Mechanical model for a collagen fibril pair in extracellular matrix

In this paper, we model the mechanics of a collagen pair in the connective tissue extracellular matrix that exists in abundance throughout animals, including the human body. This connective tissue comprises repeated units of two main structures, namely collagens as well as axial, parallel and regular anionic glycosaminoglycan between collagens. The collagen fibril can be modeled by Hooke’s law whereas anionic glycosaminoglycan behaves more like a rubber-band rod and as such can be better modeled by the worm-like chain model. While both computer simulations and continuum mechanics models have been investigated for the behavior of this connective tissue typically, authors either assume a simple form of the molecular potential energy or entirely ignore the microscopic structure of the connective tissue. Here, we apply basic physical methodologies and simple applied mathematical modeling techniques to describe the collagen pair quantitatively. We found that the growth of fibrils was intimately related to the maximum length of the anionic glycosaminoglycan and the relative displacement of two adjacent fibrils, which in return was closely related to the effectiveness of anionic glycosaminoglycan in transmitting forces between fibrils. These reveal the importance of the anionic glycosaminoglycan in maintaining the structural shape of the connective tissue extracellular matrix and eventually the shape modulus of human tissues. We also found that some macroscopic properties, like the maximum molecular energy and the breaking fraction of the collagen, were also related to the microscopic characteristics of the anionic glycosaminoglycan.     

The effects of human movement on the persistence of vector-borne diseases

With the recent resurgence of vector-borne diseases due to urbanization and development there is an urgent need to understand the dynamics of vector-borne diseases in rapidly changing urban environments. For example, many empirical studies have produced the disturbing finding that diseases continue to persist in modern city centers with zero or low rates of transmission. We develop spatial models of vector-borne disease dynamics on a network of patches to examine how the movement of humans in heterogeneous environments affects transmission. We show that the movement of humans between patches is sufficient to maintain disease persistence in patches with zero transmission. We construct two classes of models using different approaches: (i) Lagrangian models that mimic human commuting behavior and (ii) Eulerian models that mimic human migration. We determine the basic reproduction number R₀ for both modeling approaches. We show that for both approaches that if the disease-free equilibrium is stable (R₀<1) then it is globally stable and if the disease-free equilibrium is unstable (R₀>1) then there exists a unique positive (endemic) equilibrium that is globally stable among positive solutions. Finally, we prove in general that Lagrangian and Eulerian modeling approaches are not equivalent. The modeling approaches presented provide a framework to explore spatial vector-borne disease dynamics and control in heterogeneous environments. As an example, we consider two patches in which the disease dies out in both patches when there is no movement between them. Numerical simulations demonstrate that the disease becomes endemic in both patches when humans move between the two patches.     

Bifurcation analysis of the Nowak-Bangham model in CTL dynamics

This paper investigates the local bifurcations of a CTL response model published by Nowak and Bangham [M.A. Nowak, C.R.M. Bangham, Population dynamics of immune responses to persistent viruses, Science 272 (1996) 74]. The Nowak-Bangham model can have three equilibria depending on the basic reproduction number, and generates a Hopf bifurcation through two bifurcations of equilibria. The main result shows a sufficient condition for the interior equilibrium to have a unique bifurcation point at which a simple Hopf bifurcation occurs. For this proof, some new techniques are developed in order to apply the method established by Liu [W.M. Liu, Criterion of Hopf bifurcations without using eigenvalues, J. Math. Anal. Appl. 182 (1) (1994) 250]. In addition, to demonstrate the result obtained theoretically, some bifurcation diagrams are presented with numerical examples.     

Searching for generality in the patterns of parasite abundance and distribution: Ectoparasites of a South African rodent, Rhabdomys pumilio

We studied abundance and distribution of seven ectoparasite species (fleas Chiastopsylla rossi and Dynopsyllus ellobius, a louse Polyplax arvicanthis, mites Androlaelaps fahrenholzi and Laelaps giganteus and two ticks Haemaphysalis elliptica and Hyalomma truncatum) exploiting the same populations of the rodent host Rhabdomys pumilio in South Africa. We considered three general patterns of abundance and distribution, namely (i) aggregated distribution of parasites amongst individual hosts; (ii) positive relationships between mean parasite abundance and their prevalence; and (iii) applicability of a simple epidemiological model based on mean parasite abundance and its variance to predict the observed patterns of prevalence. Our aims were to evaluate the relative role of host- versus parasite-associated factors by looking at similarity amongst different parasites in these patterns. In general, all parasites demonstrated strong similarity in each of the three patterns of abundance and distribution. However, the strength of these patterns differed amongst parasite species. We conclude that these patterns are driven mainly by hosts, but differences are caused by differences between various life-history traits of parasite species. Our results support the idea that general laws apply to parasite population ecology.     

