[PDF] Feed Back And Optimal Control Models For Simple Biological Populations eBook

Author : Suzanne Lenhart
Publisher : CRC Press
Page : 272 pages
File Size : 40,28 MB
Release : 2007-05-07
Category : Mathematics
ISBN : 1584886404

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From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into the application of this theory to biological models. Focusing on mathematical concepts, the book first examines the most basic problem for continuous time ordinary differential equations (ODEs) before discussing more complicated problems, such as variations of the initial conditions, imposed bounds on the control, multiple states and controls, linear dependence on the control, and free terminal time. In addition, the authors introduce the optimal control of discrete systems and of partial differential equations (PDEs). Featuring a user-friendly interface, the book contains fourteen interactive sections of various applications, including immunology and epidemic disease models, management decisions in harvesting, and resource allocation models. It also develops the underlying numerical methods of the applications and includes the MATLAB® codes on which the applications are based. Requiring only basic knowledge of multivariable calculus, simple ODEs, and mathematical models, this text shows how to adjust controls in biological systems in order to achieve proper outcomes.

Author : Bean-San Goh
Publisher : Elsevier Science & Technology
Page : 304 pages
File Size : 17,9 MB
Release : 1980
Category : Science
ISBN :

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Management and Analysis of Biological Populations ...

Author : Rachael Lynn Miller Neilan
Publisher :
Page : 205 pages
File Size : 27,36 MB
Release : 2009
Category :
ISBN :

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This dissertation considers the use of optimal control theory in population models for the purpose of characterizing strategies of control which minimize an invasive or infected population with the least cost. Three different models and optimal control problems are presented. Each model describes population dynamics via a system of differential equations and includes the effects of one or more control methods. The first model is a system of two ordinary differential equations describing dynamics between a native population and an invasive population. Population growth terms are functions of the control, constructed so that the value of the control may affect each population differently. A novel existence result is presented for the case of quadratic growth functions. With parameters chosen to mimic the competition between cottonwood and salt cedar plants, optimal schedules of controlled flooding are displayed. The second model, a system of six ordinary differential equations, describes the spread of cholera in a human population through ingestion of Vibrio cholerae. Equations track movement of susceptible individuals to either an asymptomatic infected class or a symptomatic infected class through ingestion of bacteria, both in a hyperinfectious state and a less-infectious state. Recovered individuals temporarily move to an immune class before being placed back in the susceptible class. A new result quantifies contributions to the basic reproductive number from multiple infectious classes. Within the model, three control functions represent rehydration and antibiotic treatment, vaccination, and sanitation. The cost-effective balance of multiple cholera intervention methods is compared for two endemic populations. The third model describes the spread of disease in both time and space using a system of three parabolic partial differential equations with convection-diffusion movement terms and no-flux boundary conditions. A control function representing vaccination is incorporated. State variables track the number of susceptible, infected, and immune individuals. Detailed analysis for the characterization of the optimal control is provided. The model and optimal control results are applied to the spread of rabies among raccoons with the control function determining the timing and placement of oral vaccine baits. Results illustrate cost-effective vaccine distribution strategies for both regular and irregular patterns of rabies propagation.

Author : Paul Waltman
Publisher : Cambridge University Press
Page : 96 pages
File Size : 31,61 MB
Release : 1983
Category : Mathematics
ISBN : 9780898711882

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Single population growth models; Interacting populations; Some deterministic problems in genetics.

Author : Priti Kumar Roy
Publisher : Springer
Page : 228 pages
File Size : 38,97 MB
Release : 2015-12-08
Category : Mathematics
ISBN : 9812878521

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The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are presented in the book would serve to reveal the consequences of the logical structure of the disease transmission, quantitatively as well as qualitatively. One of the chapters introduces the optimal control approach towards the mathematical models, describing the optimal drug dosage process that is discussed with the basic deterministic models dealing with stability analysis. Another one chapter deals with the mathematical analysis for the perfect drug adherence for different drug dynamics during the treatment management. The last chapter of the book consists the stochastic approach to the disease dynamics on HIV/AIDS. This method helps to move the disease HIV/AIDS to extinction as the time to increase. This book will appeal to undergraduate and postgraduate students, as well as researchers, who are studying and working in the field of bio-mathematical modelling on infectious diseases, applied mathematics, health informatics, applied statistics and qualitative public health, etc. Social workers, who are working in the field of HIV, will also find the book useful for complements.