Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment - Selected Works from the BIOMAT Consortium Lectures, Szeged, Hungary, 2019

This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2019 International Symposium, which was held at the University of Szeged, Bolyai Institute and the Hungarian Academy of Sciences, Hungary, October 21st-25th, 2019. The topics covered in this volume include tumor and infection modeling; dynamics of co-infections; epidemic models on networks; aspects of blood circulation modeling; multidimensional modeling approach via time-frequency analysis and Edge Based Compartmental Model; and more. This book builds upon the tradition of the previous BIOMAT volumes to foster interdisciplinary research in mathematical biology for students, researchers, and professionals. 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 2019 edition of BIOMAT International Symposium received contributions by authors from 14 countries: Brazil, Cameroon, Canada, Colombia, Czech Republic, Finland, Hungary, India, Italy, Russia, Senegal, Serbia, United Kingdom and the USA. Selected papers presented at the 2017 and 2018 editions of this Symposium were also published by Springer, in the volumes "Trends in Biomathematics: Modeling, Optimization and Computational Problems" (978-3-319-91091-8) and "Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics" (978-3-030-23432-4). Rubem P. Mondaini is President of the BIOMAT Consortium/International Institute for Interdisciplinary Sciences and a Full Professor of Mathematical Biology and Biological Physics at the Federal University of Rio de Janeiro, Brazil. He holds a PhD in Theoretical Physics from the Brazilian Centre for Physical Research, Brazil. His research activities abroad include a period as a Visiting Scientist at the International Centre for Theoretical Physics (ICTP), Trieste, Italy (1978) and as a Senior Postdoc at the Department of Mathematics of King's College, University of London, UK (1986). He was also a Visiting Professor at the Centre of Physics of Condensed Matter, Lisbon, Portugal (1986) and at the Department of Chemical Engineering of Princeton University (2008). He has been the Chairman of the Annual BIOMAT Conferences since their inception during the BIOMAT 2001 Symposium in Rio de Janeiro, Brazil. Preface......Page 5 Editorial Board of the BIOMAT Consortium......Page 7 Contents......Page 9 1 Introduction: Revisiting Fisher's Fundamental Theorem......Page 11 1.1 Dynamical Fitness Landscapes: Adaptation Process......Page 12 2 Hypercycle with Two Types of Behavior......Page 14 3 Conclusion......Page 15 References......Page 16 1 Introduction......Page 18 2 The Model......Page 19 3 System's Equilibria......Page 21 3.2 The Predator-Free Equilibrium......Page 22 3.3.1 The Sign of M1......Page 23 3.3.2 An Approximation of -1......Page 24 4.1 Systems Permanence......Page 26 4.2 Bifurcations......Page 27 5 Conclusions......Page 28 References......Page 29 1 Introduction......Page 31 2 Basic Definitions and Notation......Page 33 3.1 Distance Between Nodes in a Graph......Page 34 3.2 Measures Based on Distances Between Nodes......Page 35 5 Distribution-Based Measures......Page 38 5.1 Distance Measures Between Probability Distributions......Page 39 5.2 Graph Probability Distributions......Page 40 6 Experimental Results......Page 43 6.1 Data......Page 45 6.2 Evaluation......Page 46 References......Page 47 1 Introduction......Page 50 2 Sex-Structured Population Models......Page 51 3 Sexually Transmitted Infections......Page 54 3.1 Conventional Model of Host-STI Dynamics......Page 55 3.2 Sex-Structured STI Models......Page 56 3.3 Sterilizing Infections......Page 58 3.3.1 Degree-One Homogeneous Mating Functions......Page 59 3.3.2 Allee Effect Mating Function......Page 60 3.4 Mating Enhancement......Page 61 3.5 Mating Avoidance......Page 63 4.1 Conventional Models of Predator-Prey Dynamics......Page 67 4.2 Sex-Selective