Mathematical Modeling and Control in Life and Environmental Sciences: Regional Control Problems

Aniţa, Sebastian, Capasso, Vincenzo, Scacchi, Simone

  • 出版商: Birkhauser Boston
  • 出版日期: 2024-04-30
  • 售價: $6,190
  • 貴賓價: 9.5$5,881
  • 語言: 英文
  • 頁數: 277
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031499700
  • ISBN-13: 9783031499708
  • 下單後立即進貨 (約1週~2週)

相關主題

商品描述

This monograph explores the use of mathematical modeling and control theory in a variety of contemporary challenges in mathematical biology and environmental sciences. Emphasizing an approach of learning by doing, the authors focus on a set of significant case studies emerging from real-world problems and illustrate how mathematical techniques and computational experiments can be employed in the search for sustainable solutions.
The following topics are extensively discussed:
  • Eradicability and control of a paradigmatic epidemic model, with a view to the existence of endemic states, their stability, and the existence of travelling waves
  • A spatially structured epidemic model concerning malaria as an example of vector-borne epidemics
  • Optimal harvesting problems for space-structured and age-structured population dynamics
  • Controlling epidemics in agriculture due to pest insects
  • The role of predators as a possible biocontrol agent of epidemics in agriculture
  • Control by taxation of the environmental pollution produced by human activities
The originality of this text is in its leitmotif - regional control - along the principle of "Think Globally, Act Locally." Indeed, for example, in many real spatially structured ecosystems, it is practically impossible to control the relevant system by global interventions in the whole habitat.

Proofs are given whenever they may serve as a guide to the introduction of new concepts. Each chapter includes a comprehensive description of the numerical methods used for the computational experiments, and MATLAB(c) codes for many of the numerical simulations are available for download. Several challenging open problems are also provided to stimulate future research.
This text is aimed at mathematicians, engineers, and other scientists working in areas such as biology, medicine, and economics. Graduate and advanced undergraduate students of a quantitative subject related to the analysis and applications of dynamical systems and their control will also find it to be a valuable resource.

商品描述(中文翻譯)

這本專著探討數學建模和控制理論在數學生物學和環境科學中的各種當代挑戰中的應用。作者強調以實踐學習的方式,專注於一系列來自現實世界問題的重要案例研究,並說明如何運用數學技術和計算實驗來尋求可持續解決方案。
以下主題被廣泛討論:


  • 一個典型流行病模型的消滅和控制,關注存在地方性狀態、其穩定性以及行波的存在

  • 一個關於瘧疾的空間結構流行病模型,作為傳媒傳播流行病的例子

  • 空間結構和年齡結構人口動態的最優收穫問題

  • 由於害蟲引起的農業流行病的控制

  • 捕食者作為農業流行病生物控制劑的可能角色

  • 通過稅收控制人類活動產生的環境污染

這本書的獨特之處在於其主題 - 區域控制 - 遵循“全球思考,地方行動”的原則。實際上,在許多真實的空間結構生態系統中,通過對整個棲息地進行全球干預來控制相關系統幾乎是不可能的。

在引入新概念時,提供了相應的證明作為指南。每章都包括對用於計算實驗的數值方法的全面描述,並且可以下載用於許多數值模擬的MATLAB(c)代碼。還提供了幾個具有挑戰性的開放問題,以激發未來的研究。
這本書針對數學家、工程師和其他在生物學、醫學和經濟學等領域工作的科學家。與動態系統分析和應用相關的量化學科的研究生和高年級本科生也會發現它是一個有價值的資源。