Contents -- Preface -- Editorial Board of the BIOMAT Consortium -- Professor C.E.M. Pearce - In Memoriam -- Mathematical Epidemiology -- Compartmental Age of Infection Epidemic Models Fred Brauer -- 1. Epidemic models with homogeneous mixing -- 1.1. The simple Kermack-McKendrick model -- 1.2. Models with disease deaths -- 1.3. More complicated epidemic models -- 2. The age of infection epidemic model -- 2.1. The initial exponential growth rate -- 3. Heterogeneous mixing age of infection models -- 3.1. The final size relations -- 3.2. The initial exponential growth rate -- 4. Different models for the same epidemic -- References -- Mathematical Modelling of Infectious Diseases -- Lyme Pathogen Transmission in Tick Populations with Multiple Host Species Yijun Lou, Jianhong Wu, Xiaotian Wu -- 1. Introduction -- 2. The Model and Analysis -- 2.1. The Tick Population Dynamics -- 2.2. The Global Dynamics -- 3. Numerical Simulations -- 3.1. Climate Warming Effects -- 3.2. Host Diversity Effects -- 3.2.1. Effects of Adding Alternative Hosts without Interspecific Host Competition -- 3.2.2. Effects of Adding the Alternative Host with Interspecific Host Competition -- 3.3. Sensitivity Analysis -- 4. Discussion -- Acknowledgements -- References -- Quantifying the Risk of Mosquito-Borne Infections Basing on the Equilibrium Prevalence in Humans Marcos Amaku, Francisco A.B. Coutinho, Eduardo Massad -- 1. Introduction -- 2. The Model -- 3. Estimating Risks -- 4. Discussion -- Acknowledgments -- Conflicts of Interest -- References -- Seasonal Fluctuation in Tsetse Fly Populations and Human African Trypanosomiasis: A Mathematical Model T. Madsen, D.I. Wallace, N. Zupan -- 1. Introduction -- 2. Insect population submodel -- 2.1. Insect Model Equations -- 2.2. Explanation of Equations -- 2.3. Temperature Model -- 3. Analysis of model.

3.1. Instability of the model with constant temperature D -- 3.2. Sufficient insect death leads to stability -- 3.3. Variable temperature as a switched system -- 4. Numerical results of insect submodel -- 4.1. Rogers' model revisited -- 5. Sensitivity of the model -- 6. Summary of results -- References -- Modelling Physiological Disorders -- A Mathematical Model for the Immunotherapy of Advanced Prostate Cancer Travis Portz, Yang Kuang -- 1. Introduction -- 2. The Model -- 3. Numerical Simulations -- 4. Mathematical Analysis -- 5. Discussion -- Acknowledgements -- References -- Seizure Manifold of the Epileptic Brain: A State Space Reconstruction Approach Mujahid N. Syed, Pando G. Georgiev, Panos M. Pardalos -- 1. Introduction -- 2. Review -- 2.1. Embedding -- 3. Methodology -- 3.1. Preprocessing -- Filtering Noise -- Identifying Stationarity -- Identifying Determinism -- 3.2. Manifold Generation -- Time Delay Embedding -- Embedding Dimension -- Delay Time -- 3.3. Measures of DDS -- Fractal Dimension -- Lyapunov Exponents -- Kolmogorov Entropy -- 3.4. Surrogate Tests -- Surrogate Data Test 1 -- Surrogate Data Test 2 -- Surrogate Data Test 3 -- 3.5. Low Dimensional Phase Portraits -- 4. Seizure Manifold -- 5. Criticism -- 6. Conclusion -- References -- Synchronous Calcium Induced Calcium Release (CICR) in a Multiple Site Model of the Cardiac Myocyte D.I. Wallace, J.E. Tanembaum -- 1. Introduction -- 2. Model Formulation -- 2.1. Input from cell exterior -- 2.2. SR uptake via SERCA pump -- 2.3. CICR release from SR -- 2.4. Leak from SR -- 2.5. Leak to exterior -- 2.6. Diffusion within SR and cytoplasm -- 3. Methods -- 4. Results -- 4.1. Propagation of calcium release -- 4.2. Importance of diffusion in the SR -- 4.3. The Effect of Changing i on CICR -- 4.4. Effect of Changing SERCA Pump Activity on CICR.

4.5. Effect of Changing the SR Ca2+ Release Threshold on CICR -- 4.6. Effect of Changing the Rate of Cytoplasm to ECM Ca2+ Movement on CICR -- 5. Summary -- Acknowledgements -- References -- Theoretical Immunology -- Modelling Natural Killer Cell Repertoire Development and Activation Dynamics Michal Sternberg-Simon, Ramit Mehr -- 1. Introduction -- 1.1. The immune response and its complexity -- 1.2. Natural killer cells -- 1.2.1. NK cell Function -- 1.2.2. NK cell receptors -- 1.2.3. NK cell education -- 1.2.4. NK cell development and maturation -- 1.2.5. NK cell activation - Synapses and Signaling -- 2. Using mathematical models to understand NK cell education -- 2.1. Methods for comparing repertoires -- 2.2. Repertoire formation in mice -- 2.3. Repertoire formation in humans -- 2.4. Deciding between hypotheses: The sequential vs. the Two-step selection models -- 2.5. Models of NK cell signaling -- 2.6. Simulations of the NK cell immune synapse -- 2.7. NK cell activation thresholds -- 2.8. Concluding remarks and future questions -- Acknowledgments -- References -- Saturation Effects on T-Cell Activation in a Model of a Multi-Stage Pathogen Michael Shapiro, Edgar Delgado-Eckert -- 1. Introduction -- 2. Background and definitions -- 3. Results -- 3.1. Self-establishing stages -- 4. Discussion -- Acknowledgements -- References -- Dynamic and Geometric Modelling of Biomolecular Structure -- Advances in DE NOVO Protein Design for Monomeric, Multimeric, and Conformational Switch Proteins James Smadbeck, George A. Khoury, Meghan B. Peterson, Christodoulos A. Floudas -- 1. Introduction -- 2. Review of De Novo Design Framework and Successful Experimentally Validated Designs -- 3. Monomeric De Novo Protein Design Framework -- 3.1. Method Overview -- 4. Transition Specificity Design with Minimum Mutations -- Stage One: Sequence Selection with Minimal Mutations.