Predation......Page 68 4.3 Mating-Predation Trade-off......Page 71 5 Conclusions and Extensions......Page 74 Appendix: Adaptive Dynamics......Page 75 References......Page 76 1 Introduction......Page 78 2.1 Existence and Local Stability of Equilibria......Page 79 2.2 Global Dynamics......Page 81 3 The Effect of Drug Concentration......Page 84 4 Discussion......Page 85 References......Page 87 1 Introduction......Page 88 2 Method......Page 90 2.1 Edge Based Compartmental Model (EBCM)......Page 91 2.2 Stochastic Simulation......Page 94 4 Results and Discussions......Page 95 5 Summary and Conclusion......Page 100 References......Page 102 1 Introduction......Page 104 2 The Order Preservation Property......Page 105 2.1 Step Function as Activation Function......Page 107 3 Two-Valued Case......Page 108 4 Oscillatory Behaviour in the Three-Valued Case......Page 112 5 Concluding Remarks......Page 115 References......Page 116 1 Introduction......Page 117 2 Methods......Page 119 2.1 Euler-Angles (Z-Y-Z) Configuration......Page 120 2.2 The System Energy and the Energy-Gradient......Page 121 2.3 Tait–Bryan Angles (X-Y-Z ) Configuration......Page 126 3 Results......Page 129 4 Discussion......Page 130 References......Page 131 1 Introduction......Page 132 2 The Model Description......Page 133 3 Mathematical Modeling for Bird Migration......Page 136 4 Mathematical Modeling of Stem Cell Maturation Without Regulatory Feedback......Page 139 5 Mathematical Formulation of the Intracellular Chlamydia Development Cycle......Page 143 References......Page 146 1 Introduction......Page 148 2 Time-Transformation of Time-Dependent Delay Differential Equations......Page 149 3 Normalization of a Periodic Delay......Page 153 4 Existence of a Periodic Solution......Page 156 References......Page 157 1 Introduction......Page 158 2.1 Vegetative Growth of One Tuft of Grass......Page 159 2.2 Competition Between Two Tufts of the Same or Different Species......Page 160 2.3 Parameters......Page 161 2.4 Modeling Competition......Page 162 3 Results and Discussion......Page 163 References......Page 165 1 Introduction......Page 166 2 Mathematical Model of an Indicator Passing Throughout CVS......Page 168 3 Math Equations for LDF......Page 169 4 Discussion......Page 172 References......Page 173 1 Introduction: The Concepts of Protein Domain Families and Clans......Page 174 2 The Construction of the Sample Space for Statistical Analysis......Page 177 3 The Fisher–Snedecor Distribution as Applied to Protein Domain Families and Clans: A Theoretical Derivation......Page 182 4 The Fisher–Snedecor Distribution as Applied to Protein Domain Families and Clans: A Phenomenological Derivation......Page 191 5 Sharma–Mittal Entropy Measures and Their Associated Jaccard Entropies......Page 195 6 The Distribution of Average Jaccard Entropy Measures......Page 198 7 The Efficiency of 8080 Statistics for Testing the Inclusion of Protein Domain Families......Page 203 8 Concluding Remarks......Page 207 References......Page 211 1 Introduction......Page 213 2 Model: Network, Epidemic Dynamics and Mean-Field Models......Page 214 3 Triple Counts from Neighbourhood Distribution......Page 216 4.1 Closures for the Multinomial Distribution of States of the Neighbours......Page 220 4.2 Closures for the Poisson Distribution of States of the Neighbours......Page 225 5 Comparison of the Closed Pairwise Model to Stochastic Simulations and Further Results......Page 230 6.1 Conditioning on a Link......Page 231 6.2 Closures for the Uniform Distribution of States of the Neighbours......Page 232 7 Discussion......Page 234 Appendix: Facts of the Multinomial Distribution......Page 235 References......Page 238 1 Introduction......Page 239 2 Time-Frequency Approach......Page 240 3 Dataset......Page 241 5 Confusion Matrix......Page 242 6.1 Performance of the TFA Approach Applied to the TgRON2 Protein......Page 243 6.2 Performance of the TFA for PvRON2 and