Complexity in Mathematical Biology for Sustainable Development: Modeling Climate, Disease, and Ecosystems through Difference, Differential, and Fractional Theory introduces new mathematical methods to derive complex modeling solutions for a wide range of engineering and scientific research applications. The book strikes a balance between high-level mathematical theory and technical derivations, offering step-by-step explanations, real-world case studies, and clear introductions to advanced mathematical models. Solutions include modeling and quantifying complexity, with emphasis placed on the growing need for interdisciplinary collaboration, the integration of real-time data into models, and the development of adaptive frameworks challenges such as pandemics, biodiversity loss, and climate uncertainty.
The book is designed to meet the needs of a diverse primary audience, from graduate students to professionals in fields such as computer science, public health, environmental policy, applied mathematics, and biotechnology. By providing both theoretical foundations and practical applications, the book equips readers with the skills and knowledge to tackle pressing global challenges through mathematical models, making it a valuable resource for both academic and professional development.
1. Chapter 1. Introduction to mathematical biology - p. 1 2. Chapter 2. Difference equations - p. 13 3. Abstract - p. 13 4. 2.1 Mathematical framework - p. 13 5. 2.2 First-order difference equations - p. 17 6. 2.3 Second-order difference equations - p. 25 7. 2.4 Higher order difference equations - p. 33 8. 2.5 First-order difference systems - p. 39 9. 2.6 Delay difference equations - p. 60 10. 2.7 Summary - p. 63 11. References - p. 63 12. Chapter 3. Ordinary differential equations - p. 65 13. Abstract - p. 65 14. 3.1 Mathematical tools for differential equations - p. 66 15. 3.2 First-order differential equations - p. 72 16. 3.3 Higher order differential equations - p. 78 17. 3.4 First-order differential equation systems - p. 84 18. 3.5 Bifurcation theory and transitions in system behavior - p. 93 19. 3.6 Differential equations with time delay: modeling memory and reaction lags - p. 102 20. 3.7 Differential equations with piecewise constant arguments: bridging continuous and discrete dynamics - p. 108 21. 3.8 Summary - p. 113 22. References - p. 113 23. Chapter 4. Fractional-order differential equations - p. 115 24. Abstract - p. 115 25. 4.1 Mathematical preliminaries and operators - p. 115 26. 4.2 Stability of fractional-order systems and the modified Routh–Hurwitz criteria - p. 120 27. 4.3 Bifurcation analysis in fractional-order systems - p. 131 28. 4.4 Numerical methods and discretization - p. 138 29. 4.5 Dimensionalization in fractional models - p. 146 30. 4.6 Summary - p. 151 31. References - p. 152 32. Chapter 5. Weighted graphs, networks, and statistical models - p. 153 33. Abstract - p. 153 34. 5.1 Weight graphs and networks - p. 153 35. 5.2 Statistical models - p. 177 36. 5.3 Summary - p. 202 37. References - p. 202 38. Chapter 6. Mathematical models in ecosystems and natural systems - p. 205 39. Abstract - p. 205 40. 6.1 Population dynamics models - p. 206 41. 6.2 Habitat fragmentation and connectivity loss - p. 245 42. 6.3 Sustainability insights: overexploitation, pollution, and ecosystem collapse - p. 256 43. 6.4 Summary - p. 266 44. References - p. 267 45. Chapter 7. Human health and sustainable development - p. 273 46. Abstract - p. 273 47. 7.1 Foundations of epidemic models - p. 274 48. 7.2 Advanced and realistic disease dynamics - p. 283 49. 7.3 Influenza and respiratory epidemics - p. 307 50. 7.4 Pandemics through history - p. 329 51. 7.5 Socioeconomic drivers of infectious diseases - p. 345 52. 7.6 Summary - p. 357 53. References - p. 357 54. Chapter 8. Climate change models - p. 363 55. Abstract - p. 363 56. 8.1 Introduction to climate dynamics - p. 364 57. 8.2 Atmospheric CO₂ and greenhouse gas modeling - p. 390 58. 8.3 Temperature anomalies and global warming trends - p. 397 59. 8.4 Energy consumption, carbon emissions, and ecological footprint - p. 409 60. 8.5 Extreme weather events and climate variability - p. 418 61. 8.6 Sustainable cities and urban environments - p. 422 62. 8.7 Summary - p. 426 63. References - p. 427 64. Chapter 9. Applications to sustainable development goals - p. 431 65. Abstract - p. 431 66. 9.1 Biodiversity and conservation - p. 432 67. 9.2 Food security and agricultural sustainability - p. 454 68. 9.3 Water resources, hydrological models, and environmental stress - p. 479 69. 9.4 Health and well-being - p. 487 70. 9.5 Summary - p. 504 71. References - p. 505 72. Chapter 10. Applications and future perspectives of mathematical biology - p. 509 73. Abstract - p. 509 74. 10.1 Mathematical models for ecological and biological conservation - p. 510 75. 10.2 Mathematical models in biotechnology and genetic engineering - p. 529 76. 10.3 Mathematical applications for human health - p. 545 77. 10.4 Integration of mathematical biology and sustainable development goals - p. 564 78. 10.5 Systematic approach and multidisciplinary studies - p. 576 79. 10.6 Summary - p. 584 80. References - p. 584 81. Chapter 11. Conclusion - p. 589 82. Index - p. 593
Complexity in Mathematical Biology for Sustainable Development: Modeling Climate, Disease, and Ecosystems through Difference, Differential, and Fractional Theory introduces new mathematical methods to derive complex modeling solutions for a wide range of engineering and scientific research applications. The book strikes a balance between high-level mathematical theory and technical derivations, offering step-by-step explanations, real-world case studies, and clear introductions to advanced mathematical models. Solutions include modeling and quantifying complexity, with emphasis placed on the growing need for interdisciplinary collaboration, the integration of real-time data into models, and the development of adaptive frameworks challenges such as pandemics, biodiversity loss, and climate uncertainty.
