Thieme y department of mathematics arizona state university tempe, az 85287, usa mathematical population dynamics proceedings of the 2nd international conference, rutgers univ. We study the stability and hopf bifurcation of the positive equilibrium of the model by using a bifurcation theory in the context of integrated semigroups. R package for agestructured population dynamics, stagepop, which offers true time delays in continuous time domain using deterministic delay differential equations16. Pdf continuoustime agestructured models in population. Mathematical models in biology lecture, held in the wintersemester 20032004 johannes muller technical university munich centre for mathematical sciences. All books are in clear copy here, and all files are secure so dont worry about it. The objective of these lectures is to apply the theory of linear and nonlinear semigroups of operators to models of structured population dynamics. Agestructured discretetime population dynamics model. Mathematical theory of agestructured population dynamics. Chaos theory is a branch of mathematics focusing on the study of chaosstates of dynamical systems whose apparentlyrandom states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to initial conditions. Existence and stability of equilibria in agestructured.
We establish the existence of the optimal control and the convergence of a certain fractional step scheme. Our results show that the relation between the elasticities of substitution of labor across ages plays a crucial role in the way the demographic changes affect both in the short and in the long run the optimal educational policy. Intensive programme mathematical models in life and social. In this paper, we investigate an sirs epidemic model with chronological age structure in a demographic steady state. This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models. Chaos theory is an interdisciplinary theory stating that, within the apparent randomness of chaotic complex systems, there are underlying. Stability analysis of an agestructured seirs model with time. The aim of the present paper is to apply these techniques for the numerical evaluation of the non linear age structured population model b. Applying an age structured optimalcontrol model, we derive features of the optimal age specific education rate.
The structure of the solution is also investigated. From the beginning, the main concerns of demography have extended beyond the variations in population size and distribution to the age structure dynamics of the population. We developed a new age structured deterministic model for the transmission dynamics of chikungunya virus. In fact, the major problems with which we have been confronted relate to population dynamics, as was clearly recognized by thomas robert malthus in the eighteenth century. The basic approach to agestructured population dynamics. Society for industrial and applied mathematics siam, 2005. Mathematical problems in the description of age structured populations. Hopf bifurcation for a spatially and age structured. Age structured population dynamics in demography and epidemiology. The basic approach to agestructured population dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods.
The dynamics are obtained from iterations of a leslie matrix 1. Please click button to get mathematical theory of age structured population dynamics book now. Mathematical theory of agestructured population dynamics by mimmo iannelli, 1995, giardini editori e stampatori edition, in english. During the past three decades, the agestructured sir epidemic model has been. Mathematical biology 9 springerverlag 1984 existence and stability of equilibria in age structured population dynamics j. The basic reproduction ratio of the model is obtained and we show that it is the threshold. Analytic algorithms for some models of nonlinear age. The first part of this paper is devoted to a complete description of the dynamics of a continuously structured population model coupled with a dynamical resource. Some of the theoretical and epidemiological findings. This paper is devoted to the study of a spatially and age structured population dynamics model.
Mathematical theory of age structured population dynamics, volume 7 of applied mathematics monograph c. How can mathematics be used to gain an understanding of population dynamics. Siam journal on applied mathematics society for industrial. Mathematical theory of age structured population dynamics. This book is the first one in which basic demographic models are rigorously formulated by using modern age structured population dynamics, extended to study realworld population problems.
We show how to use the method of characteristic lines to. Optimal harvesting for agestructured population dynamics. Analysis of agestructured population models with an additional structure horst r. Age structure is a crucial factor in understanding population pheno. In this monograph, many applications that illustrate both the theory and a wide variety of biological issues are given, along with an interdisciplinary case study that illustrates the connection of.
Age structured population dynamics in demography and epidemiology hisashi inaba auth. We investigate two optimal harvesting problems related to age dependent population dynamics. In the model, it is assumed that the energy each individual obtains from the resource is channeled between growth and reproduction in a proportion that depends on the individuals size. Existence and uniqueness of a positive solution for the model are demonstrated. Chapter 9 continuoustime agestructured models in population. Age structured models have been applied in the epidemic dynamics for decades. The mathematical methods involved in the study of age structured populations include. Optimal harvesting for a nonlinear agedependent population. This theory bridges the gap between the characteristics of individual organisms in a population and the dynamics of the total population as a whole. This educational video illustrates the dynamics of an agestructured population.
We present continuoustime models for age structured populations and disease transmission. A mathematical model of malaria transmission with structured. Here, i present an alternative agestructured population dynamics model based on the population dynamics and disease. Dec 11, 2009 mathematical theory of age structured population dynamics by mimmo iannelli, 1995, giardini editori e stampatori edition, in english. Here we investigate an optimal harvesting problem for a nonlinear age dependent population dynamics. Age structure is a crucial factor in understanding population phenomena, and the essential ideas in demography. Agestructured population encyclopedia of mathematics. We present continuoustime models for agestructured populations and disease transmission. Interest in the temporal fluctuations of biological populations can be traced to the dawn of civilization. Mathematical models in population dynamics and ecology. Continuous monocyclic and polycyclic age structured models of. Then the host population is assumed to be a demographic stable population, that is, its total size is growing exponentially but its age pro.
In this paper, we formulate a mathematical model of nonautonomous ordinary differential equations describing the dynamics of malaria transmission with age structure for the vector population. Agestructured population dynamics in demography and. In 1986, the dynamics of structured populations was discussed by metz et al. Handbook of statistics integrated population biology and. The dynamics are obtained from iterations of a leslie matrix 1, whose coefficients are adapted from 2. The model is analyzed to gain insights into the qualitative features of its associated equilibria. Hisashi inaba this book is the first one in which basic demographic models are rigorously formulated by using modern age structured population dynamics, extended to study realworld population problems. Then, the mathematical theory of the age structured population dynamics was proposed by iannelli. We show how to use the method of characteristic lines to analyze the model dynamics and to write an age structured population model as an. Mar 18, 2016 this educational video illustrates the dynamics of an age structured population. We show how to use the method of characteristic lines to analyze the model dynamics and to write an age. Analysis of age structured population models with an additional structure horst r. The basic approach to age structured population dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods.
Iannelli, mathematical theory of age structured population dynamics, giardini editori e stampatori, pisa, 1995. Mathematical problems in the description of age structured. Mathematical model of three agestructured transmission. Continuoustime age structured models in population dynamics and epidemiology jia li and fred brauer abstractwe present continuoustime models for age structured populations and disease transmission. Age structure is a crucial factor in understanding population phenomena, and the essential ideas in demography and epidemiology cannot be understood without mathematical formulation.
Analysis of agestructured population models with an. Pdf an introduction to mathematical population dynamics. Agestructured population dynamics in demography and epidemiology. We formulate a model describing the dynamics for the spatial propagation of an sis epidemic within a population, with age structure, living in an environment divided into two sites. The biting rate of mosquitoes is considered as a positive periodic function which depends on climatic factors. Sekine, a mathematical model for chagas disease with infection age dependent infectivity, math. This paper focuses on the study of continuous age structured models, or more general, physiologically structured models, which used for detailed and accurate study of population dynamics in many ecological, biological applications and medicine. Sep 01, 2004 read on the stability of separable solutions of a sexual age structured population dynamics model, mathematical biosciences on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. This book is the first one in which basic demographic models are rigorously formulated by using modern agestructured population dynamics, extended to study realworld population problems. In fact age dependent fertility and mortality rates are among the most basic parameters in the theory of population dynamics and demography.
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