Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells: Selected Works from the 20th BIOMAT Consortium Lectures, Rio de Janeiro, Brazil, November 1-6 2020

"This volume gathers together selected, peer-reviewed papers presented at the BIOMAT 2020 International Symposium, which was virtually held on November 1-6, 2020, with an organization staff based in Rio de Janeiro, Brazil. Topics covered in this volume include infection modeling, with an emphasis on different aspects of the COVID-19 and novel Coronavirus spread; a description of the effectiveness of quarantine measures via dynamic analysis of SLIR model; hemodynamic simulations in time-dependent domains; an optimal control model for the Ebola disease; and the co-existence of chaos and control in the context of biological models. Texts in agroforestry, economic development, and wastewater treatment processes complete this volume. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. The 20th edition of the BIOMAT International Symposium has received contributions by authors from 18 countries: Algeria, Brazil, Cameroon, Canada, Chile, China (Hong Kong), Colombia, Germany, Hungary, India, Italy, Morocco, Nigeria, Russia, Senegal, South Africa, USA, and Uzbekistan. Previous BIOMAT volumes with selected works from 2017, 2018, and 2019 were also published by Springer."--Back cover Preface Editorial Board of the BIOMAT Consortium Contents Mathematical Modeling of Macroalgae-Borne Pathogen Transmission in Corals 1 Introduction 2 The Basic Model 3 Equilibria and Their Stability 4 Discussion References Oscillatory Behavior of a Delayed Ratio-Dependent Predator–Prey System with Michaelis–Menten Functional Response 1 Introduction 2 The System with Delay 2.1 Exponential Fading Memory 2.2 Memory with a Hump 3 The Case of One Prey and Two Predators 4 Stability of the Bifurcating Periodic Solution References Dynamical Analysis of Phytoplankton–Zooplankton Interaction Model by Using Deterministic and Stochastic Approach 1 Introduction 2 The Mathematical Model 3 Some Preliminary Results 3.1 Positive Invariance 3.2 Equilibria 3.2.1 Plankton-Free Equilibrium 3.2.2 Plankton-Free Equilibrium 3.2.3 Coexistence Equilibrium 3.3 Hopf Bifurcation at Coexistence 4 The Stochastic Model 4.1 Stochastic Stability of the Coexistence Equilibrium 5 Numerical Simulations 5.1 Effects of N0 5.2 Effects of D 5.3 Effects of μ1 5.4 Effects of μ2 5.5 Effects of K 5.6 Effects of ρ 5.7 Hopf Bifurcation 5.8 Environmental Fluctuations 6 Discussion References Predicting the COVID-19 Spread Using Compartmental Model and Extreme Value Theory with Application to Egypt and Iraq 1 Introduction 2 Methods 2.1 Compartmental Model for COVID-19 Transmission 2.1.1 Derivation of the Basic Reproduction Number 2.2 Return Level Estimation 3 Results 3.1 Parameter Estimation for Iraq and Egypt 3.2 Reproduction Numbers 3.3 Prediction of the Second Wave of the COVID-19 Epidemic 4 Discussion References Geometry of Fitness Surfaces and Dynamics of Replicator Systems 1 Introduction: Extremum Principles in Evolution 2 Fitness Landscapes of Replicator Systems 2.1 Game-Theoretical Approach and Evolutionary Stable Strategies 2.2 Lotka–Volterra System References In-Host Dynamics of the Human Papillomavirus (HPV) in the Presence of Immune Response 1 Introduction 2 Model Formulation 3 Preliminary Analysis of the HPV Model 3.1 Positivity and Boundedness of Solutions 4 The Disease-Free Equilibrium and the Reproduction Number R0 4.1 Global Stability Analysis of the Disease-Free Equilibrium 4.2 The Endemic Equilibrium 4.3 The CTL-Activated Reproduction Number RK 5 Sensitivity Analysis of R0. 