The spatial spread and final size of the deterministic non-reducible n-type epidemic

A model has been formulated in [6] to describe the spatial spread of an epidemic involving n types of individual, and the possible wave solutions at different speeds were investigated. The final size and pandemic theorems are now established for such an epidemic. The results are relevant to the measles, host-vector, carrier-borne epidemics, rabies and diseases involving an intermediate host. Diseases in which some of the population is vaccinated, and models that divide the population into several strata are also covered.     

Synthesis,isomerism, and hypotensive activity of thiethane-containing hydrazones of uracilylacetic acid

By the reaction of 2-[6-methyl-1-(thiethane-3-yl)uracil-3-yl]acetic acid hydrazide with aryl aldehydes and acetophenone derivatives, acylhydrazones have been obtained, which exist in DMSO solutions as a mixture of two stereoisomers of an E _C=N-isomer, due to the hindered internal rotation around the hydrazide bond. It has been found that the compounds synthesized exhibit a hypotensive activity.     

K Permeability of Nitella clavata in the Depolarized State

Membrane current responses to sudden potential changes were recorded in solutions of various [K]_o on 52 internodal cells of Nitella clavata. The membrane current after sudden depolarization had a component sensitive to [K]_o which increased with time from 0.3 to 2.0 s and remained steady thereafter. This late current became zero at values of E and [K]_o which suggests that the current was nearly all carried by K⁺. The potassium conductivity represented by this current increased with depolarization, with a half-maximum value at about -70 mV, and saturation at about -30 to -20 mV. The potassium conductance also increased with increasing [K]_o, but less rapidly than predicted for constant potassium permeability. This failure of the conductance to increase with [K]_o was relatively the same at all membrane potentials and may be explained by a model with a finite number of channels. No attempt was made to model the dependence of g_K on time after depolarization or on membrane potential. However, the finding that the membrane potential did not affect the way in which the permeability depended on [K]_o suggests that the membrane potential change does not affect the affinity of the sites, and that the increase in g_K with time after depolarization is brought about by an increase in the number of channels with such sites.     

Crystal structures of ferricyanide-oxidized [Fe-S] clusters in Azotobacter vinelandii ferredoxin I

Crystals of Azotobacter vinelandii ferredoxin I (FdI) have been soaked in solutions containing K₃Fe(CN)₆ in order to study the oxidation of the [3Fe-4S] and [4Fe-4S] clusters in the protein. Ferricyanide treatment results in partial loss of Fe and S from each cluster accompanied by alteration of Fe-S bonds. The effects of oxidation can be quantitated by crystallographic refinement when each [Fe-S] cluster is modeled as having a single, average structure with non-standard geometry. The oxidized clusters refined at 2.1-Å resolution display statistically significant deviations from geometric ideality. If interpreted in terms of atomic shifts these deviations indicate that each cluster first loses an inorganic S atom. In each case an Fe atom bonded to this S separates from the remaining atoms of the cluster such that the [3Fe-4S] and [4Fe-4S] clusters partially decompose into a single Fe plus 2Fe and 3Fe fragments. The extent of structural changes observed are essentially the same in crystals soaked at 3?:?1, 9?:?1 and 30?:?1 mole ratio of K₃ Fe(CN)₆?:?FdI, suggesting that the crystal lattice permits limited oxidation reactions to occur at a low mole ratio but restricts conformational changes from occurring that may be required for more extensive oxidative reactions at higher mole ratio. The results are relevant to understanding the transformations which may take place when [Fe-S] proteins are deliberately oxidized with ferricyanide.     

Bicuculline-insensitive GABA binding to catfish neuronal membranes

GABA receptor binding to mammalian neuronal membranes has been classified into at least 2 subtypes—GABA_A and GABA_B binding sites. In catfish brain GABA_A receptor sites have previously been demonstrated. Evidence is now presented that under appropriate conditions which rule out GABA_A receptor binding, [³H]GABA binds to membranes prepared from catfish brain. This binding is bicuculline-insensitive but differs enough from mammalian GABA_B binding to cast some doubt on the idea that GABA_B receptors exist in catfish brain. Specific binding was detected that was saturable and exhibited a dissociation constant of 4μM. (±)Baclofen, a potent inhibitor in rat brain, was a weak inhibitor, producing a maximum of 43% inhibition. This inhibitory effect could be enhanced, however, in the presence of 320 μM isoguvacine. [³H]GABA binding was unaffected by bicuculline. Thus bicuculline-insensitive GABA binding sites exist in catfish brain but they differ in a number of ways from the GABA_B receptor site found in mammals. Furthermore, a third [³H]GABA binding site appears to exist that is both baclofen- and bicuculline-insensitive, yet is inhibited by high concentrations of isoguvacine, a known GABA_A agonist.     

