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Willson Kwok, PhD, MBA, PA

KwokConnect, Like and Follow me:




Cell Biology



  • Alt, Chaplain, Griebel, and Lenz, eds. Polymer and Cell Dynamics: Multiscale Modeling and Numerical Simulations. Birkhäuser Basel, 2003.
  • Aluru, ed. Handbook of Computational Molecular Biology. Chapman & Hall/CRC, 2005.
  • Bock and Goode, eds. Ion Channels: From Atomic Resolution Physiology to Functional Genomics. John Wiley, 2002.
  • Burton, ed. Mathematical Biology: A Conference on Theoretical Aspects of Molecular Science. Pergamon Press, 1981.
  • Clote and Backofen. Computational Molecular Biology. Wiley, 2000.
  • Collado-Vides, Magasanik, and Smith, eds. Integrative Approaches to Molecular Biology. MIT Press, 1996.
  • Crippen and Havel. Distance Geometry and Molecular Conformation. John Wiley, 1988.
  • Cronin. Mathematics of Cell Electrophysiology. Marcel Dekker, 1981.
  • Davis. The Microbial Models of Molecular Biology: From Genes to Genomes. Oxford University Press, 2003.
  • Deutsch, Dormann, and Maini. Cellular Automaton Modeling of Biological Pattern Formation. Springer, 2005.
  • Deutsch, Howard, Falcke, and Zimmermann. Function and Regulation of Cellular Systems. Springer, 2004.
  • Fall, Marland, Wagner, and Tyson. Computational Cell Biology. Springer, 2002.
  • Floudas and Pardalos, eds. Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches. Kluwer Academic, 2000.
  • Friedman, ed. Tutorials in Mathematical Biosciences III: Cell Cycle, Proliferation, and Cancer. Springer, 2006.
  • Goldstein and Wofsy, eds. Cell Biology. American Mathematical Society, 1994.
  • Gunst. A Random Model for Plant Cell Population Growth. Mathematisch Centrum, 1989.
  • Heinmets. Quantitative Cellular Biology: An Approach to the Quantitative Analysis of Life Processes. Marcel Dekker, 1970.
  • Jiang, Xu, and Zhang, eds. Current Topics in Computational Molecular Biology. MIT Press, 2002.
  • Jungck and Stanley. Microbes Count!. Canterbury Press, 2003.
  • Kernevez. Enzyme Mathematics. North-Holland, 1980.
  • Knolle. Cell Kinetic Modelling and the Chemotherapy of Cancer. Springer-Verlag, 1988.
  • Macken and Perelson. Branching Processes Applied to Cell Surface Aggregation Phenomena. Springer-Verlag, 1985.
  • Macken and Perelson. Stem Cell Proliferation and Differentiation: A Multitype Branching Process Model. Springer-Verlag, 1988.
  • McPherson. Introduction to Macromolecular Crystallography. Wiley-Liss, 2002.
  • Pozrikidis, ed. Modeling and Simulation of Capsules and Biological Cells. Chapman & Hall/CRC, 2003.
  • Schlick. Molecular Modeling and Simulation. Springer, 2002.
  • Segel, ed. Mathematical Models in Molecular and Cellular Biology. Cambridge University Press, 1980.
  • Segel. Modeling Dynamic Phenomena in Molecular and Cellular Biology. Cambridge University Press, 1984.
  • Sneyd, ed. Tutorials in Mathematical Biosciences II: Mathematical Modeling of Calcium Dynamics and Signal Transduction. Springer, 2005.
  • Tsai. Computational Biochemistry. Wiley, 2002.
  • Voit. Computational Analysis of Biochemical Systems. Cambridge University Press, 2000.
  • Wood et al. Biochemistry: A Problems Approach. W. A. Benjamin, 1974.
  • Yakovlev and Zorin. Computer Simulation in Cell Radiobiology. Springer-Verlag, 1988.
  • Yockey. Information Theory and Molecular Biology. Cambridge University Press, 1992.

Developmental Biology



  • Bookstein. Measurement of Biological Shape and Shape Change. Springer-Verlag, 1978.
  • Gilbert. Developmental Biology. Sinauer Associates, 2003.
  • Jäger, Rost, and Tautu. Biological Growth and Spread: Mathematical Theories and Applications. Springer-Verlag, 1980.
  • Jean. Phyllotaxis: A Systemic Study in Plant Morphogenesis. Cambridge University Press, 1994.
  • MacLeod and Forey, eds. Morphology, Shape and Phylogenetics. CRC, 2002.
  • Nehaniv, ed. Mathematical and Computational Biology: Computational Morphogenesis, Hierarchical Complexity, and Digital Evolution. American Mathematical Society, 1999.
  • Prusinkiewicz and Hanan. Lindenmayer Systems, Fractals, and Plants. Springer-Verlag, 1989.
  • Sekimura et al., eds. Morphogenesis and Pattern Formation in Biological Systems. Springer, 2003.
  • Thom. Structural Stability and Morphogenesis: An Outline of a General Theory of Models. Benjamin Cummings, 1975.
  • Thom. Mathematical Models of Morphogenesis. Halsted Press, 1983.
  • Thompson. On Growth and Form. Dover, 1992.
  • Vitanyi. Lindenmayer Systems: Structure, Languages, and Growth Functions. Mathematisch Centrum, 1980.
  • Williams. The Shoot Apex and Leaf Growth: A Study in Quantitative Biology. Cambridge University Press, 1975.