Stage Two: Transition Specificity via FAMBE-pH -- 5. Multimeric Protein Design -- 6. Protein WISDOM -- 7. Conclusion -- Acknowledgements -- References -- Mathematical Models and Techniques of Biomolecular Geometric Analysis K.L. Xia, F. Xin, Y. Tong, G.W. Wei -- 1. Introduction -- 2. Theory and models -- 2.1. Minimal molecular surface model -- 2.1.1. PB based surface construction -- 3. Computational algorithms -- 3.1. Surface generation from PDB -- 3.2. Surface generation from EMD -- 3.3. Geometric features -- 4. Discussion on principal curvature flows -- 5. Conclusion -- References -- Towards a New Bio-Quantum Model for Signaling and Repair of DNA Damage A. Martinez Aragon, J. D. de Toledo Arruda-Neto, Y. Medina Guevara -- 1. Introduction -- 2. Model -- 2.1. The double strand break. Solitons -- 2.2. ATM- Signal Reception -- 2.3. Navigation. Free water dipole laser -- 2.4. Recognition: the issue of residual static field of the DSB -- 3. Conclusions -- References -- Population Dynamics -- Viral Evolution and Adaptation as a Multivariate Branching Process F. Antoneli, F. Bosco, D. Castro, L. M. Janini -- 1. Introduction -- 2. Phenotypic Models for Viral Evolution -- 2.1. Definition of the Model -- 2.2. Basic Properties of the Phenotypic Model -- 3. The Simple Phenotypic Model -- 3.1. The Sub-critical Regime: Lethal Mutagenesis -- 3.2. The Super-critical Case: Relaxation and Equilibrium -- 3.2.1. Relaxation towards equilibrium -- 3.2.2. The Dynamical Stationary State -- 3.3. The Critical Case: Extinction Threshold -- 4. Conclusions and Outlook -- Acknowledgments -- References -- Associative Learning of a Lexicon in a Noisy Cross-Situational Scenario P.F.C. Tilles, J.F. Fontanari -- 1. Introduction -- 2. Cross-situational learning scenario and associative learning algorithm -- 3. Single-word learning -- 4. Finite size scaling analysis -- 5. Conclusion.

Acknowledgments -- References -- Relationship between Rainfall and Control Effectiveness of the Aedes aegypti Population through a Non-linear Dynamical Model: Case of Lavras City, Brazil L.B. Barsante, R.T.N. Cardoso, J.L. Acebal, M.M. Morais, A.E. Eiras -- 1. Introduction -- 2. Formulation of the model -- 3. Analysis of Equilibrium and Stability -- 4. Results -- 4.1. Conclusion -- Acknowledgments -- References -- Spatiotemporal Dynamics of Telegraph Reaction-Diffusion Predator-Prey Models Eliseo Hernandez-Martinez, Hector Puebla, Teresa Perez Munoz, Margarita Gonzalez Brambila, Jorge X. Velasco-Hernandez -- 1. Introduction -- 2. Spatiotemporal Prey-Predator Interactions -- 3. Telegraph reaction-diffusion equation -- 4. Numerical Schemes -- 5. Numerical Simulations -- 5.1. Holling type II functional response -- 5.2. Predator-prey model with cross-diffusion -- 6. Conclusions -- Acknowledgements -- References -- Population Dynamics of Spider Monkey (Ateles hybridus) in a Fragmented Landscape of Colombia J.M. Cordovez, J.R. Arteaga B., M. Marino, A.G. de Luna, A. Link -- 1. Introduction -- 2. Mathematical Model -- 2.1. State variables -- 2.2. Model parameters -- 2.3. Model diagram and equations -- 2.4. Steady state -- 2.5. Stability -- 2.6. Parameters for numerical simulations -- 2.7. Model simulations -- 3. Results -- 3.1. Control scenario -- 3.2. Variable patch connection quality -- 3.3. Variable number of patches -- 3.4. Variable patch size -- 3.5. Variable number of connections between patches -- 4. Discussion -- References -- Computational Biology -- The Contribution of Stop Codon Frequency and Purine Bias to the Classification of Coding Sequences N. Carels, D. Frias -- 1. Introduction -- 2. Material and Methods -- 2.1. Basic considerations on the base composition and their consequences -- 2.2. Rice sequences -- 2.3. Human sequences.

2.4. Classification method.