An assessment of preferential attachment as a mechanism for human sexual network formation

Recent research into the properties of human sexual-contact networks has suggested that the degree distribution of the contact graph exhibits power-law scaling. One notable property of this power-law scaling is that the epidemic threshold for the population disappears when the scaling exponent rho is in the range 2 < rho < or = 3. This property is of fundamental significance for the control of sexually transmitted diseases (STDs) such as HIV/AIDS since it implies that an STD can persist regardless of its transmissibility. A stochastic process, known as preferential attachment, that yields one form of power-law scaling has been suggested to underlie the scaling of sexual degree distributions. The limiting distribution of this preferential attachment process is the Yule distribution, which we fit using maximum likelihood to local network data from samples of three populations: (i) the Rakai district, Uganda; (ii) Sweden; and (iii) the USA. For all local networks but one, our interval estimates of the scaling parameters are in the range where epidemic thresholds exist. The estimate of the exponent for male networks in the USA is close to 3, but the preferential attachment model is a very poor fit to these data. We conclude that the epidemic thresholds implied by this model exist in both single-sex and two-sex epidemic model formulations. A strong conclusion that we derive from these results is that public health interventions aimed at reducing the transmissibility of STD pathogens, such as implementing condom use or high-activity anti-retroviral therapy, have the potential to bring a population below the epidemic transition, even in populations exhibiting large degrees of behavioural heterogeneity.     

Mathematical analysis of a model describing evolution of an asexual population in a changing environment

We investigate a mathematical model for an asexual population with non-overlapping (discrete) generations, that exists in a changing environment. Sexual populations are also briefly discussed at the end of the paper. It is assumed that selection occurs on the value of a single polygenic trait, which is controlled by a finite number of loci with discrete-effect alleles. The environmental change results in a moving fitness optimum, causing the trait to be subject to a combination of stabilising and directional selection.This model is different from that investigated by Waxman and Peck [Genetics 153 (1999) 1041] where overlapping generations and continuous effect alleles were considered. In this paper, we consider non-overlapping generations and discrete effect alleles. However in [Genetics 153 (1999) 1041] and the present work, there is the same pattern of environmental change, namely a constant rate of change of the optimum.From [Genetics 153 (1999) 1041], no rigorous theoretical conclusion can be drawn about the form of the solutions as t grows large. Numerical work carried out in [Genetics 153 (1999) 1041] suggests that the solution is a lagged travelling wave solution, but no mathematical proof exists for the continuous model. Only partial results, regarding existence of travelling wave solutions and perturbed solutions, have been established (see [Nonlin. Anal. 53 (2003) 683; An integral equation describing an asexual population in a changing environment, Preprint]). For the discrete case of this paper, under the assumption that the ratio between the unit of genotypic value and the speed of environment change is a rational number, we are able to give rigorous proof of the following conclusion: the population follows the environmental change with a small lag behind, moreover, the lag is represented using a calculable quantity.     

The importance of low atmospheric CO2 and fire in promoting the spread of grasslands and savannas

The distribution and abundance of trees can be strongly affected by disturbance such as fire. In mixed tree/grass ecosystems, recurrent grass‐fuelled fires can strongly suppress tree saplings and therefore control tree dominance. We propose that changes in atmospheric [CO₂] could influence tree cover in such metastable ecosystems by altering their postburn recovery rates relative to flammable herbaceous growth forms such as grasses. Slow sapling recovery rates at low [CO₂] would favour the spread of grasses and a reduction of tree cover. To test the possible importance of [CO₂]/fire interactions, we first used a Dynamic Global Vegetation Model (DGVM) to simulate biomass in grassy ecosystems in South Africa with and without fire. The results indicate that fire has a major effect under higher rainfall conditions suggesting an important role for fire/[CO₂] interactions. We then used a demographic model of the effects of fire on mesic savanna trees to test the importance of grass/tree differences in postburn recovery rates. We adjusted grass and tree growth in the model according to the DGVM output of net primary production at different [CO₂] relative to current conditions. The simulations predicted elimination of trees at [CO₂] typical of the last glacial period (180 ppm) because tree growth rate is too slow (15 years) to grow to a fire‐proof size of ca. 3 m. Simulated grass growth would produce an adequate fuel load for a burn in only 2 years. Simulations of preindustrial [CO₂] (270 ppm) predict occurrence of trees but at low densities. The greatest increase in trees occurs from preindustrial to current [CO₂] (360 ppm). The simulations are consistent with palaeo‐records which indicate that trees disappeared from sites that are currently savannas in South Africa in the last glacial. Savanna trees reappeared in the Holocene. There has also been a large increase in trees over the last 50–100 years. We suggest that slow tree recovery after fire, rather than differential photosynthetic efficiencies in C₃ and C₄ plants, might have been the significant factor in the Late Tertiary spread of flammable grasslands under low [CO₂] because open, high light environments would have been a prerequisite for the spread of C₄ grasses. Our simulations suggest further that low [CO₂] could have been a significant factor in the reduction of trees during glacial times, because of their slower regrowth after disturbance, with fire favouring the spread of grasses.     

