Mathematical Biology and Biological Physics

Description

This is a book on interdisciplinary topics of the Mathematical and Biological Sciences. The treatment is both pedagogical and advanced in order to motivate research students as well as to fulfill the requirements of professional practitioners. There are comprehensive reviews written by senior experts on the important problems of growth and agglomeration in biology, on the algebraic modelling of the genetic code and on multi-step biochemical pathways. There are new results on the state of the art research in the pattern recognition of probability distribution of amino acids, on somitogenesis through reaction-diffusion models, on the mathematical modelling of infectious diseases, on the biophysical modelling of physiological disorders, on the sensitive analysis of parameters of malaria models, on the stability and hopf bifurcation of ecological and epidemiological models, on the viral infection of bee colonies and on the structure and motion of proteins. All these contributions are also strongly recommended to professionals from other scientific areas aiming to work on these interdisciplinary fields. Content: Preface Editorial Board of the BIOMAT Consortium Professor C.A. Floudas -- In Memoriam Comprehensive Introduction to Agglomeration and Growth and Models 1. Introduction 2. Stochastic matrices 2.1. Definitions and properties 2.2. Linear growth 2.3. The Fibonacci sequence 2.4. Stochastic matrix description 2.5. Agglomeration of chains 3. Agglomeration in two dimensions 3.1. Planar tilings 3.2. Curved structures 4. Lotka-Volterra equations 4.1. Classical predator-prey model 4.2. The origin of chirality in living organisms 4.3. Model with finite substrate References The Pattern Recognition of Probability Distributions of Amino Acids in Protein Families 1. Introduction 2. The Organization of the Sample Space of Probability 3. The Master Equation for Probability Evolution 4. The Distribution of Amino Acids as a Marginal Probability Distribution 5. The Domain of the Variables (a), (a). The Pattern Recognition Based on Level Curves 6. Final Numerical Calculations and Graphical Representation 7. Concluding Remarks References Modelling the Electrical Activity of the Heart 1. Introduction 2. Dynamical Model 2.1. Numerical results 3. Modelling ECG Signals 4. Conclusions References How the Interval Between Primary and Booster Vaccination Affects Long-Term Disease Dynamics 1. Introduction 2. Methodology 2.1. Agents-environment framework 2.2. Disease model 2.3. Vaccination model 2.4. Computational implementation 2.5. Parmeterization and timing of booster vaccination 3. Results 4. Concluding Remarks References Stability and Hopf Bifurcation in a Multi-delayed Eco-epidemiological Model 1. Introduction 2. Preliminary results 2.1. Positivity and boundedness of the solutions 3. Equilibria and permanence of the system 3.1. Permanence of the system 4. Stability of the coexistence equilibrium 5. Direction and stability of Hopf bifurcation 6. Numerical simulation 7. Discussion References Propagation of Extrinsic Perturbation in Multistep Biochemical Pathways 1. Introduction 2. Models and Methods 3. Results and Discussion 3.1. Stability analysis of the pathway with bias 3.2. Dynamics of the pathway with bias 3.3. Effect of random perturbation 4. Conclusions References Catastrophic Transitions in Coral Reef Biome under Invasion and Overfishing 1. Introduction 2. The Basic Model 3. Boundedness and Permanence of the System 4. Equilibria and Their Stability 5. Hopf Bifurcation 6. Numerical Simulations 7. Discussion Appendix References Dynamics of Hepatitis C Viral Load with Optimal Control Treatment Strategy 1. Introduction 2. Model 1 and Its Control 3. Model 2 and the Control Problem 4. Numerical Results 5. Conclusion References Somitogenesis and Turing Pattern 1. Introduction 2. The Model 3. Results 4. Conclusion References