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International Journal of Biomathematics 2016年第4期9卷 1-14页

作者： Cuicui Liao Xiaohua Ding Jiuzhen Liang Department of Information and Computing Science Jiangnan University No. 1800 Lihu Avenue Wuxi Jiangsu 214122 P. R. China Department of Mathematics Harbin Institute of Technology at Weihai No. 2 Wenhua West Road Weihai Shandong 264209 P. R. China Department of Internet of ThingsJiangnan University No. 1800 Lihu Avenue Wuxi Jiangsu 214122 P. R. China

We propose an efficient numerical method for two population models, based on the nonstandard finite difference （NSFD） schemes and composition methods with complex time steps. The NSFD scheme is able to give positive numerical solutions that satisfy the conservation law, which is a key property for biological population models. The accuracy is improved by using the composition methods with complex time steps. Numerical tests on the plankton nutrient model and whooping cough model are presented to show the efficiency and advantage of the proposed numerical method.

关键词： Nonstandard finite difference schemes composition methods with complextime steps population models positive numerical solutions conservation laws.

GLOBAL ATTRACTIVITY OF population models WITH DELAYS AND DIFFUSION

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Journal of Systems Science & Complexity 2005年第3期18卷 396-403页

作者： QIU Zhipeng Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094 Department of Mathematics, University of Science and Technology of China, Hefei 230026, China. Department of Applied Mathematics Nanjing University of Science and Technology 江苏 Nanjing 210094

In this paper, the asymptotic behavior of three types of population models with delays and diffusion is studied. The first represents one species growth in the patch Ω and periodic environment and with delays recruitment, the second models a single species dispersal among the m patches of a heterogeneous environment, and the third models the spread of bacterial infections. Sufficient conditions for the global attractivity of periodic solution are obtained by the method of monotone theory and strongly concave operators. Some earlier results are extended to population models with delays and diffusion.

关键词： delays population models global attractivity reaction-diffusion

Construction of Dulac functions for mathematical models in population biology

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International Journal of Biomathematics 2015年第3期8卷 135-154页

作者： Osvaldo Osuna Cruz Vargas-De-Leon Instituto de Fisica y Matematicas Universidad MichoacanaEdif. C-3 Cd. Universitaria CP 58040 Morelia Michoacan Mexico Unidad de Medicina Experimental Hospital General de Mexico "Dr. Eduardo Liceaga" DF 06726 Mdxieo

In this paper, we present a method for constructing a Dulac function for mathematical models in population biology, in the form of systems of ordinary differential equations in the plane.

关键词： population models epidemic models chemostat models Dulac function nonexistence of periodic orbits.

One hundred years of population ecology:Successes,failures and the road ahead

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Integrative Zoology 2015年第3期10卷 233-240页

作者： Charles J.KREBS Department of Zoology University of British ColumbiaVancouverCanada and Institute for Applied EcologyUniversity of CanberraCanberraAustralia

population ecology is the most mature of the three subdisciplines of ecology partly because it has a solid mathematical foundation and partly because it can address the primary questions of distribution and abundance with experimental *** there is much left to do to integrate our population knowledge into community and ecosystem ecology to help address the global issues of food security and the conservation of *** different approaches are now being developed to bring about this integration and much more research will be necessary to decide which if any will be most useful in achieving our goals of explaining the changes we see in the distribution and abundance of animals and *** web ecology would appear to be the best approach at present because it uses the detailed information of the population ecology of particular species in combination with data on consumer-resource interactions to apply to the applied problems of biodiversity conservation,food security,pest management and disease *** we can use our understanding of population ecology to address the practical problems of our time in a creative way,we will benefit both the human population and the Earth’s *** remains to be done.

