一个设立海洋保护区的捕鱼模型的生物经济分析

考虑一个设立海洋保护区的捕鱼模型．从生物学和经济学两个角度研究海洋保护区的作用．给出所研究系统的生物和经济平衡点以及平衡点的局部稳定性,不稳定性,全局稳定性的条件．研究结果说明设立海洋保护区对于保护海洋资源是一种有效途径,保护区内的鱼群即使在对非保护区进行连续捕捞的情形下也能够保持在一个适当的水平．进一步研究了最优收获策略,并对所得结果的生物经济解释予以说明．     

Mathematical Analysis of a Two Strain HIV/AIDS Model with Antiretroviral Treatment

A two strain HIV/AIDS model with treatment which allows AIDS patients with sensitive HIV-strain to undergo amelioration is presented as a system of non-linear ordinary differential equations. The disease-free equilibrium is shown to be globally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than unity. The centre manifold theory is used to show that the sensitive HIV-strain only and resistant HIV-strain only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. Qualitative analysis of the model including positivity, boundedness and persistence of solutions are presented. The model is numerically analysed to assess the effects of treatment with amelioration on the dynamics of a two strain HIV/AIDS model. Numerical simulations of the model show that the two strains co-exist whenever the reproduction numbers exceed unity. Further, treatment with amelioration may result in an increase in the total number of infective individuals (asymptomatic) but results in a decrease in the number of AIDS patients. Further, analysis of the reproduction numbers show that antiretroviral resistance increases with increase in antiretroviral use.     

A Bioeconomic Model of a Multi-site Fishery with Nonlinear Demand Function: Number of Sites Optimizing the Total Catch

We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fish and boat movement between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that the movements of the boats and resource as well as the variation of the price go on at a fast time scale. We use methods of aggregation of variables in order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model and perform local stability analysis. Two main cases can occur. The first one corresponds to over-exploitation leading to fish extinction. At extinction, the fishing effort tends to a positive value. The second case corresponds to a durable fishery equilibrium which is globally asymptotically stable. In the later case, we show that there exists a number of fishing sites that optimizes the total catch of the fishery.     

A Mathematical Model of Lymphangiogenesis in a Zebrafish Embryo

The lymphatic system of a vertebrate is important in health and diseases. We propose a novel mathematical model to elucidate the lymphangiogenic processes in zebrafish embryos. Specifically, we are interested in the period when lymphatic endothelial cells (LECs) exit the posterior cardinal vein and migrate to the horizontal myoseptum of a zebrafish embryo. We wonder whether vascular endothelial growth factor C (VEGFC) is a morphogen and a chemotactic factor for these LECs. The model considers the interstitial flow driving convection, the reactive transport of VEGFC, and the changing dynamics of the extracellular matrix in the embryo. Simulations of the model illustrate that VEGFC behaves very differently in diffusion and convection-dominant scenarios. In the former case, it must bind to the matrix to establish a functional morphogen gradient. In the latter case, the opposite is true and the pressure field is the key determinant of what VEGFC may do to the LECs. Degradation of collagen I, a matrix component, by matrix metallopeptidase 2 controls the spatiotemporal dynamics of VEGFC. It controls whether diffusion or convection is dominant in the embryo; it can create channels of abundant VEGFC and scarce collagen I to facilitate lymphangiogenesis; when collagen I is insufficient, VEGFC cannot influence the LECs at all. We predict that VEGFC is a morphogen for the migrating LECs, but it is not a chemotactic factor for them.     

一个具有突变体的种群模型的变结构控制

基于一个具有突变体的种群模型,提出了相应的控制模型.根据变结构控制原理,针对控制模型,分别设计了变结构控制器和近似变结构控制器,使突变体灭绝.最后通过数值仿真,验证了所得结论的正确性.     

Qualitative and Dynamical Analysis of a Bionomic Fishery Model with Prey Refuge

Acta Biotheoretica - Viruses are the simplest of pathogens, but possess sophisticated molecular mechanisms to manipulate host behavior, frequently utilizing molecular mimicry. Severe acute...     