PfRON2 Proteins......Page 244 6.3 Performance of the TFA for IRGb2-b1 Mouse Protein......Page 245 References......Page 247 1 Introduction......Page 249 2.1 Deterministic SIR Model......Page 251 2.2 Optimization Model......Page 252 3 Decision Making with Stochastic SIR......Page 255 3.1 Stochastic SIR Model......Page 256 3.2 Vaccination Model......Page 258 4 Conclusions......Page 260 References......Page 262 1 Introduction......Page 263 2 Model Formation......Page 264 2.1 Positivity and Boundedness of Solutions......Page 266 3.1 Existence and Stability Analysis of the Equilibrium Points......Page 267 4 Analysis of Optimal Control......Page 270 4.1 Characterization of Optimal Control......Page 271 5 Numerical Simulations......Page 273 6 Conclusion......Page 274 References......Page 277 1 Introduction......Page 278 2 Model Formulation......Page 280 3.1 Positive Invariance, Boundedness......Page 282 3.2 Boundedness......Page 283 3.3 Extinction Criterion......Page 284 4.2 Stability Analysis......Page 285 4.5 The Behaviour of the System Around E2=(0,0,0,w2)......Page 286 4.7 The Behaviour of the System Around E4=(x4,0,yi4,w4)......Page 287 4.8 The Behaviour of the System Around E*=(x*,ys*,yi*,w*)......Page 288 4.9 Hopf Bifurcation......Page 289 5 Numerical Simulations......Page 290 5.2 Effects of m2......Page 291 5.3 Effects of λ1......Page 292 5.4 Effects of λ2......Page 293 5.5 Combined Effects of m1 and m2......Page 294 5.6 Combined Effects of λ1 and λ2......Page 295 5.7 Combined Effects of μ and λ1......Page 296 6 Conclusion......Page 297 References......Page 299 1 Introduction......Page 301 2 The Model......Page 302 3 Equilibria and Their Stability......Page 306 4.1 Bifurcation from the Boundary Equilibrium E3......Page 311 4.2 Bifurcation from the Interior Equilibrium E4......Page 318 5 Discussion......Page 319 Appendix 1......Page 320 Appendix 2......Page 325 References......Page 335 1 Introduction......Page 337 2.1 Mathematical Background......Page 338 2.2 Study Population......Page 339 4 Discussion and Conclusion......Page 340 References......Page 342 1 Introduction......Page 344 2 Model Formation......Page 345 3.1 Basic Reproduction Number......Page 348 3.2 Existence and Stability Analysis of the Equilibrium Points......Page 349 4 TB Sub-model......Page 351 4.1 Existence and Stability Analysis of the Equilibrium Points......Page 352 5.1 Stability Analysis of the Disease-free Equilibrium Point......Page 353 6 Numerical Simulations......Page 354 7 Conclusion......Page 355 References......Page 359 1 Introduction......Page 360 2.1 Discrete Model......Page 361 2.2 Corresponding Continuum Model and Properties of Its Solutions......Page 364 2.3.1 Numerical Methods and Set-Up of Numerical Simulations......Page 365 2.3.2 Main Results......Page 367 3 Discrete and Continuum Models for the Mechanical Interaction Between Healthy and Cancer Cells During Tumour Growth......Page 368 3.1 Discrete Model......Page 369 3.2 Corresponding Continuum Model and Properties of Its Solutions......Page 371 3.3.1 Numerical Methods and Set-Up of Numerical Simulations......Page 372 3.3.2 Main Results......Page 374 4 Conclusions and Possible Developments of the Models......Page 375 References......Page 377 1 Introduction......Page 382 2.1 Herpes Simplex Virus, Type 2 (HSV-2)......Page 383 2.2 Clostridium Difficile Infection (CDI)......Page 386 2.3 Tuberculosis (TB)......Page 389 3.1 HSV–2......Page 391 3.3 TB......Page 392 4 Discussion......Page 393 References......Page 394 1 Introduction......Page 396 2 Basic Experimental Facts about the Genetic Code......Page 398 2.1 Biomolecular Background of the Genetic Code Expression......Page 399 2.2 Basic Properties of the Genetic Code......Page 400 3 p-Adic Mathematical Background......Page 401 4 Modeling of the Genetic Code......Page 405 5.1 Genetic Code as the Language of Life......Page 406 5.2 Codons in the Form of an Ultrametric Tree......Page 408 5.3 