Brucellosis, botflies, and brainworms: the impact of edge habitats on pathogen transmission and species extinction

Ecological interactions between species that prefer different habitat types but come into contact in edge regions at the interfaces between habitat types are modeled via reaction-diffusion systems. The primary sort of interaction described by the models is competition mediated by pathogen transmission. The models are somewhat novel because the spatial domains for the variables describing the population densities of the interacting species overlap but do not coincide. Conditions implying coexistence of the two species or the extinction of one species are derived. The conditions involve the principal eigenvalues of elliptic operators arising from linearizations of the model system around equilibria with only one species present. The conditions for persistence or extinction are made explicit in terms of the parameters of the system and the geometry of the underlying spatial domains via estimates of the principal eigenvalues. The implications of the models with respect to conservation and refuge design are discussed. Received: 10 June 1999 / Revised version: 7 July 2000 / Published online: 20 December 2000     

Solving Volterra-Lotka systems with diffusion by monotone iteration

In this paper we first present a theorem for a monotone iteration method, where the conditions for the considered operators are affine invariant. Then we apply this method to systems of nonlinear elliptic differential equations arising from the Volterra-Lotka model with diffusion. Finally an extended predator-prey system is considered. One numerical example is given.     

Population models with singular equilibrium

A class of models of biological population and communities with a singular equilibrium at the origin is analyzed; it is shown that these models can possess a dynamical regime of deterministic extinction, which is crucially important from the biological standpoint. This regime corresponds to the presence of a family of homoclinics to the origin, so-called elliptic sector. The complete analysis of possible topological structures in a neighborhood of the origin, as well as asymptotics to orbits tending to this point, is given. An algorithmic approach to analyze system behavior with parameter changes is presented. The developed methods and algorithm are applied to existing mathematical models of biological systems. In particular, we analyze a model of anticancer treatment with oncolytic viruses, a parasite-host interaction model, and a model of Chagas' disease.     

Analytical SAR computation in a multilayer elliptic cylinder: the near-field line-current radiation case

In this paper, a previously proposed analytical procedure for the computation of the specific absorption rate (SAR) inside a biological elliptic cylinder model is extended to the case in which the body is illuminated under near-field conditions. The elliptic model is made up of layers of different biological tissues and the source is constituted by a line-current distribution. The recursive procedure in which the field is expressed in terms of Mathieu function is modified to express the incident electromagnetic wave produced by the line current. The new procedure makes it possible to check and validate numerical solutions obtained by accurate numerical techniques for SAR prediction, under more realistic illumination condition.     

Coexistence in a simple food chain with diffusion

We show the global existence of classical positive solutions in each component of a Lotka-Volterra system with diffusion and logistic growing conditions. We are mainly interested in the search of coexistence states solving the associated elliptic problem under homogeneous Dirichlet boundary conditions.     

Dynamics of chemostat in which one microbial population grows on multiple complementary nutrients

The equations of a chemostat in which one microbial population grows on multiple rate-limiting nutrients are formulated. The dynamics of a chemostat involving growth on complementary nutrients is studied through stability analysis of the system of equations. Some conditions are derived that relate the dynamic behavior of the chemostat to its operating conditions and can be applied to any model for the specific growth rate of the population. It is shown that, if maintenance of the population is neglected, the system exhibits no sustained or damped oscillations. If maintenance of the population is considered, damped oscillations are observed for some operating conditions.     

Disease in prey population and body size of intermediate predator reduce the prevalence of chaos-conclusion drawn from Hastings–Powell model

In ecology the disease in the prey population plays an important role in controlling the dynamical behaviour of the system. We modify Hastings and Powell’s (HP) [Hastings, A., Powell, T., 1991. Chaos in three-species food chain. Ecology 72 (3), 896–903] model by introducing disease in the prey population. The conditions for which the modified HP model system represents extinction, permanence or impermanence of population are worked out. The modified model is analyzed to obtain different conditions for which the system exhibits stability around the biologically feasible equilibria. Through numerical simulations we display that the modified system enters into stable solutions depending upon the force of infection in prey population as well as body size of intermediate predator. Our results demonstrate that disease in prey population and body size of intermediate predator are the key parameters for controlling the chaotic dynamics observed in original HP model.     

