This volume develops mathematical models for biological and natural systems.
This volume develops mathematical models for biological and natural systems. It integrates differential equations, probability, and data-driven methods.
Part I. Foundations of Mathematical Biology
Chapter 1. Modeling Biological Systems
1.1 Model formulation 1.2 Deterministic vs stochastic models 1.3 Scales: molecular to ecosystem 1.4 Parameter estimation 1.5 Examples
Chapter 2. Population Dynamics
2.1 Exponential growth 2.2 Logistic growth 2.3 Carrying capacity 2.4 Applications 2.5 Examples
Chapter 3. Interacting Populations
3.1 Predator–prey models 3.2 Competition models 3.3 Lotka–Volterra equations 3.4 Applications 3.5 Examples
Part II. Epidemiology
Chapter 4. Basic Epidemic Models
4.1 SIR model 4.2 SEIR extensions 4.3 Threshold parameters 4.4 Applications 4.5 Examples
Chapter 5. Disease Dynamics
5.1 Transmission mechanisms 5.2 Vaccination strategies 5.3 Endemic equilibria 5.4 Applications 5.5 Examples
Chapter 6. Stochastic Epidemic Models
6.1 Random outbreaks 6.2 Markov models 6.3 Simulation 6.4 Applications 6.5 Examples
Part III. Systems Biology
Chapter 7. Gene Regulation
7.1 Gene networks 7.2 Feedback loops 7.3 Modeling approaches 7.4 Applications 7.5 Examples
Chapter 8. Biochemical Networks
8.1 Reaction kinetics 8.2 Mass-action models 8.3 Stability analysis 8.4 Applications 8.5 Examples
Chapter 9. Cellular Dynamics
9.1 Cell cycles 9.2 Signaling pathways 9.3 Multiscale models 9.4 Applications 9.5 Examples
Part IV. Ecology and Evolution
Chapter 10. Ecosystems
10.1 Food webs 10.2 Energy flow 10.3 Stability 10.4 Applications 10.5 Examples
Chapter 11. Evolutionary Dynamics
11.1 Fitness landscapes 11.2 Mutation and selection 11.3 Replicator equations 11.4 Applications 11.5 Examples
Chapter 12. Spatial Models
12.1 Diffusion and dispersal 12.2 Reaction-diffusion systems 12.3 Pattern formation 12.4 Applications 12.5 Examples
Part V. Neuroscience and Behavior
Chapter 13. Neuron Models
13.1 Hodgkin–Huxley model 13.2 Integrate-and-fire models 13.3 Applications 13.4 Examples 13.5 Connections
Chapter 14. Neural Networks
14.1 Network dynamics 14.2 Learning rules 14.3 Stability 14.4 Applications 14.5 Examples
Chapter 15. Behavioral Models
15.1 Decision processes 15.2 Collective behavior 15.3 Applications 15.4 Examples 15.5 Connections
Part VI. Data and Computation
Chapter 16. Statistical Methods in Biology
16.1 Data analysis 16.2 Parameter estimation 16.3 Model selection 16.4 Applications 16.5 Examples
Chapter 17. Computational Biology
17.1 Simulation methods 17.2 Bioinformatics 17.3 Sequence analysis 17.4 Applications 17.5 Examples
Chapter 18. Machine Learning in Biology
18.1 Predictive models 18.2 Pattern recognition 18.3 Applications 18.4 Examples 18.5 Connections
Part VII. Applications
Chapter 19. Medicine
19.1 Disease modeling 19.2 Treatment optimization 19.3 Drug dynamics 19.4 Applications 19.5 Examples
Chapter 20. Environmental Science
20.1 Climate-biology interactions 20.2 Resource management 20.3 Conservation 20.4 Applications 20.5 Examples
Chapter 21. Biotechnology
21.1 Synthetic biology 21.2 Genetic engineering 21.3 Industrial applications 21.4 Applications 21.5 Examples
Part VIII. Research Directions
Chapter 22. Advanced Topics
22.1 Multiscale modeling 22.2 Systems medicine 22.3 Evolutionary computation 22.4 Modern developments 22.5 Emerging areas
Chapter 23. Open Problems
23.1 Model validation 23.2 Data integration 23.3 Complexity of biological systems 23.4 Computational challenges 23.5 Future directions
Chapter 24. Historical and Conceptual Notes
24.1 Development of mathematical biology 24.2 Key contributors 24.3 Evolution of models 24.4 Cross-disciplinary impact 24.5 Summary
Appendix
A. Common biological models B. Parameter estimation methods C. Proof techniques checklist D. Simulation tools E. Cross-reference to other MSC branches