灵芝子实体原基双向电泳和总蛋白质提取方法的建立

比较了Tris-饱和酚法和三氯乙酸(TCA)/丙酮沉淀法对灵芝子实体原基总蛋白质的提取效果。用Image Master 2D Platinum6.0软件分析两种方法所提蛋白质的双向电泳图谱,分别得到565和273个蛋白质点;(TCA)/丙酮沉淀法在碱性端低分子量区域有些蛋白质斑点存在拖尾现象,Tris-饱和酚法能有效去除样品中的盐分,使蛋白质的聚焦效果更好,蛋白点数增加。Tris-饱和酚法可做为灵芝子实体原基总蛋白质的提取方法并为其他药用真菌总蛋白质的提取提供参考,同时为本实验室后续研究灵芝双向性固体发酵雷公藤的蛋白差异表达奠定了基础。     

一类带有肝炎B病毒感染的数学模型的全局稳定性分析（英文）

本文主要分析了一类具有肝炎B病毒感染且带有治愈率的典型的数学模型（HBV）.通过稳定性分析,得到了该模型的无病平衡点与地方病平衡点全局稳定的充分条件,并且证明了当基本再生数R0〈1, HBV感染消失;当R0〉1,HBV感染持续.     

Timescales of population rarity and commonness in random environments

This is a mathematical study of the interactions between non-linear feedback (density dependence) and uncorrelated random noise in the dynamics of unstructured populations. The stochastic non-linear dynamics are generally complex, even when the deterministic skeleton possesses a stable equilibrium. There are three critical factors of the stochastic non-linear dynamics; whether the intrinsic population growth rate (lambda) is smaller than, equal to, or greater than 1; the pattern of density dependence at very low and very high densities; and whether the noise distribution has exponential moments or not. If lambda < 1, the population process is generally transient with escape towards extinction. When lambda > or = 1, our quantitative analysis of stochastic non-linear dynamics focuses on characterizing the time spent by the population at very low density (rarity), or at high abundance (commonness), or in extreme states (rarity or commonness). When lambda >1 and density dependence is strong at high density, the population process is recurrent: any range of density is reached (almost surely) in finite time. The law of time to escape from extremes has a heavy, polynomial tail that we compute precisely, which contrasts with the thin tail of the laws of rarity and commonness. Thus, even when lambda is close to one, the population will persistently experience wide fluctuations between states of rarity and commonness. When lambda = 1 and density dependence is weak at low density, rarity follows a universal power law with exponent -3/2. We provide some mathematical support for the numerical conjecture [Ferriere, R., Cazelles, B., 1999. Universal power laws govern intermittent rarity in communities of interacting species. Ecology 80, 1505-1521.] that the -3/2 power law generally approximates the law of rarity of 'weakly invading' species with lambda values close to one. Some preliminary results for the dynamics of multispecific systems are presented.     

Improving estimates of the basic reproductive ratio: using both the mean and the dispersal of transition times

In both within-host and epidemiological models of pathogen dynamics, the basic reproductive ratio, R(0), is a powerful tool for gauging the risk associated with an emerging pathogen, or for estimating the magnitude of required control measures. Techniques for estimating R(0), either from incidence data or in-host clinical measures, often rely on estimates of mean transition times, that is, the mean time before recovery, death or quarantine occurs. In many cases, however, either data or intuition may provide additional information about the dispersal of these transition times about the mean, even if the precise form of the underlying probability distribution remains unknown. For example, we may know that recovery typically occurs within a few days of the mean recovery time. In this paper we elucidate common situations in which R(0) is sensitive to the dispersal of transition times about their respective means. We then provide simple correction factors that may be applied to improve estimates of R(0) when not only the mean but also the standard deviation of transition times out of the infectious state can be estimated.