Over-exploitation of a broadcast spawning marine invertebrate: Decline of the white abalone

Marine invertebrates have long been consideredto be resistant to overfishing. However, agrowing number of exploited taxa have declinedsubstantially and even disappeared from partsof their former range. We consider the case ofthe white abalone (Haliotis sorenseni);the first marine invertebrate proposed for theUS endangered species list. This high-valuespecies was one of five abalones targeted inthe California and Mexico fisheries; it is nowrare and protected from fishing. The biologicalcharacteristics of this deep-living abaloneindicate that it was particularly vulnerable toover-exploitation; reduction of density orgroup size is now known to lead to declines infertilization success and recruitment failure.Warning signs of potential problems existedboth pre- and post-exploitation but were notrecognized. In particular, serial depletion wasnot detected because catch was not analyzedspatially, perhaps because total landings werereasonably stable for the short period ofexploitation. Recent submersible surveys led toestimates that white abalone now number lessthan 2,600 animals or 0.1% of the estimatedpre-exploitation population size. Densities andestimated population sizes are less than 100animals, at all but one location. Alternateexplanations for the decline in abundance wereconsidered and only exploitation-linkedfactors, such as sub-legal mortality andillegal fishing, were likely contributors.Episodic recruitment appears to be acharacteristic of broadcast-spawning,long-lived species and may make themparticularly vulnerable to over-exploitation.Management strategies based on size limits thatallow a few years of spawning prior to reachingminimum legal size are insufficient.Sustainable fisheries will require multipleprotected areas to preserve brood stockaggregations necessary for successfulfertilization.     

价格成本变化的具有Smith增长和崔-L增长的生物种群的经济捕获模型

主要研究了具有Smith增长曲线和崔-L增长曲线的两类生物种群模型。建立了价格成本变化的数学生物经济捕获模型,讨论了模型的定性性质,证明了平衡解的存在性及其稳定性．     

一个带白噪声的可变时滞Lotka-Volterra人口模型(英文)

因为人口模型经常遭遇环境噪音的影响,本文将如下Lotka-Volterra模型(t)=diag(x(t))[b+Ax(t)+Bx(t-δ(t))]随机扰动为It型随机微分方程dx(t)=diag(x(t))[(b+Ax(t)+Bx(t-δ(t)))dt+(Qx(t)+Rx(t-δ(t))dw(t)].在这个随机模型中对系数b,A,B不需任何限制,我们证明了环境噪音不仅会压制人口的爆炸还会使得方程的解随机一致有界.     

A Mathematical Model of Valveless Pumping: A Lumped Model with Time-Dependent Compliance,Resistance, and Inertia

A new lumped model of flow driven by pumping without valves is presented, motivated by biomedical applications: the circulation of the human fetus before the development of the heart valves and mechanism of blood flow during the external cardiopulmonary resuscitation (CPR). The phenomenon of existence of a unidirectional net flow around a loop of tubing that consists of two different compliances is called valveless pumping. The lumped parameter model of valveless pumping in this paper is governed by the ordinary differential equations for pressure and flow, with time-dependent compliance, resistance, and inertia. This simple model can represent the essential features of valveless pumping we observed in earlier mathematical models and physical experiments of valveless pumping. We demonstrate that not only parameters of the driving function, such as frequency or amplitude, but also physical parameters, such as wall thickness and tube stiffness, are important in determining the direction and magnitude of a net flow. In this system, we report two new and interesting phenomena of valveless pumping: One is that the shifted peak frequency can be predicted by the pulsewave speed and the other is that time-dependent resistance is a crucial factor in generating valveless pumping. We also demonstrate that this lumped model can be extended to a one-dimensional flow model of valveless pumping and explain why a linear case, the case of the constant compliance, resistance, and inertia, generates almost zero net flow. This emphasizes that the nonlinearity of valveless pumping is also an important factor to generate a net flow in a closed loop model of valveless pumping.     

一个具暂时免疫且总人数可变的传染病动力学模型

建立了一个具常恢复率和接触率依赖于总人数的SIRS传染病动力学模型,讨论了系统平衡点的存在性和稳定性,对双线性传染率的特殊情形,给出了传染病平衡点的全局稳定性结论,推广和改进了已有的相应结果。     

A Human-Bovine Schistosomiasis Mathematical Model with Treatment and Mollusciciding

Acta Biotheoretica - To mitigate the spread of schistosomiasis, a deterministic human-bovine mathematical model of its transmission dynamics accounting for contaminated water reservoirs, including...     

Estimation of Maximum Sustainable Yield for Lesser Sciaenids Fishery of North-Eastern Arabian Sea using Surplus Production Model with Environmental Effects

Journal of Ichthyology - Fishes of family Sciaenidae, popularly known as croakers, form a major fishery along the north-west coast of India. In general, sciaenids can be divided in to two major...     

A Mathematical Model of Rift Valley Fever with Human Host

Rift Valley Fever is a vector-borne disease mainly transmitted by mosquito. To gain some quantitative insights into its dynamics, a deterministic model with mosquito, livestock, and human host is formulated as a system of nonlinear ordinary differential equations and analyzed. The disease threshold [Formula: see text] is computed and used to investigate the local stability of the equilibria. A sensitivity analysis is performed and the most sensitive model parameters to the measure of initial disease transmission [Formula: see text] and the endemic equilibrium are determined. Both [Formula: see text] and the disease prevalence in mosquitoes are more sensitive to the natural mosquito death rate, d(m). The disease prevalence in livestock and humans are more sensitive to livestock and human recruitment rates, [Formula: see text] and [Formula: see text], respectively, suggesting isolation of livestock from humans is a viable preventive strategy during an outbreak. Numerical simulations support the analytical results in further exploring theoretically the long-term dynamics of the disease at the population level.     

