Mathematical Modelling of Environmental and Ecological Systems

Description

This volume contains a cross-section of the papers presented at the International Symposium on Mathematical Modelling of Ecological, Environmental and Biological Systems held in Kanpur, India, in August 1985. The choice of topics emphasizes many aspects of ecological and environmental matters including air and water pollution, ecotoxicology, resource management, epidemiology, and population and community ecology.

It is intended that this volume will focus international attention upon some problems in the ecological and environmental sciences that can be impacted by mathematical modelling and analysis.

Front Cover 2
Mathematical Modelling of Environmental and Ecological Systems 5
Copyright Page 6
ACKNOWLEDGEMENTS 7
PREFACE 9
FORWORD 11
LIST OF AUTHORS 13
Table of Contents 15
KEYNOTE ADDRESS: Some Sobering Environmental Concerns and Flickering Prospects of Cures, by Thomas G. Hallam 17
PART I: AIR POLLUTION 25
- Chapter 1. Some aspects of mathematical modelling of atmospheric transport and chemistry 27
  - 2 INTRODUCTION 27
  - 1 ABSTRACT 27
  - 3 MATHEMATICAL BASIS 28
  - 4 CHEMICAL PROCESSES 36

Front Cover 2
Mathematical Modelling of Environmental and Ecological Systems 5
Copyright Page 6
ACKNOWLEDGEMENTS 7
PREFACE 9
FORWORD 11
LIST OF AUTHORS 13
Table of Contents 15
KEYNOTE ADDRESS: Some Sobering Environmental Concerns and Flickering Prospects of Cures, by Thomas G. Hallam 17
PART I: AIR POLLUTION 25
- Chapter 1. Some aspects of mathematical modelling of atmospheric transport and chemistry 27
  - 2 INTRODUCTION 27
  - 1 ABSTRACT 27
  - 3 MATHEMATICAL BASIS 28
  - 4 CHEMICAL PROCESSES 36
  - 5 MODEL INPUTS 39
  - 5 MODEL SIMULATIONS 42
  - 6 CONCLUDING REMARKS 48
  - 7 ACKNOWLEDGEMENTS 49
  - 8 REFERENCES 50
- Chapter 2. Attenuation of air pollution by green belt 53
  - 1 ABSTRACT 53
  - 2 INTRODUCTION 53
  - 3 MODEL 54
  - 4 APPLICATION EXAMPLES OF GREEN BELT MODEL 62
  - 5 LIMITATIONS OF THE MODEL AND NEED FOR MORE RESEARCH WORK 77
  - 6 REFERENCES 79
- Chapter 3. Dispersion of a reactive air pollutant in a two layered environment 81
  - 1 ABSTRACT 81
  - 2 INTRODUCTION 81
  - 3 DISPERSION OF AIR POLLUTANT FROM A POINT SOURCE 82
  - 4 DISPERSION OF POLLUTANT FROM A LINE SOURCE 86
  - 5 EFFECT OF GREEN BELT 90
  - 6 REFERENCES 96
- Chapter 4. Disperson from a time dependent point source: Application to methyl isocynate leakage in Bhopal, India 99
  - 2 INTRODUCTION 99
  - 1 ABSTRACT 99
  - 3 DISPERSION FROM AN ELEVATED POINT SOURCE 100
  - 4 DISPERSION FROM A POINT SOURCE NEAR THE GROUND 103
  - 5 APPLICATION TO MIC LEAKAGE IN BHOPAL, INDIA 108
  - 6 APPENDIX A 110
  - 7 APPENDIX B 113
  - 8 REFERENCES 115
- PART II: WATER POLLUTION 117
  - Chapter 5. Taking advantage of topography in the siting of discharges in rivers 119
    - 1 ABSTRACT 119
    - 2 INTRODUCTION 119
    - 3 TRANSVERSE DIFFUSION EQUATION 120
    - 4 EXACT SOLUTIONS FOR STEADY DISCHARGES 121
    - 5 APPROXIMATE SOLUTIONS FOR STEADY DISCHARGES 124
    - 6 INVERSE APPROACH 125
    - 7 STEADY DISCHARGES IN NARROW RIVERS 127
    - 8 SUDDEN DISCHARGES IN STRAIGHT RIVERS 130
    - 11 ACKNOWLEDGEMENTS 132
    - 9 SUDDEN DISCHARGES IN VARYING RIVERS 132
    - 12 REFERENCES 132
    - 10 CONCLUDING REMARKS 132
  - Chapter 6. Analytical solution of 3-D unsteady state diffusion equation for a pollutant from a point source discharge in offshor 135
    - 1 ABSTRACT 135
    - 2 INTRODUCTION 135
    - 3 THE POLLUTANT DISPERSION EQUATION 136
    - 4 ANALYTICAL SOLUTION 138
    - 5 AN APPLICATION 141
    - 6 ACKNOWLEDGEMENTS 145
    - 7 REFERENCES 145
  - PART III: POPULATION ECOLOGY 147
    - Chapter 7. Modelling survival in chemically stressed populations 149
      - 2 INTRODUCTION 149
      - 1 ABSTRACT 149
      - 3 GENERIC MODELS OF POPULATION-TOXICANT INTERACTIONS 150
      - 4 FLUCTUATIONS IN DEMOGRAPHIC PARAMETERS 153
      - 5 DENSITY DEPENDENT SURVIVAL ANALYSES 155
      - 6 SURVIVAL IN DISCRETE MODELS 156
      - 7 SUMMARY 158
      - 8 REFERENCES 159
    - Chapter 8. On the general structure of epidemic models 161
      - 1 ABSTRACT 161
      - 2 INTRODUCTION 161
      - 3 THE GENERAL "ODE" MODEL 161
      - 4 APPLICATIONS 168
      - 5 MODELS WITH DYNAMIC TOTAL POPULATION 169
      - 6 REFERENCES 175
    - Chapter 9. Equilibria and oscillations in age-structured population growth models 177
      - 1 INTRODUCTION 177
      - 2 SINGLE SPECIES GROWTH MODELS 179
      - 3 INTERACTING SPECIES 189
      - 4. PERIODIC OSCILLATIONS 195
      - 5 CONCLUDING REMARKS 198
      - REFERENCES 199
    - PART IV: COMMUNITY ECOLOGY 201
      - Chapter 10. Young predation and time delays 203
        
