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Mathematical Models for Society and Biology

Mathematical Models for Society and Biology
A Book

by Edward Beltrami

  • Publisher : Academic Press
  • Release : 2013-06-19
  • Pages : 288
  • ISBN : 0124046932
  • Language : En, Es, Fr & De
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Mathematical Models for Society and Biology, 2e, is a useful resource for researchers, graduate students, and post-docs in the applied mathematics and life science fields. Mathematical modeling is one of the major subfields of mathematical biology. A mathematical model may be used to help explain a system, to study the effects of different components, and to make predictions about behavior. Mathematical Models for Society and Biology, 2e, draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For this new edition, author Edward Beltrami uses mathematical models that are simple, transparent, and verifiable. Also new to this edition is an introduction to mathematical notions that every quantitative scientist in the biological and social sciences should know. Additionally, each chapter now includes a detailed discussion on how to formulate a reasonable model to gain insight into the specific question that has been introduced. Offers 40% more content – 5 new chapters in addition to revisions to existing chapters Accessible for quick self study as well as a resource for courses in molecular biology, biochemistry, embryology and cell biology, medicine, ecology and evolution, bio-mathematics, and applied math in general Features expanded appendices with an extensive list of references, solutions to selected exercises in the book, and further discussion of various mathematical methods introduced in the book

Instructor's Manual to Accompany Mathematical Models for Society and Biology

Instructor's Manual to Accompany Mathematical Models for Society and Biology
A Book

by Beltrami

  • Publisher : Academic Press
  • Release : 2002-01-26
  • Pages : 129
  • ISBN : 9780120855629
  • Language : En, Es, Fr & De
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A Course in Mathematical Biology

A Course in Mathematical Biology
Quantitative Modeling with Mathematical and Computational Methods

by Gerda de Vries,Thomas Hillen,Mark Lewis,Johannes Mller,Birgitt SchÓnfisch

  • Publisher : SIAM
  • Release : 2006-07-01
  • Pages : 309
  • ISBN : 0898716128
  • Language : En, Es, Fr & De
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This is the only book that teaches all aspects of modern mathematical modeling and that is specifically designed to introduce undergraduate students to problem solving in the context of biology. Included is an integrated package of theoretical modeling and analysis tools, computational modeling techniques, and parameter estimation and model validation methods, with a focus on integrating analytical and computational tools in the modeling of biological processes. Divided into three parts, it covers basic analytical modeling techniques; introduces computational tools used in the modeling of biological problems; and includes various problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, including many exercises related to biological questions. In addition, 25 open-ended research projects are provided, suitable for students. An accompanying Web site contains solutions and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB?.

Mathematical Models in Developmental Biology

Mathematical Models in Developmental Biology

by Jerome K. Percus,Stephen Childress

  • Publisher : American Mathematical Soc.
  • Release : 2015-06-19
  • Pages : 249
  • ISBN : 147041080X
  • Language : En, Es, Fr & De
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The path from relatively unstructured egg to full organism is one of the most fascinating trajectories in the biological sciences. Its complexity calls for a very high level of organization, with an array of subprocesses in constant communication with each other. These notes introduce an interleaved set of mathematical models representative of research in the last few decades, as well as the techniques that have been developed for their solution. Such models offer an effective way of incorporating reliable data in a concise form, provide an approach complementary to the techniques of molecular biology, and help to inform and direct future research. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

A Primer in Mathematical Models in Biology

A Primer in Mathematical Models in Biology

by Lee A. Segel,Leah Edelstein-Keshet

  • Publisher : SIAM
  • Release : 2013-01-01
  • Pages : 424
  • ISBN : 1611972507
  • Language : En, Es, Fr & De
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This textbook introduces differential equations, biological applications, and simulations and emphasizes molecular events (biochemistry and enzyme kinetics), excitable systems (neural signals), and small protein and genetic circuits. A Primer on Mathematical Models in Biology will appeal to readers because it grew out of a course that the popular and highly respected applied mathematician Lee Segel taught at the Weizmann Institute and it represents his unique perspective; combines clear and useful mathematical methods with applications that illustrate the power of such tools; and includes many exercises in reasoning, modeling, and simulations.