关键词： abundance geographic distributions history of ecology population models

SPATIALIZATION MODEL OF population BASED ON DATASET OF LAND USE AND LAND COVER CHANGE IN CHINA

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Chinese Geographical Science 2002年第2期12卷 114-119页

作者： ZHUANGDa－fang LIUMing－liang 等 InstituteofGeographicSciencesandNaturalResourcesResearch theChineseAcademyofSciencesBeijing100101P.R.China InstituteofGeographicSciencesandNaturalResourcesResearch theChineseAcademyofSciencesBeijin

The spatialization of population of counties in China is significant. Firstly, we can gain the estimated values of population density adaptive to different kinds of regions. Secondly, we can integrate effectively population data with other data including natural resources, environment, society and economy, build 1km GRIDs of natural resources reserves per person, population density and other economic and environmental data, which are necessary to the national management and macro adjustment and control of natural resources and dynamic monitoring of population. In order to establish population information system serving national decision making, three steps ought to be followed:1) establishing complete geographical spatial data foundation infrastructure including the establishment of electric map of residence with high resolution using topographical map with large scale and high resolution satellite remote sensing data, the determination of attribute information of housing and office buildings, and creating complete set of attribute database and rapid data updating; 2) establishing complete census systems including improving the transformation efficiency from census data to digital database and strengthening the link of census database and geographical spatial database, meanwhile, the government should attach great importance to the establishment and integration of population migration database; 3) considering there is no GIS software specially serving the analysis and management of population data, a practical approach is to add special modules to present software system, which works as a bridge actualizing the digitization and spatialization of population geography research.

关键词： spatialization models population models LUCC dataset populationspatialization deqing county

Mathematical study of fractional-order biological population model using optimal homotopy asymptotic method

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International Journal of Biomathematics 2016年第6期9卷 17-33页

作者： S. Sarwar M. A. Zahid S. Iqbal Department of Mathematics Shanghai University Shanghai 200444 P. R. China Department of Mathematics COMSATS Institute of Information Technology Sahiwal Campus 57000 Pakistan Department of Informatics and Systems School of Systems and TechnologyUniversity of Management and Technology Lahore Pakistan

In this paper, we study the fractional-order biological population models （FI3PMs） with Malthusian~ Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asymptotic method （OHAM） for partial differ- ential equations （PDEs） is extended and successfully implemented to solve FBPMs. Third-order approximate solutions are obtained and compared with the exact solutions. The numerical results unveil that the proposed extension in the OHAM for fractional- order differential problems is very effective and simple in computation. The results reveal the effectiveness with high accuracy and extremely efficient to handle most complicated biological population models.

关键词： Biological models population models fractional calculus optimal homotopyasymptotic method partial differential equations.

A Two-Step Growth Curve: Approach to the von Bertalanffy and Gompertz Equations

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Advances in Pure Mathematics 2016年第5期6卷 321-330页

作者： Laura Rogers-Bennett Donald W. Rogers California Department of Fish and Wildlife and Karen C. Drayer Wildlife Health Center UC Davis CA USA Bodega Marine Laboratory Bodega Bay CA USA Chemistry Department Long Island University Brooklyn NY USA Friday Harbor Laboratories Whiteley Center University of Washington Friday Harbor WA USA

Many curves have been proposed and debated to model individual growth of marine invertebrates. Broadly, they fall into two classes, first order (e.g. von Bertalanffy) and sigmoidal (e.g. Gompertz). We provide an innovative approach which demonstrates that the growth curves are not mutually exclusive but that either may arise from a simple three-stage growth model with two steps (k1 and k2) depending on the ratio of the growth parameters . The new approach predicts sigmoidal growth when is close to 1, but if either growth from stage A to stage B or B to C is fast relative to the other, the slower of the two steps becomes the growth limiting step and the model reduces to first order growth. The resulting curves indicate that there is a substantial difference in the estimated size at time t during the period of active growth. This novel two-step rate model generates a growth surface that allows for changes in the rate parameters over time as reflected in the new parameter n(t) = k1(t) - k2(t). The added degree of freedom brings about individual growth trajectories across the growth surface that is not easily mapped using conventional growth modeling techniques. This two (or more) stage growth model yields a growth surface that allows for a wide range of growth trajectories, accommodating staged growth, growth lags, as well as indeterminate growth and can help resolve debates as to which growth curves should be used to model animal growth. This flexibility can improve estimates of growth parameters used in population models influencing model outcomes and ultimately management decisions.=

关键词： Growth Model Growth Surface Rate Equation Staged Growth population models