Dimerization of human complement proteins C3 and C4 in dilute lauryl sulfate buffer after reaction with methylamine

In the presence of methylamine and dilute lauryl sulfate (pH 8.0), the human C3 and C4 complement proteins dimerize almost completely. Under these conditions, the related complement protein C5 does not show any tendency to form dimers. This is shown by x-ray and neutron scattering at 9 degrees C and 0.15 M ionic strength. The radii of gyration of the C3 and C4 dimers are very similar, 7.7 and 7.4 nm, and the cross-sectional radii of gyration are the same, 3.4 nm. The scattering curves of the C3 and C4 dimers as well as their Fourier transforms, the p(r)-curves, can be explained by scattering from a model consisting of an elongated elliptic cylinder with semiaxes 6.5 and 2.1 nm and length of 23 nm. This elongated elliptic cylinder model is consistent with the elliptic cylinder model of C4 (Osterberg, R., Eggertsen, G., Lundwall, A., and Sj?quist, J. (1984) Int. J. Biol. Macromol. 6, 195-198) provided that the protein molecules dimerize via their cross-sectional surfaces. Also, the model is consistent with the model of the related protein, alpha 2-macroglobulin, where the four subunits are supposed to form pairwise dimers of an elliptic cylindrical form (Osterberg, R., and Malmensten, B. (1984) Eur. J. Biochem. 143, 541-544).     

一类扩散循环系统正解的存在性与稳定性

利用上下解方法及全藕合线性互惠系统的最大值原理,研究了一类非线性椭圆系统,给出了其正解存在的充分必要条件,同时也得到了其正解局部稳定的某些结果．     

Elliptical contact of thin biphasic cartilage layers: exact solution for monotonic loading

A three-dimensional unilateral contact problem for articular cartilage layers is considered in the framework of the biphasic cartilage model. The articular cartilages bonded to subchondral bones are modeled as biphasic materials consisting of a solid phase and a fluid phase. It is assumed that the subchondral bones are rigid and shaped like elliptic paraboloids. The obtained analytical solution is valid for monotonically increasing loading conditions.     

Behavioral choices based on patch selection: a model using aggregation methods

The aim of this work is to study the influence of patch selection on the dynamics of a system describing the interactions between two populations, generically called 'population N' and 'population P'. Our model may be applied to prey-predator systems as well as to certain host-parasite or parasitoid systems. A situation in which population P affects the spatial distribution of population N is considered. We deal with a heterogeneous environment composed of two spatial patches: population P lives only in patch 1, while individuals belonging to population N migrate between patch 1 and patch 2, which may be a refuge. Therefore they are divided into two patch sub-populations and can migrate according to different migration laws. We make the assumption that the patch change is fast, whereas the growth and interaction processes are slower. We take advantage of the two time scales to perform aggregation methods in order to obtain a global model describing the time evolution of the total populations, at a slow time scale. At first, a migration law which is independent on population P density is considered. In this case the global model is equivalent to the local one, and under certain conditions, population P always gets extinct. Then, the same model, but in which individuals belonging to population N leave patch 1 proportionally to population P density, is studied. This particular behavioral choice leads to a dynamically richer global system, which favors stability and population coexistence. Finally, we study a third example corresponding to the addition of an aggregative behavior of population N on patch 1. This leads to a more complicated situation in which, according to initial conditions, the global system is described by two different aggregated models. Under certain conditions on parameters a stable limit cycle occurs, leading to periodic variations of the total population densities, as well as of the local densities on the spatial patches.     

Stability analysis of a two-species model with transitions between population interactions

Stability of a simple two-species system is investigated. This model assumes that the kind of inter-specific interactions is not fixed, and that it depends on the system state, i.e., undergoes transitions between different population interactions due to variation in population densities. The main goal is to show the effects of the transitions between different population interactions on the two-species coexistence, and on the stability conditions of multiple equilibria.     