Bistability dynamics in simulations of neural activity in high-extracellular-potassium conditions

Modulation of extracellular potassium concentration ([K]_o) has a profound impact on the excitability of neurons and neuronal networks. In the CA3 region of the rat hippocampus synchronized epileptiform bursts occur in conditions of increased [K]_o. The dynamic nature of spontaneous neuronal firing in high [K]_o is therefore of interest. One particular interest is the potential presence of bistable behaviors such as the coexistence of stable repetitive firing and fixed rest potential states generated in individual cells by the elevation of [K]_o. The dynamics of repetitive activity generated by increased [K]_o is investigated in a 19-compartment hippocampal pyramidal cell (HPC) model and a related two-compartment reduced HPC model. Results are compared with those for the Hodgkin-Huxley equations in similar conditions. For neural models, [K]_o changes are simulated as a shift in the potassium reversal potential (E _K ). Using phase resetting and bifurcation analysis techniques, all three models are shown to have specific regions of E _K that result in bistability. For activity in bistable parameter regions, stimulus parameters are identified that switch high-potassium model behavior from repetitive firing to a quiescent state. Bistability in the HPC models is limited to a very small parameter region. Consequently, our results suggest that it is likely some HPCs in networks exposed to high [K]_o continue to burst such that a stable, quiescent network state does not exist. In [K]_o ranges where HPCs are not bistable, the population may still exhibit bistable behaviors where synchronous population events are reversibly annihilated by phase resetting pulses, suggesting the existence of a nonsynchronous network attractor.     

Modeling influenza seasonality in the tropics and subtropics

Climate drivers such as humidity and temperature may play a key role in influenza seasonal transmission dynamics. Such a relationship has been well defined for temperate regions. However, to date no models capable of capturing the diverse seasonal pattern in tropical and subtropical climates exist. In addition, multiple influenza viruses could cocirculate and shape epidemic dynamics. Here we construct seven mechanistic epidemic models to test the effect of two major climate drivers (humidity and temperature) and multi-strain co-circulation on influenza transmission in Hong Kong, an influenza epidemic center located in the subtropics. Based on model fit to long-term influenza surveillance data from 1998 to 2018, we found that a simple model incorporating the effect of both humidity and temperature best recreated the influenza epidemic patterns observed in Hong Kong. The model quantifies a bimodal effect of absolute humidity on influenza transmission where both low and very high humidity levels facilitate transmission quadratically; the model also quantifies the monotonic but nonlinear relationship with temperature. In addition, model results suggest that, at the population level, a shorter immunity period can approximate the co-circulation of influenza virus (sub)types. The basic reproductive number R₀ estimated by the best-fit model is also consistent with laboratory influenza survival and transmission studies under various combinations of humidity and temperature levels. Overall, our study has developed a simple mechanistic model capable of quantifying the impact of climate drivers on influenza transmission in (sub)tropical regions. This model can be applied to improve influenza forecasting in the (sub)tropics in the future.     

Electrochemical synthesis and crystal structures of nickel(II), copper(II), zinc(II) and cadmium(II) complexes with N,N′-bis[(4-methylphenyl)sulfonyl]ethylenediamine

The electrochemical oxidation of anodic metal (nickel, copper, zinc and cadmium) in acetonitrile solutions containing N,N′-bis[(4-methylphenyl)sulfonyl]ethylenediamine H₂L and an additional nitrogen coligand, such as 1,10-phenanthroline, yielded mixed complexes of general formula [ML(phen)₂] (M=Ni, Cu, Zn and Cd). The compounds have been characterized by microanalysis, IR and UV-Vis (Ni, Cu complexes) spectroscopy, FAB mass spectrometry, ¹H NMR spectroscopic studies (Zn, Cd complexes) and EPR spectroscopy (Cu and Ni complexes). All compounds have also been characterized by single crystal X-ray diffraction. The molecular structures of these compounds consist of individual monomeric molecules in which the metal atom is in an [MN₆] distorted octahedral environment.     