6 Numerical Simulations 7 Discussion and Conclusion References Global Properties and Optimal Control Strategies of a Generalized Ebola Virus Disease Model 1 Introduction 2 Sensitivity Analysis 3 The Model Formulation and Equilibria 4 The Optimal Control 4.1 Existence of an Optimal Control 4.2 Optimality System 5 Numerical Simulations 6 Conclusion References On Whole-Graph Embedding Techniques 1 Introduction 2 Approaches to Whole-Graph Embedding 2.1 Graph Kernels 2.2 Neural Network- and Deep Learning-Based Embeddings 2.3 Matrix Factorization 3 Graph Classification with Distribution-Based Measures 4 Experimental Results 4.1 Data 4.1.1 Synthetic Graphs 4.1.2 Real Graphs 4.2 Empirical Comparison of Methods 4.3 Performance Evaluation 5 Conclusions References Semigroup Approaches of Cell Proliferation Models 1 Introduction 2 Cell Cycle Model with Unequal Division and Random Transition 3 Cell Cycle Model with Mutation Accumulation and Telomere Hierarchies 4 Cell Cycle Model with Quiescence References Viability Analysis of Labor Force in an Agroforestry System 1 Introduction 2 Mathematical Model 2.1 Base Model 2.2 Modified Model 2.3 Equilibrium Points 3 Viability 3.1 Preliminary 3.2 Sustainable Thresholds 3.2.1 One-Dimensional Case 3.2.2 Two-Dimensional Case 3.3 Viability: Equilibrium Points 4 Results 5 Discussion: Key Challenges and Ways Forward References Modeling Covid-19 Considering Asymptomatic Cases and Avoided Contacts 1 Introduction 2 Model Formulation 2.1 The Mathematical Model 2.2 Parameter Values 3 Qualitative Analysis of the Model 3.1 Basic Reproduction Number R0 3.2 Equilibrium Points and Their Stability 4 Numerical Simulations and Biological Interpretation of the Results 5 Discussion of the Results References On the Stability of Periodic Solutions of an Impulsive System Arising in the Control of Agroecosystems 1 Introduction 2 Analysis of the Model 2.1 Definitions and Assumptions 2.2 Stability of ζ 2.3 Stability of the Remaining τ-Periodic Solution 2.3.1 Stability of ζf 2.3.2 Stability of ζv Appendix Appendix A1 Appendix A2 Appendix A3 References A Jaccard-Like Symbol and Its Usefulness in the Derivation of Amino Acid Distributions in Protein Domain Families 1 Introduction 2 Saddle Points of the Constrained Lagrangian and Minima of the Euclidean Norm of Its Gradient 3 The Meaning of Constraints on the Variational Process for the Derivation of Probabilistic Distributions 4 The Jaccard-Like Functional Measure 5 A Proposal for Information Measure and the Synergy of the Probabilistic Distributions 6 Some Useful Remarks and Planning for Future Work References When Ideas Go Viral—Complex Bifurcations in a Two-Stage Transmission Model 1 Introduction 2 Existence and Local Stability of Equilibria 3 Numerical Bifurcation Analysis 4 Discussion Appendix A References Dynamic Analysis of SLIR Model Describing the Effectiveness of Quarantine Against the Spread of COVID-19 1 Introduction 2 Positivity and Boundedness of Solutions 3 Analysis of the Model 3.1 The Basic Reproduction Number 3.2 Steady States 3.3 Global Stability 4 Numerical Simulations 5 Conclusion References Non-FSI 3D Hemodynamic Simulations in Time-Dependent Domains 1 Introduction 2 Fluid–Structure Interaction 3 Navier–Stokes Equations in Time-Dependent Domain 4 Multiscale Hemodynamic Model in Compliant Bifurcations References Co-existence of Chaos and Control in Generalized Lotka–Volterra Biological Model: A Comprehensive Analysis 1 Introduction 2 Problem Formulation 