An Invitation to Biomathematics

An Invitation to Biomathematics
A Book

by Raina Robeva,James R. Kirkwood,Robin Lee Davies,Leon Farhy,Boris P. Kovatchev,Martin Straume,Michael L. Johnson

  • Publisher : Academic Press
  • Release : 2007-08-28
  • Pages : 480
  • ISBN : 9780080550992
  • Language : En, Es, Fr & De
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Essential for all biology and biomathematics courses, this textbook provides students with a fresh perspective of quantitative techniques in biology in a field where virtually any advance in the life sciences requires a sophisticated mathematical approach. An Invitation to Biomathematics, expertly written by a team of experienced educators, offers students a solid understanding of solving biological problems with mathematical applications. This text succeeds in enabling students to truly experience advancements made in biology through mathematical models by containing computer-based hands-on laboratory projects with emphasis on model development, model validation, and model refinement. The supplementary work, Laboratory Manual of Biomathematics is available separately ISBN 0123740223, or as a set ISBN: 0123740290) * Provides a complete guide for development of quantification skills crucial for applying mathematical methods to biological problems * Includes well-known examples from across disciplines in the life sciences including modern biomedical research * Explains how to use data sets or dynamical processes to build mathematical models * Offers extensive illustrative materials * Written in clear and easy-to-follow language without assuming a background in math or biology * A laboratory manual is available for hands-on, computer-assisted projects based on material covered in the text

An Introduction to Mathematical Modeling in Physiology, Cell Biology, and Immunology

An Introduction to Mathematical Modeling in Physiology, Cell Biology, and Immunology
American Mathematical Society, Short Course, January 8-9, 2001, New Orleans, Louisiana

by James Sneyd

  • Publisher : American Mathematical Soc.
  • Release : 2002
  • Pages : 177
  • ISBN : 0821828169
  • Language : En, Es, Fr & De
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In many respects, biology is the new frontier for applied mathematicians. This book demonstrates the important role mathematics plays in the study of some biological problems. It introduces mathematicians to the biological sciences and provides enough mathematics for bioscientists to appreciate the utility of the modelling approach. The book presents a number of diverse topics, such as neurophysiology, cell biology, immunology, and human genetics. It examines how research is done, what mathematics is used, what the outstanding questions are, and how to enter the field. Also given is a brief historical survey of each topic, putting current research into perspective. The book is suitable for mathematicians and biologists interested in mathematical methods in biology.

Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance

Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance
A Book

by Carlos A. Braumann

  • Publisher : Wiley
  • Release : 2019-04-29
  • Pages : 304
  • ISBN : 1119166063
  • Language : En, Es, Fr & De
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A comprehensive introduction to the core issues of stochastic differential equations and their effective application Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance offers a comprehensive examination to the most important issues of stochastic differential equations and their applications. The author — a noted expert in the field — includes myriad illustrative examples in modelling dynamical phenomena subject to randomness, mainly in biology, bioeconomics and finance, that clearly demonstrate the usefulness of stochastic differential equations in these and many other areas of science and technology. The text also features real-life situations with experimental data, thus covering topics such as Monte Carlo simulation and statistical issues of estimation, model choice and prediction. The book includes the basic theory of option pricing and its effective application using real-life. The important issue of which stochastic calculus, Itô or Stratonovich, should be used in applications is dealt with and the associated controversy resolved. Written to be accessible for both mathematically advanced readers and those with a basic understanding, the text offers a wealth of exercises and examples of application. This important volume: Contains a complete introduction to the basic issues of stochastic differential equations and their effective application Includes many examples in modelling, mainly from the biology and finance fields Shows how to: Translate the physical dynamical phenomenon to mathematical models and back, apply with real data, use the models to study different scenarios and understand the effect of human interventions Conveys the intuition behind the theoretical concepts Presents exercises that are designed to enhance understanding Offers a supporting website that features solutions to exercises and R code for algorithm implementation Written for use by graduate students, from the areas of application or from mathematics and statistics, as well as academics and professionals wishing to study or to apply these models, Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance is the authoritative guide to understanding the issues of stochastic differential equations and their application.