The book is designed to meet the needs of a diverse primary audience, from graduate students to professionals in fields such as computer science, public health, environmental policy, applied mathematics, and biotechnology. By providing both theoretical foundations and practical applications, the book equips readers with the skills and knowledge to tackle pressing global challenges through mathematical models, making it a valuable resource for both academic and professional development.
1. Chapter 1. Introduction to mathematical biology - p. 1 2. Chapter 2. Difference equations - p. 13 3. Abstract - p. 13 4. 2.1 Mathematical framework - p. 13 5. 2.2 First-order difference equations - p. 17 6. 2.3 Second-order difference equations - p. 25 7. 2.4 Higher order difference equations - p. 33 8. 2.5 First-order difference systems - p. 39 9. 2.6 Delay difference equations - p. 60 10. 2.7 Summary - p. 63 11. References - p. 63 12. Chapter 3. Ordinary differential equations - p. 65 13. Abstract - p. 65 14. 3.1 Mathematical tools for differential equations - p. 66 15. 3.2 First-order differential equations - p. 72 16. 3.3 Higher order differential equations - p. 78 17. 3.4 First-order differential equation systems - p. 84 18. 3.5 Bifurcation theory and transitions in system behavior - p. 93 19. 3.6 Differential equations with time delay: modeling memory and reaction lags - p. 102 20. 3.7 Differential equations with piecewise constant arguments: bridging continuous and discrete dynamics - p. 108 21. 3.8 Summary - p. 113 22. References - p. 113 23. Chapter 4. Fractional-order differential equations - p. 115 24. Abstract - p. 115 25. 4.1 Mathematical preliminaries and operators - p. 115 26. 4.2 Stability of fractional-order systems and the modified Routh–Hurwitz criteria - p. 120 27. 4.3 Bifurcation analysis in fractional-order systems - p. 131 28. 4.4 Numerical methods and discretization - p. 138 29. 4.5 Dimensionalization in fractional models - p. 146 30. 4.6 Summary - p. 151 31. References - p. 152 32. Chapter 5. Weighted graphs, networks, and statistical models - p. 153 33. Abstract - p. 153 34. 5.1 Weight graphs and networks - p. 153 35. 5.2 Statistical models - p. 177 36. 5.3 Summary - p. 202 37. References - p. 202 38. Chapter 6. Mathematical models in ecosystems and natural systems - p. 205 39. Abstract - p. 205 40. 6.1 Population dynamics models - p. 206 41. 6.2 Habitat fragmentation and connectivity loss - p. 245 42. 6.3 Sustainability insights: overexploitation, pollution, and ecosystem collapse - p. 256 43. 6.4 Summary - p. 266 44. References - p. 267 45. Chapter 7. Human health and sustainable development - p. 273 46. Abstract - p. 273 47. 7.1 Foundations of epidemic models - p. 274 48. 7.2 Advanced and realistic disease dynamics - p. 283 49. 7.3 Influenza and respiratory epidemics - p. 307 50. 7.4 Pandemics through history - p. 329 51. 7.5 Socioeconomic drivers of infectious diseases - p. 345 52. 7.6 Summary - p. 357 53. References - p. 357 54. Chapter 8. Climate change models - p. 363 55. Abstract - p. 363 56. 8.1 Introduction to climate dynamics - p. 364 57. 8.2 Atmospheric CO₂ and greenhouse gas modeling - p. 390 58. 8.3 Temperature anomalies and global warming trends - p. 397 59. 8.4 Energy consumption, carbon emissions, and ecological footprint - p. 409 60. 8.5 Extreme weather events and climate variability - p. 418 61. 8.6 Sustainable cities and urban environments - p. 422 62. 8.7 Summary - p. 426 63. References - p. 427 64. Chapter 9. Applications to sustainable development goals - p. 431 65. Abstract - p. 431 66. 9.1 Biodiversity and conservation - p. 432 67. 9.2 Food security and agricultural sustainability - p. 454 68. 9.3 Water resources, hydrological models, and environmental stress - p. 479 69. 9.4 Health and well-being - p. 487 70. 9.5 Summary - p. 504 71. References - p. 505 72. Chapter 10. Applications and future perspectives of mathematical biology - p. 509 73. Abstract - p. 509 74. 10.1 Mathematical models for ecological and biological conservation - p. 510 75. 10.2 Mathematical models in biotechnology and genetic engineering - p. 529 76. 10.3 Mathematical applications for human health - p. 545 77. 10.4 Integration of mathematical biology and sustainable development goals - p. 564 78. 10.5 Systematic approach and multidisciplinary studies - p. 576 79. 10.6 Summary - p. 584 80. References - p. 584 81. Chapter 11. Conclusion - p. 589 82. Index - p. 593