Correlations in Multi-Locus Genetic Systems: A Mathematical Model

A spin model with parallels to a multi-locus genetic model is presented which makes it possible to calculate the correlation between allelic states at any two loci in a population at equilibrium. The main features are: (1) The decay of correlation with distance may be expressed essentially as a linear combination of two exponentials, one of which dominates when the two loci are sufficiently far apart. (2) The correlation between two loci a specified distance apart is increased as the number of loci in the entire system increases. The results are compared with those of other theoretical models and discussed in the light of available experimental data. Possible ways of generalizing the model are outlined. However, additional experimental data is clearly needed to indicate the genetic relevance of work of this nature.     

Oxygen-Driven Tumour Growth Model: A Pathology-Relevant Mathematical Approach

Xenografts -as simplified animal models of cancer- differ substantially in vasculature and stromal architecture when compared to clinical tumours. This makes mathematical model-based predictions of clinical outcome challenging. Our objective is to further understand differences in tumour progression and physiology between animal models and the clinic.To achieve that, we propose a mathematical model based upon tumour pathophysiology, where oxygen -as a surrogate for endocrine delivery- is our main focus. The Oxygen-Driven Model (ODM), using oxygen diffusion equations, describes tumour growth, hypoxia and necrosis. The ODM describes two key physiological parameters. Apparent oxygen uptake rate (kR′) represents the amount of oxygen cells seem to need to proliferate. The more oxygen they appear to need, the more the oxygen transport. kR′ gathers variability from the vasculature, stroma and tumour morphology. Proliferating rate (k _p) deals with cell line specific factors to promote growth. The K _H,K _N describe the switch of hypoxia and necrosis. Retrospectively, using archived data, we looked at longitudinal tumour volume datasets for 38 xenografted cell lines and 5 patient-derived xenograft-like models.Exploration of the parameter space allows us to distinguish 2 groups of parameters. Group 1 of cell lines shows a spread in values of kR′ and lower k _p, indicating that tumours are poorly perfused and slow growing. Group 2 share the value of the oxygen uptake rate (kR′) and vary greatly in k _p, which we interpret as having similar oxygen transport, but more tumour intrinsic variability in growth.However, the ODM has some limitations when tested in explant-like animal models, whose complex tumour-stromal morphology may not be captured in the current version of the model. Incorporation of stroma in the ODM will help explain these discrepancies. We have provided an example. The ODM is a very simple -and versatile- model suitable for the design of preclinical experiments, which can be modified and enhanced whilst maintaining confidence in its predictions.     

The Haxo and Blinks Electrode: A Mathematical Model

Fick's diffusion equations have been solved for the Haxo and Blinks electrochemical determination of photosynthetic O(2) evolution. The model shows the method to be quantitative in the case of a "long" chamber measuring constant rates of O(2) evolution. Transients are amplitude distorted by an amount depending on the space distribution of the O(2) sources. A correction equation applied to the raw data permits the recovery of the original signal.     

Mathematical Study of a Staged-Progression HIV Model with Imperfect Vaccine

A staged-progression HIV model is formulated and used to investigate the potential impact of an imperfect vaccine. The vaccine is assumed to have several desirable characteristics such as protecting against infection, causing bypass of the primary infection stage, and offering a disease-altering therapeutic effect (so that the vaccine induces reversal from the full blown AIDS stage to the asymptomatic stage). The model, which incorporates HIV transmission by individuals in the AIDS stage, is rigorously analyzed to gain insight into its qualitative features. Using a comparison theorem, the model with mass action incidence is shown to have a globally-asymptotically stable disease-free equilibrium whenever a certain threshold, known as the vaccination reproduction number, is less than unity. Furthermore, the model with mass action incidence has a unique endemic equilibrium whenever this threshold exceeds unity. Using the Li-Muldowney techniques for a reduced version of the mass action model, this endemic equilibrium is shown to be globally-asymptotically stable, under certain parameter restrictions. The epidemiological implications of these results are that an imperfect vaccine can eliminate HIV in a given community if it can reduce the reproduction number to a value less than unity, but the disease will persist otherwise. Furthermore, a future HIV vaccine that induces the bypass of primary infection amongst vaccinated individuals (who become infected) would decrease HIV prevalence, whereas a vaccine with therapeutic effect could have a positive or negative effect at the community level.