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

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