Firstly, the basic reproduction number associated with the bacterial population, i.e. the expected number of daughter cells per bacterium, is given explicitly in terms of biological parameters. Secondly, an alternative quantity is introduced based on the number of bacteria produced within the intestine by one bacterium originally in the external media. The latter depends on the parameters in a simpler way and provides more biological insight than the standard reproduction number, allowing the design of experimental procedures. Both quantities coincide and are equal to one at the extinction threshold, below which the bacterial population becomes extinct. Optimal values of both reproduction numbers are derived assuming parameter trade-offs.     

A Portable Chemotaxis Platform for Short and Long Term Analysis

Flow-based microfluidic systems have been widely utilized for cell migration studies given their ability to generate versatile and precisely defined chemical gradients and to permit direct visualization of migrating cells. Nonetheless, the general need for bulky peripherals such as mechanical pumps and tubing and the complicated setup procedures significantly limit the widespread use of these microfluidic systems for cell migration studies. Here we present a simple method to power microfluidic devices for chemotaxis assays using the commercially available ALZET® osmotic pumps. Specifically, we developed a standalone chemotaxis platform that has the same footprint as a multiwell plate and can generate well-defined, stable chemical gradients continuously for up to 7 days. Using this platform, we validated the short-term (24 hours) and long-term (72 hours) concentration dependent PDGF-BB chemotaxis response of human bone marrow derived mesenchymal stem cells.     

Stuttering Interneurons Generate Fast and Robust Inhibition onto Projection Neurons with Low Capacity of Short Term Modulation in Mouse Lateral Amygdala

The stuttering interneurons (STi) represent one minor subset of interneuron population and exhibit characteristic stuttering firing upon depolarization current injection. While it has been long held that the GABAergic inhibitory transmission largely varies with the subtype identity of presynaptic interneurons, whether such a rule also applies to STi is largely unknown. Here, by paired recording of interneuron and their neighboring projection neuron in lateral amygdala, we found that relative to the fast spiking and late spiking interneurons, the STi-evoked unitary postsynaptic currents onto the projection neurons had markedly larger amplitude, shorter onset latency and faster rising and decay kinetics. The quantal content and the number of vesicles in the readily releasable pool were also larger in synapses made by STi versus other interneurons. Moreover, the short-term plasticity, as reflected by the paired pulse depression and depolarization-induced suppression of inhibition, was the least prominent in the output synapses of STi. Thus, the fast and robust inhibition together with its low capacity of short term modulation may suggest an important role for STi in preventing the overexcitation of the projection neurons and thus gating the information traffic in amygdala.     

Multigeneration Reproduction Ratios and the Effects of Clustered Unvaccinated Individuals on Epidemic Outbreak

An SIR epidemiological community-structured model is constructed to investigate the effects of clustered distributions of unvaccinated individuals and the distribution of the primary case relative to vaccination levels. The communities here represent groups such as neighborhoods within a city or cities within a region. The model contains two levels of mixing, where individuals make more intra-group than inter-group contacts. Stochastic simulations and analytical results are utilized to explore the model. An extension of the effective reproduction ratio that incorporates more spatial information by predicting the average number of tertiary infections caused by a single infected individual is introduced to characterize the system. Using these methods, we show that both the vaccination coverage and the variation in vaccination levels among communities affect the likelihood and severity of epidemics. The location of the primary infectious case and the degree of mixing between communities are also important factors in determining the dynamics of outbreaks. In some cases, increasing the efficacy of a vaccine can in fact increase the effective reproduction ratio in early generations, due to the effects of population structure on the likely initial location of an infection.     

Holding Multiple Items in Short Term Memory: A Neural Mechanism

Human short term memory has a capacity of several items maintained simultaneously. We show how the number of short term memory representations that an attractor network modeling a cortical local network can simultaneously maintain active is increased by using synaptic facilitation of the type found in the prefrontal cortex. We have been able to maintain 9 short term memories active simultaneously in integrate-and-fire simulations where the proportion of neurons in each population, the sparseness, is 0.1, and have confirmed the stability of such a system with mean field analyses. Without synaptic facilitation the system can maintain many fewer memories active in the same network. The system operates because of the effectively increased synaptic strengths formed by the synaptic facilitation just for those pools to which the cue is applied, and then maintenance of this synaptic facilitation in just those pools when the cue is removed by the continuing neuronal firing in those pools. The findings have implications for understanding how several items can be maintained simultaneously in short term memory, how this may be relevant to the implementation of language in the brain, and suggest new approaches to understanding and treating the decline in short term memory that can occur with normal aging.     

IDEA: Interactive Display for Evolutionary Analyses

Background  

The availability of complete genomic sequences for hundreds of organisms promises to make obtaining genome-wide estimates of substitution rates, selective constraints and other molecular evolution variables of interest an increasingly important approach to addressing broad evolutionary questions. Two of the programs most widely used for this purpose are codeml and baseml, parts of the PAML (Phylogenetic Analysis by Maximum Likelihood) suite. A significant drawback of these programs is their lack of a graphical user interface, which can limit their user base and considerably reduce their efficiency.