        1 INTRODUCTION 203
        
        2 MODEL EQUATIONS 204
        
        3 SOME SPECIAL CASES 207
        
        4 RESULTS 208
        
        5 CONCLUSIONS 211
        
        6 REFERENCES 214
      - Chapter 11. Uniform persistence and global stability in models involving mutualism I. Predator-prey-mutualistic systems 217
        
        1 INTRODUCTION 217
        
        2 TWO-SPECIES MODELS 218
        
        3 THE THREE-SPECIES MODEL 219
        
        4 REGION OF ATTRACTION 220
        
        5 PERSISTENCE AND EXTINCTION IN FACULTATIVE MUTUALISM WITH THE PREY 221
        
        6. PERSISTENCE IN OBLIGATE MUTUALISM WITH A PREDATOR 222
        
        7 GLOBAL STABILITY OF THE EQUILIBRIUM 223
        
        8 AN EXAMPLE 225
        
        9 DISCUSSION 226
        
        10. REFERENCES 226
      - PARTV: RESOURCE MANAGEMENT 227
        
        Chapter 12. Dynamic interactions between economic, ecological and demographic variables 229
        
        2 A SIMPLE ECONOMIC MODEL 229
        
        1 INTRODUCTION 229
        
        3 NATURAL RESOURCES AND POPULATION CONTROL 234
        
        4 ENDOGENOUS POPULATION CHANGE 238
        
        5 CONCLUDING REMARKS 241
        
        6 REFERENCES 241
        
        Chapter 13. Economic growth models: Effects of logistic population and technology 243
        
        1 ABSTRACT 243
        
        2 INTRODUCTION 243
        
        3 MODEL WITH LOGISTIC POPULATION AND TECHNOLOGY: NO SCARCE RESOURCE 244
        
        4 MODEL WITH LOGISTIC POPULATION AND TECHNOLOGY: EXHAUSTIBLE RESOURCE 249
        
        6 REFERENCES 254
        
        5 SUMMARY 254
        
        Chapter 14. A dynamic predator-prey model for the utilization of fishery resources; A case of trawling in Lake Kasumigaura 257
        
        1 INTRODUCTION 257
        
        2 A SUMMARY OF THE FISHERY MANAGEMENT OF LAKE KASUMIGAURA 259
        
        3 THE MODEL OF FISHERY RESOURCES 262
        
        4 MODELS OF FISHERY RESOURCE UTILIZATION 265
        
        5 EMPIRICAL ESTIMATES 268
        
        6 WHY DO GOOD OLD DAYS HARDLY RETURN? 271
        
        7 CONCLUDING REMARKS 276
        
        9 REFERENCES 277
        
        8 ACKNOWLEDGEMENTS 277

Description

TOC

Reviews (0)