Periodic orbits arising from Hopf bifurcations in a Volterra prey-predator model

 In this paper we derive a formula which enables the stability of periodic solutions to a Volterra integro-differential system to be determined. This system which has been studied by Cushing [1], models a predator-prey interaction with distributed delays. The results are obtained by using the algorithm developed by Kazarinoff, Wan and van den Driessche [2] based on the centre manifold formulas of Hassard and Wan [3]. We discuss an example of the formula for the case of weak kernels and show that under certain conditions stable periodic solutions arising from Hopf bifurcations at different critical values of the parameters can exist together. Received 30 December 1994; received in revised form 12 December 1995     

Ribozymes: Analytical Solution of the One-substrate, Two-intermediate Reversible Scheme for Enzyme Reactions

The paper presents a kinetic analysis of a reversible enzymatic reaction S⇄P involving two intermediate compounds under the condition [E]₀ ≫ [S]₀ + [P]₀. For the case of mono-exponential behavior, we derive an equation for k _obs as a function of [E]₀, which emphasizes the pitfalls of oversimplifying kinetic schemes (such as the Michaelis-Menten model) for ribozyme studies. This novel apparent rate constant, which has been arrived at through mechanistic considerations, is analyzed, and the characteristic parameters obtained. The equation, which seems to fit experimental data better than conventional approximations, is used to analyze a single turnover study on an ADC1 ribozyme drawn from hepatitis delta virus RNA. The microscopic kinetic constants for such enzyme are evaluated and its mono-exponential behavior verified.     

Kinetic manifestations of allosteric interactions in models of regulatory enzymes with "indirect" co-operativity

The shape of the plots of initial reaction rate (ν) versus initial substrate concentration ([S]₀) and versus initial concentration of allosteric effector ([F]₀) for the model of allosteric enzyme of Monod, Wyman &; Changeux (1965) and for the model of dissociating regulatory enzyme has been analysed by means of the inconstant exponent (q) for substrate or effector concentration, respectively. It has been shown that allosteric interactions in above-mentioned models with “indirect” co-operativity may be manifested not only by the sigmoidal shape of the plot of ν versus [S]₀ or ν versus [F]₀ (with one point of inflexion) but also by the increase in the magnitude of exponent q in progress of saturation process of the enzyme by the substrate or by the effector in the absence of the sigmoidal shape of these plots. It has been shown also that the plot of ν versus [S]₀ has two inflexion points when the parameters have certain definite values. One of these inflexion points (or even both at definite values of the parameters) is hardly discernible. At certain definite values of the parameters two inflexion points may be kinetically manifested by such phenomenon as “negative” co-operativity (q < 1). This is possible if one of the interconvertable enzyme forms exceeds another not only in the affinity to the substrate but also in the value of the rate constant for catalytic breakdown of the enzyme-substrate complex.     

一类S-I传染病模型行波解的存在性

本文研究了一类具有扩散且是非线性传染率的SI传染病模型,分析了模型的行波解的存在性条件,给出了最小波速与产生单调和振荡行波解的条件,并且进行了计算机仿真．     

Modifications of the amide bond and conformational constraints in pseudopeptide analogues

We have investigated the conformational effects of modifying the amide group in model dipeptides. The N-methyl amide ψ[CO-NMe], N-hydroxy amide ψ[CO-N(OH)], N-amino amide ψ[ CO-N (NH₂)], retro amide ψ[ NH-CO], reduced amide in the neutral ψ[CH₂-NH] and protonated ψ[CH₂-N ⁺ H₂] state, and hydrazide ψ[CO-NH-NH] have been introduced as surrogates of the amide link in pseudopeptide derivatives of the Pro-Gly or Ala-Gly model dipeptides protected on both termini by an amide group. These compounds have been studied in solution by proton nmr and ir spectroscopy, and in the solid state by x-ray diffraction, giving an extended data set of experimental structural and conformational information on pseudopeptide sequences. The conformational effects depend both on the nature and the position of the modified amide link. Some modifications appear to have no intrinsic conformational induction (N-amino and retro amide), but destabilize any local folded structure by hydrogen-bond breaking. Because of the formation of strong intramolecular interactions, others are capable of stabilizing a β-turn (for example protonated reduced amide), or of inducing a particular local conformation such as a β- or γ-like turn (for example N-hydroxy amide). The particular geometry of the cis N-methyl amide and of the “hydrazino” proline favors the formation of a sharp turn of the main chain. All these structural data are of interest to the design of bioactive peptide mimics. © 1993 John Wiley & Sons, Inc.     