3 Synchronization Theory via Active Control Design 4 A Simple Numerical Example 5 Numerical Simulations and Discussions 6 Conclusion References Global Dynamics of a Model for Anaerobic Wastewater Treatment Process 1 Introduction 1.1 Anaerobic Wastewater Treatment Process 1.2 Mathematical Models for Anaerobic Wastewater Treatment Process 2 Model Formulation 3 Global Dynamics 4 Numerical Simulations 5 Discussion References Spatiotemporal Dynamics of Fractional Hepatitis B Virus Infection Model with Humoral and Cellular Immunity 1 Introduction 2 Global Stability 3 Numerical Simulations 4 Conclusions References A 3D Fractional Step Computational Modeling of Nerve Impulse Transmission Through an Axonal Membrane: Incorporating Calcium Buffer and Extrusion 1 Introduction and Motivation 2 Materials and Methods 2.1 Representation of the Computational Domain 2.2 Modeling the Nernst–Planck Equation 2.3 Modeling the Modified Cable Equation 2.4 Calcium Buffer and Extrusion 2.5 Initial and Boundary Conditions 2.6 Summary of Governing Equations 2.7 Variational Formulation of the Problem 2.8 Numerical Scheme 2.8.1 Time Marching Scheme 3 Results and Discussion 3.1 Numerical Result 1: Electrophysiological Behavior of the Model in Absence of Stimulation 3.2 Numerical Result 2: Electrophysiological Validation of the Model 3.2.1 Excitability 3.2.2 Action Potential Morphology 4 Conclusion References Covid-19 Superspreading Events Network Analysis from Agent-Based Model with Mobility Restriction 1 Introduction 2 Materials and Methods 2.1 Agent-Based Model 2.2 Network Analysis 3 Results and Discussion 4 Conclusions References Distinct Prognostic Values of BCL2 Anti-apoptotic Members in Lung Cancer: An In-Silico Analysis 1 Introduction 2 Materials and Methods 2.1 Gene Alteration Analysis Through cBioportal 2.2 Prognostic Analysis Through KMplotter 2.3 miRNA Regulation Analysis Through miRSystem 3 Results 3.1 Genomic Alterations in Target Genesin Lung Cancer 3.2 Distinct Prognostic Values of the Selected BCl2 Anti-apoptotic Members 3.2.1 Prognostic Significance of Selected BCL2 Anti-apoptotic Members in All Lung Cancer Patients 3.2.2 Prognostic Significance of Selected BCL2 Anti-apoptotic Members in All Lung Cancer Patients with Different Tumor Histology 3.2.3 Prognostic Significance of Selected BCL2 Anti-apoptotic Members in All Lung Cancer Patients with Different Smoking History 3.3 Potential miRNA Regulators of Selected Target Genes 4 Discussion References Economic Development Process: A Compartmental Analysis of a Model with Two Delays 1 Introduction 2 The DEA Model 3 Basic Results 3.1 Positivity and Boundedness of Solutions 3.2 Equilibria 4 Stability Analysis of the System Without Delays (τ1=τ2=0) 4.1 Local Stability Analysis for F1 4.2 Local Stability Analysis for F2 4.3 Local Stability Analysis for F3 5 Stability Analysis of the System with Time Delays 5.1 Linearization and Characteristic Equation 5.2 Stability Analysis When τ1>0 and τ2=0 5.2.1 Stability Analysis at Equilibrium F1 5.2.2 Stability Analysis at Equilibrium F2 Stability analysis and Hopf bifurcation Direction and stability of the Hopf bifurcation 5.2.3 Stability Analysis at Equilibrium F3 Hopf bifurcation Direction and stability of the Hopf bifurcation 5.3 Stability Analysis When τ1=0 and τ2>0 5.4 Stability Analysis of Equilibrium F3 When τ1>0 and τ2>0 5.4.1 Stability Switching Curves 5.4.2 Crossing Direction 6 Numerical Simulations 6.1 Numerical Examples When τ1 = τ2 = 0 6.2 Numerical Examples When τ1>0, τ2>0 7 Conclusion and Discussion References Index