Simone Scacchi

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 wavesA spatially structured epidemic model concerning malaria as an example of vector-borne epidemicsOptimal harvesting problems for space-structured and age-structured population dynamicsControlling epidemics in agriculture due to pest insectsThe role of predators as a possible biocontrol agent of epidemics in agricultureControl by taxation of the environmental pollution produced by human activitiesThe 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© 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.

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 wavesA spatially structured epidemic model concerning malaria as an example of vector-borne epidemicsOptimal harvesting problems for space-structured and age-structured population dynamicsControlling epidemics in agriculture due to pest insectsThe role of predators as a possible biocontrol agent of epidemics in agricultureControl by taxation of the environmental pollution produced by human activitiesThe 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© 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.

This book covers the main mathematical and numerical models in computational electrocardiology, ranging from microscopic membrane models of cardiac ionic channels to macroscopic bidomain, monodomain, eikonal models and cardiac source representations. These advanced multiscale and nonlinear models describe the cardiac bioelectrical activity from the cell level to the body surface and are employed in both the direct and inverse problems of electrocardiology. The book also covers advanced numerical techniques needed to efficiently carry out large-scale cardiac simulations, including time and space discretizations, decoupling and operator splitting techniques, parallel finite element solvers. These techniques are employed in 3D cardiac simulations illustrating the excitation mechanisms, the anisotropic effects on excitation and repolarization wavefronts, the morphology of electrograms in normal and pathological tissue and some reentry phenomena. The overall aim of the book is to present rigorously the mathematical and numerical foundations of computational electrocardiology, illustrating the current research developments in this fast-growing field lying at the intersection of mathematical physiology, bioengineering and computational biomedicine. This book is addressed to graduate student and researchers in the field of applied mathematics, scientific computing, bioengineering, electrophysiology and cardiology.

This book covers the main mathematical and numerical models in computational electrocardiology, ranging from microscopic membrane models of cardiac ionic channels to macroscopic bidomain, monodomain, eikonal models and cardiac source representations. These advanced multiscale and nonlinear models describe the cardiac bioelectrical activity from the cell level to the body surface and are employed in both the direct and inverse problems of electrocardiology. The book also covers advanced numerical techniques needed to efficiently carry out large-scale cardiac simulations, including time and space discretizations, decoupling and operator splitting techniques, parallel finite element solvers. These techniques are employed in 3D cardiac simulations illustrating the excitation mechanisms, the anisotropic effects on excitation and repolarization wavefronts, the morphology of electrograms in normal and pathological tissue and some reentry phenomena. The overall aim of the book is to present rigorously the mathematical and numerical foundations of computational electrocardiology, illustrating the current research developments in this fast-growing field lying at the intersection of mathematical physiology, bioengineering and computational biomedicine. This book is addressed to graduate student and researchers in the field of applied mathematics, scientific computing, bioengineering, electrophysiology and cardiology.