Dynamics of a plant-herbivore-predator system with plant-toxicity

A system of ordinary differential equations is considered that models the interactions of two plant species populations, an herbivore population, and a predator population. We use a toxin-determined functional response to describe the interactions between plant species and herbivores and use a Holling Type II functional response to model the interactions between herbivores and predators. In order to study how the predators impact the succession of vegetation, we derive invasion conditions under which a plant species can invade into an environment in which another plant species is co-existing with a herbivore population with or without a predator population. These conditions provide threshold quantities for several parameters that may play a key role in the dynamics of the system. Numerical simulations are conducted to reinforce the analytical results. This model can be applied to a boreal ecosystem trophic chain to examine the possible cascading effects of predator-control actions when plant species differ in their levels of toxic defense.     

The process of gas exchange in the pulmonary circulation incorporating the contribution of axial diffusion

A mathematical model is made to describe the process of gas exchange in the pulmonary circulation incorporating the contribution of axial diffusion. The model takes into account the transport mechanisms of molecular diffusion, convection and facilitated diffusion due to the presence of haemoglobin as a carrier of the gases. The mathematical formulation leads to a coupled system of non-linear elliptic partial differential equations. A numerical scheme is described to solve such a system. It is found that the axial diffusion does not have an appreciable effect on the transport of the species in the blood.     

脉冲浮游生物植化相克模型解的渐近行为

讨论了一类在周期变化环境中的浮游生物植化相克的竞争模型．模型由一个修正的周期系数Lotka-Volterra竞争模型及一些周期脉冲作用条件描述．利用脉冲微分方程的比较原理研究了系统的全局渐近性质,获得了系统持续生存的一组充分条件．     

具有阶段结构的自食单种群生长模型的稳定性及最有收获策略

本文讨论了一生中具有两个生长阶段－成年与未成年的种群模型,该模型收获成年种群并且成年种群食自身所产的卵,即模型为自食模型,得到了正平衡点全局渐近稳定的条件及收获成年种群的阈值和最优收获策略。     

Global dynamics of a ratio-dependent predator-prey system

Recently, ratio-dependent predator-prey systems have been regarded by some researchers to be more appropriate for predator-prey interactions where predation involves serious searching processes. However, such models have set up a challenging issue regarding their dynamics near the origin since these models are not well-defined there. In this paper, the qualitative behavior of a class of ratio-dependent predator-prey system at the origin in the interior of the first quadrant is studied. It is shown that the origin is indeed a critical point of higher order. There can exist numerous kinds of topological structures in a neighborhood of the origin including the parabolic orbits, the elliptic orbits, the hyperbolic orbits, and any combination of them. These structures have important implications for the global behavior of the model. Global qualitative analysis of the model depending on all parameters is carried out, and conditions of existence and non-existence of limit cycles for the model are given. Computer simulations are presented to illustrate the conclusions.     

Modeling shifts in microbial populations associated with health or disease

Stable microbial communities associated with health can be disrupted by altered environmental conditions. Periodontal diseases are associated with changes in the resident oral microflora. For example, as gingivitis develops, a key change in the microbial composition of dental plaque is the ascendancy of Actinomyces spp. and gram-negative rods at the expense of Streptococcus spp. We describe the use of an in vitro model to replicate this population shift, first with a dual-species model (Actinomyces naeslundii and Streptococcus sobrinus) and then using a microcosm model of dental plaque. The population shift was induced by environmental changes associated with gingivitis, first by the addition of artificial gingival crevicular fluid and then by a switch to a microaerophilic atmosphere. In addition to the observed population shifts, confocal laser scanning microscopy also revealed structural changes and differences in the distribution of viable and nonviable bacteria associated with the change in environmental conditions. This model provides an appropriate system for the further understanding of microbial population shifts associated with gingivitis and for the testing of, for example, antimicrobial agents.