Mathematical Models in Biological Discovery

Mathematical Models in Biological Discovery
A Book

by D L Solomon,C F Walter

  • Publisher : Unknown Publisher
  • Release : 1977-03-01
  • Pages : 252
  • ISBN : 9783642930584
  • Language : En, Es, Fr & De
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Mathematical Modeling of Biological Systems, Volume I

Mathematical Modeling of Biological Systems, Volume I
Cellular Biophysics, Regulatory Networks, Development, Biomedicine, and Data Analysis

by Andreas Deutsch,Lutz Brusch,Helen Byrne,Gerda de Vries,Hanspeter Herzel

  • Publisher : Springer Science & Business Media
  • Release : 2007-06-15
  • Pages : 382
  • ISBN : 0817645586
  • Language : En, Es, Fr & De
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Volume I of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. The chapters are thematically organized into the following main areas: cellular biophysics, regulatory networks, developmental biology, biomedical applications, data analysis and model validation. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.

Mathematical Models of Tumor-Immune System Dynamics

Mathematical Models of Tumor-Immune System Dynamics
A Book

by Amina Eladdadi,Peter Kim,Dann Mallet

  • Publisher : Springer
  • Release : 2014-11-06
  • Pages : 275
  • ISBN : 1493917935
  • Language : En, Es, Fr & De
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This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction between the immune system and a growing tumor. The multidimensional nature of these complex interactions requires a cross-disciplinary approach to capture more realistic dynamics of the essential biology. The papers presented in this volume explore these issues and the results will be of interest to graduate students and researchers in a variety of fields within mathematical and biological sciences.

Mathematical Models in Biology

Mathematical Models in Biology
A Book

by Leah Edelstein-Keshet

  • Publisher : SIAM
  • Release : 1988
  • Pages : 586
  • ISBN : 9780898719147
  • Language : En, Es, Fr & De
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Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.

Cellular Automaton Modeling of Biological Pattern Formation

Cellular Automaton Modeling of Biological Pattern Formation
Characterization, Examples, and Analysis

by Andreas Deutsch,Sabine Dormann

  • Publisher : Birkhäuser
  • Release : 2018-03-09
  • Pages : 464
  • ISBN : 1489979808
  • Language : En, Es, Fr & De
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This text explores the use of cellular automata in modeling pattern formation in biological systems. It describes several mathematical modeling approaches utilizing cellular automata that can be used to study the dynamics of interacting cell systems both in simulation and in practice. New in this edition are chapters covering cell migration, tissue development, and cancer dynamics, as well as updated references and new research topic suggestions that reflect the rapid development of the field. The book begins with an introduction to pattern-forming principles in biology and the various mathematical modeling techniques that can be used to analyze them. Cellular automaton models are then discussed in detail for different types of cellular processes and interactions, including random movement, cell migration, adhesive cell interaction, alignment and cellular swarming, growth processes, pigment cell pattern formation, tissue development, tumor growth and invasion, and Turing-type patterns and excitable media. In the final chapter, the authors critically discuss possibilities and limitations of the cellular automaton approach in modeling various biological applications, along with future research directions. Suggestions for research projects are provided throughout the book to encourage additional engagement with the material, and an accompanying simulator is available for readers to perform their own simulations on several of the models covered in the text. QR codes are included within the text for easy access to the simulator. With its accessible presentation and interdisciplinary approach, Cellular Automaton Modeling of Biological Pattern Formation is suitable for graduate and advanced undergraduate students in mathematical biology, biological modeling, and biological computing. It will also be a valuable resource for researchers and practitioners in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science. PRAISE FOR THE FIRST EDITION “An ideal guide for someone with a mathematical or physical background to start exploring biological modelling. Importantly, it will also serve as an excellent guide for experienced modellers to innovate and improve their methodologies for analysing simulation results.” —Mathematical Reviews