p-Adic Structure of the Set of Codons......Page 411 5.4 Vertebrate Mitochondrial and Standard Code: (5,2)-adic Model......Page 412 5.5.1 p-Adic Properties of Amino Acids......Page 415 5.5.3 Euclidean Representation of p-adic Genetic Code......Page 416 6 Concluding Remarks......Page 418 References......Page 419 Index......Page 422 This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2019 International Symposium, which was held at the University of Szeged, Bolyai Institute and the Hungarian Academy of Sciences, Hungary, October 21st-25th, 2019. The topics covered in this volume include tumor and infection modeling; dynamics of co-infections; epidemic models on networks; aspects of blood circulation modeling; multidimensional modeling approach via time-frequency analysis and Edge Based Compartmental Model; and more. This book builds upon the tradition of the previous BIOMAT volumes to foster interdisciplinary research in mathematical biology for students, researchers, and professionals. 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 2019 edition of BIOMAT International Symposium received contributions by authors from 13 countries: Brazil, Cameroon, Canada, Colombia, Czech Republic, Finland, Hungary, India, Italy, Russia, Senegal, Serbia, United Kingdom and the USA. Selected papers presented at the 2017 and 2018 editions of this Symposium were also published by Springer, in the volumes "Trends in Biomathematics: Modeling, Optimization and Computational Problems" (978-3-319-91091-8) and "Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics" (978-3-030-23432-4).-- Provided by publisher This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2018 International Symposium, which was held at the University Hassan II, Morocco, from October 29th to November 2nd, 2018. The topics covered include applications of mathematical modeling in hepatitis B, HIV and Chikungunya infections; tumor cell dynamics; inflammatory processes; chemotherapeutic drug effects; and population dynamics. Also discussing the application of techniques like the generalized stochastic Milevsky-Promislov model, numerical simulations and convergence of discrete and continuous models, it is an invaluable resource on interdisciplinary research in mathematical biology for students, researchers, and professionals.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, ideasand techniques, promoting truly international cooperation for problem discussion. The 2018 edition of BIOMAT International Symposium received contributions by authors from seventeen countries: Algeria, Brazil, Cameroon, Canada, Chad, Colombia, France, Germany, Hungary, Italy, Mali, Morocco, Nigeria, Poland, Portugal, Russia, and Senegal. Selected papers presented at the 2017 edition of this Symposium were also published by Springer, in the volume “Trends in Biomathematics: Modeling, Optimization and Computational Problems” (978-3-319-91091-8). "This book brings together carefully selected, peer-reviewed works on mathematical biology presented at the BIOMAT International Symposium on Mathematical and Computational Biology, which was held at the Institute of Numerical Mathematics, Russian Academy of Sciences, in October 2017, in Moscow. Topics covered include, but are not limited to, the evolution of spatial patterns on metapopulations, problems related to cardiovascular diseases and modeled by boundary control techniques in hemodynamics, algebraic modeling of the genetic code, and multi-step biochemical pathways. Also, new results are presented on topics like pattern recognition of probability distribution of amino acids, somitogenesis through reaction-diffusion models, mathematical modeling of infectious diseases, and many others. Experts, scientific practitioners, graduate students and professionals working in various interdisciplinary fields will find this book a rich resource for research and applications alike."-- Provided by publisher