Influence of normative data’s walking speed on the computation of conventional gait indices

The pathology’s impact on gait pattern may be overestimated by conventional gait indices (Gillette Gait Index – GGI, Gait Deviation Index – GDI, Gait Profile Score – GPS), since impairments’ consequences on kinematics may be amplified by a change in walking speed. The objectives of this study were to evaluate the influence of walking speed on the computation of gait indices and to propose a corrective method to cancel the effects of walking speed. Spatiotemporal parameters and kinematics of fifty-four asymptomatic participants (30 M/24 W, 37.9 ± 13.7 years, 72.8 ± 13.3 kg, 1.74 ± 0.10 m) were collected at four speed conditions (C₁:[0,0.4] m s⁻¹, C₂:[0.4,0.8] m s⁻¹, C₃:[0.8,1.2] m s⁻¹, C₄:spontaneous). Four values of each index were computed for each trial using successively the four conditions as normative data repository. Mean values over all participants were statistically compared (paired t-tests, 95% confidence level). Indices values computed with normative at equivalent walking speed were not statistically different from reference values. Meanwhile, deviations appeared when the walking speed discrepancy between conditions and normative increased. These drifts related to walking speed mismatch have been quantified and fitting functions proposed. A correction was applied to indices. GGI was efficiently adjusted while GDI and GPS remain different from their reference values for C₁ and C₂. Gait indices must be interpreted cautiously in function of the normative data repository’s walking speed used for computation. Furthermore, a coupled use of conventional and corrected gait indices could lead to a better comprehension of the contribution of impairments and walking speed on gait deviations and overall gait quality.     

A Comparison of Continuous and Discrete-time West Nile Virus Models

The first recorded North American epidemic of West Nile virus was detected in New York state in 1999, and since then the virus has spread and become established in much of North America. Mathematical models for this vector-transmitted disease with cross-infection between mosquitoes and birds have recently been formulated with the aim of predicting disease dynamics and evaluating possible control methods. We consider discrete and continuous time versions of the West Nile virus models proposed by Wonham et al. [Proc. R. Soc. Lond. B 271:501–507, 2004] and by Thomas and Urena [Math. Comput. Modell. 34:771–781, 2001], and evaluate the basic reproduction number as the spectral radius of the next-generation matrix in each case. The assumptions on mosquito-feeding efficiency are crucial for the basic reproduction number calculation. Differing assumptions lead to the conclusion from one model [Wonham, M.J. et al., [Proc. R. Soc. Lond. B] 271:501–507, 2004] that a reduction in bird density would exacerbate the epidemic, while the other model [Thomas, D.M., Urena, B., Math. Comput. Modell. 34:771–781, 2001] predicts the opposite: a reduction in bird density would help control the epidemic.     

Chloride and osmotic contractures in skinned frog muscle fibers

Summary Single contractures were elicited in segments of skinned frog muscle fibers when the segments were moved from relaxing-loading solutions to various test solutions. The effective test solutions produced an increase in the concentration of chloride ions in the myofilament space, [Cl] _ms , and/or presumably caused the sarcoplasmic reticulum to undergo a change in volume. The contractures were quantified in terms of their maximum tension and time-integral. Two outer segments from each fiber underwent a contracture in a control solution (chloride ions were substituted for all of the methanesulfonate ions in the relaxing solution). The mean values of tension and area in the control contractures of each fiber were divided into the corresponding values from a test contracture obtained in the central segment of the same fiber. Test contractures obtained upon increasing [Cl] _ms and increasing the product, [K] _ms ×[Cl] _ms , were compared to contractures that were obtained by increasing [Cl] _ms while keeping [K] _ms ×[Cl] _ms constant. The former contractures were greater in magnitude for a given [Cl] _ms . Whereas the former solutions may have caused an increase in the volume of the sarcoplasmic reticulum and altered the electrical potential across the membranes of the sarcoplasmic reticulum as well, only a change in potential was presumed to have occurred in the latter solutions. Other types of contractures were investigated to show that both swelling of the sarcoplasmic reticulum and changes in the electrical potential of its membranes can cause release of calcium ions and elicit contractures in skinned fibers.     

An SEI model for sarcoptic mange among chamois

We consider a simple model to study the dynamics of sarcoptic mange in a population of chamois. The epidemiological patterns observed during an epidemic in Italy are reconstructed and key parameters of the model are estimated from field data. In particular, we calculate the basic reproductive ratio R ₀, a threshold value for chamois density for the occurrence of an epidemic and the speed of propagation of the epidemic wave. The model is then used to obtain indications on the effect of culling as a possible control measure in a closed population and extended to analyse the spatial diffusion of the epidemic. Our results are in agreement with mange epidemiology and observations, and suggest that intervention could be efficacious in reducing the impact of an epidemic.