Mathematical Modeling

Mathematical Modeling
Models, Analysis and Applications

by Sandip Banerjee

  • Publisher : CRC Press
  • Release : 2014-02-07
  • Pages : 276
  • ISBN : 1482229161
  • Language : En, Es, Fr & De
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Almost every year, a new book on mathematical modeling is published, so, why another? The answer springs directly from the fact that it is very rare to find a book that covers modeling with all types of differential equations in one volume. Until now. Mathematical Modeling: Models, Analysis and Applications covers modeling with all kinds of differential equations, namely ordinary, partial, delay, and stochastic. The book also contains a chapter on discrete modeling, consisting of differential equations, making it a complete textbook on this important skill needed for the study of science, engineering, and social sciences. More than just a textbook, this how-to guide presents tools for mathematical modeling and analysis. It offers a wide-ranging overview of mathematical ideas and techniques that provide a number of effective approaches to problem solving. Topics covered include spatial, delayed, and stochastic modeling. The text provides real-life examples of discrete and continuous mathematical modeling scenarios. MATLAB® and Mathematica® are incorporated throughout the text. The examples and exercises in each chapter can be used as problems in a project. Since mathematical modeling involves a diverse range of skills and tools, the author focuses on techniques that will be of particular interest to engineers, scientists, and others who use models of discrete and continuous systems. He gives students a foundation for understanding and using the mathematics that is the basis of computers, and therefore a foundation for success in engineering and science streams.

MATHEMATICAL MODELS – Volume III

MATHEMATICAL MODELS – Volume III

by Jerzy A. Filar,Jacek B Krawczyk

  • Publisher : EOLSS Publications
  • Release : 2009-09-19
  • Pages : 398
  • ISBN : 1848262442
  • Language : En, Es, Fr & De
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Mathematical Models is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on Mathematical Models discusses matters of great relevance to our world such as: Basic Principles of Mathematical Modeling; Mathematical Models in Water Sciences; Mathematical Models in Energy Sciences; Mathematical Models of Climate and Global Change; Infiltration and Ponding; Mathematical Models of Biology; Mathematical Models in Medicine and Public Health; Mathematical Models of Society and Development. These three volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.

Mathematical Models for Biological Pattern Formation

Mathematical Models for Biological Pattern Formation
A Book

by Philip K. Maini,Hans G. Othmer

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 327
  • ISBN : 1461301335
  • Language : En, Es, Fr & De
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This 121st IMA volume, entitled MATHEMATICAL MODELS FOR BIOLOGICAL PATTERN FORMATION is the first of a new series called FRONTIERS IN APPLICATION OF MATHEMATICS. The FRONTIERS volumes are motivated by IMA pro grams and workshops, but are specially planned and written to provide an entree to and assessment of exciting new areas for the application of mathematical tools and analysis. The emphasis in FRONTIERS volumes is on surveys, exposition and outlook, to attract more mathematicians and other scientists to the study of these areas and to focus efforts on the most important issues, rather than papers on the most recent research results aimed at an audience of specialists. The present volume of peer-reviewed papers grew out of the 1998-99 IMA program on "Mathematics in Biology," in particular the Fall 1998 em phasis on "Theoretical Problems in Developmental Biology and Immunol ogy." During that period there were two workshops on Pattern Formation and Morphogenesis, organized by Professors Murray, Maini and Othmer. James Murray was one of the principal organizers for the entire year pro gram. I am very grateful to James Murray for providing an introduction, and to Philip Maini and Hans Othmer for their excellent work in planning and preparing this first FRONTIERS volume. I also take this opportunity to thank the National Science Foundation, whose financial support of the IMA made the Mathematics in Biology pro gram possible.

Towards a Mathematical Theory of Complex Biological Systems

Towards a Mathematical Theory of Complex Biological Systems
A Book

by Carlo Bianca,Concetta Bianca,N. Bellomo

  • Publisher : World Scientific
  • Release : 2011
  • Pages : 208
  • ISBN : 9814340537
  • Language : En, Es, Fr & De
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This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy. The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others. Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, celular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling.

Mathematical Models in Cell Biology and Cancer Chemotherapy

Mathematical Models in Cell Biology and Cancer Chemotherapy
A Book

by M. Eisen

  • Publisher : Springer Science & Business Media
  • Release : 2013-03-13
  • Pages : 431
  • ISBN : 364293126X
  • Language : En, Es, Fr & De
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The purpose of this book is to show how mathematics can be applied to improve cancer chemotherapy. Unfortunately, most drugs used in treating cancer kill both normal and abnormal cells. However, more cancer cells than normal cells can be destroyed by the drug because tumor cells usually exhibit different growth kinetics than normal cells. To capitalize on this last fact, cell kinetics must be studied by formulating mathematical models of normal and abnormal cell growth. These models allow the therapeutic and harmful effects of cancer drugs to be simulated quantitatively. The combined cell and drug models can be used to study the effects of different methods of administering drugs. The least harmful method of drug administration, according to a given criterion, can be found by applying optimal control theory. The prerequisites for reading this book are an elementary knowledge of ordinary differential equations, probability, statistics, and linear algebra. In order to make this book self-contained, a chapter on cell biology and a chapter on control theory have been included. Those readers who have had some exposure to biology may prefer to omit Chapter I (Cell Biology) and only use it as a reference when required. However, few biologists have been exposed to control theory. Chapter 7 provides a short, coherent and comprehensible presentation of this subject. The concepts of control theory are necessary for a full understanding of Chapters 8 and 9.

Mathematical Models in Biological Discovery

Mathematical Models in Biological Discovery
A Book

by D.L. Solomon,C.F. Walter

  • Publisher : Springer Science & Business Media
  • Release : 2013-03-13
  • Pages : 242
  • ISBN : 3642930573
  • Language : En, Es, Fr & De
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When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians", many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address the topic during an annual meeting of the AAAS was irresistable. In order to try to maintain the integrity ;,f the original intent of the symposium, it was entitled, "Contributions of Mathematical Models to Biological Discovery". This symposium was organized by Daniel Solomon and myself, held during the 141st annual meeting of the AAAS in New York during January, 1975, sponsored by sections G and N (Biological and Medical Sciences) of the AAAS and the North American Regions of the Biometric Society, and supported by grant BMS 75-0280) from the National Science Foundation. What follows in this volume are papers by nine of the participants who not only felt that they had something to say in a symposium entitled, "Contributions of Mathematical Models to Biological Discovery", but who falso were willing to record their ideas in more detail here.

Mathematical Models for Therapeutic Approaches to Control Psoriasis

Mathematical Models for Therapeutic Approaches to Control Psoriasis
A Book

by Priti Kumar Roy,Abhirup Datta

  • Publisher : Springer
  • Release : 2019-07-18
  • Pages : 89
  • ISBN : 9811390207
  • Language : En, Es, Fr & De
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This book discusses several mathematical models highlighting the disease dynamics of psoriasis and its control. It explains the control of keratinocyte concentration through a negative feedback mechanism and the effect of including a realistic time delay in that system. The effect of cytokine release is described in a mathematical model of psoriasis and further elucidated in two different mathematical pathways: the ordinary differential equation model system, and the fractional-order differential equation model system. The book also identifies the role of CD8+ T-cells in psoriasis by investigating the interaction between dendritic cells and CD8+ T-cells. Presenting an approach to control the fractional-order system to prevent excess production of keratinocyte cell population, the book is intended for researchers and scientists in the field of applied mathematics, health informatics, applied statistics and qualitative public health, as well as bio-mathematicians interested in the mathematical modeling of autoimmune diseases like psoriasis.