  • Ågren and Bosatta. Theoretical Ecosystem Ecology - Understanding Element Cycles. Cambridge, 1998.
  • Alstad. Basic Populus Models of Ecology. Prentice Hall, 2001.
  • Anderson and May. The Dynamics of Human Host-Parasite Systems. Princeton, 1986.
  • Anderson and May. Infectious Diseases of Humans: Dynamics and Control. Oxford, 1991.
  • Bossel. Modeling and Simulation. AK Peters, 1994.
  • Bulmer. Theoretical Evolutionary Ecology. Sinauer, 1994.
  • Burgman, Ferson, and Akcakaya. Risk Assessment in Conservation Biology. Chapman and Hall, 1993.
  • Byrd and Cothern. Introduction to Risk Analysis. Government Institutes, 2000.
  • Case. Theoretical Ecology. Oxford, 1999.
  • Caswell. Matrix Population Models. Sinauer Associates, 2000.
  • Clark. Mathematical Bioeconomics: The Optimal Management of Renewable Resources. Wiley, 1976.
  • Cohen. Community Food Webs: Data and Theory. Springer-Verlag, 1990.
  • Cohen. Food Webs and Niche Space. Princeton University Press, 1978.
  • Cohen, ed. Applications of Control Theory in Ecology. Springer-Verlag, 1987.
  • Cullen. Linear Models in Biology - Linear Systems Analysis with Biological Applications. Halsted Press, 1985.
  • Cushing. An Introduction to Structured Population Dynamics. SIAM, 1998.
  • Cushing, Costantino, Dennis, Desharnais, Henson. Chaos in Ecology: Experimental Nonlinear Dynamics. Academic Press, 2003.
  • Dale. Ecological Modeling for Resource Management. Springer, 2003.
  • DeAngelis. Dynamics of Nutrient Cycling and Food Webs. Chapman and Hall, 1992.
  • DeAngelis and Gross. Individual-Based Models and Approaches in Ecology. Chapman and Hall, 1992.
  • Diamond and Case, eds. Community Ecology. Harper & Row, 1986.
  • Donovan and Welden. Spreadsheet Exercises in Conservation Biology. Sinauer Associates, 2001.
  • Donovan and Welden. Spreadsheet Exercises in Ecology and Evolution. Sinauer Associates, 2001.
  • France and Thornley. Mathematical Models in Agriculture. Butterworths, 1984.
  • Freedman. Deterministic Mathematical Models in Population Ecology. Marcel Dekker, 1980.
  • Gardner, ed. Predicting Spatial Effects in Ecological Systems. American Mathematical Society, 1993.
  • Gause. The Struggle for Existence. Williams and Wilkins, 1971.
  • Gotelli. Primer of Ecology. Sinauer Associates, 2001.
  • Gurney and Nisbet. Ecological Dynamics. Oxford, 1998.
  • Hallam and Levin. Mathematical Ecology: An Introduction. Biomathematics 17, Springer-Verlag, 1986.
  • Hoff and Bevers. Spatial Optimization in Ecological Applications. Columbia University, 2002.
  • Jeffries. Mathematical Modeling in Ecology - A Workbook for Students. Birkhäuser, 1999.
  • Kot. Elements of Mathematical Ecology. Cambridge, 2001.
  • Levin. Fragile Dominion: Complexity and the Commons. Perseus Books, 1999.
  • Levin, editor-in-chief. Encyclopedia of Biodiversity, Volumes 1-5. Academic Press, 2001.
  • Levin and Hallam, eds. Mathematical Ecology. Springer-Verlag, 1984.
  • Levin, Hallam, and Gross, eds. Applied Mathematical Ecology. Biomathematics 18, Springer-Verlag, 1989.
  • Logofet. Matrices and Graphs - Stability Problems in Mathematical Ecology. CRC, 1993.
  • MacArthur and Wilson. The Theory of Island Biogeography. Princeton University Press, 1967
  • Maini and Othmer. Mathematical Models for Biological Pattern Formation. Springer, 2001.
  • Mangel and Clark. Dynamic Modeling in Behavioral Ecology. Princeton University Press, 1988.
  • May. Stability and Complexity in Model Ecosystems. Princeton University Press, 1973.
  • May, ed. Thoeretical Ecology: Principles and Applications. W. B. Saunders Company, 1976.
  • Maynard Smith. Models in Ecology. Cambridge, 1974.
  • Morris and Doak. Quantitative Conservation Biology. Sinauer Associates, 2002.
  • Okubo and Levin. Diffusion and Ecological Problems. Springer, 2001.
  • Oster and Wilson. Caste and Ecology in the Social Insects. Princeton University Press, 1978.
  • Pakes and Maller. Mathematical Ecology of Plant Species Competition. Cambridge University Press, 1990.
  • Patil and Rosenzweig. Contemporary Quantitative Ecology and Related Econometrics. International Cooperative Publishers, 1979.
  • Patten and Jo, eds. Complex Ecology: The Part-Whole Relation in Ecosystems. Prentice Hall, 1995.
  • Pielou. Introduction to Mathematical Ecology. Wiley, 1970.
  • Pielou. Mathematical Ecology. Wiley, 1977.
  • Pielou. Population and Community Ecology: Principles and Methods. Gordon and Breach, 1974.
  • Podolsky. New Phenology: Elements of Mathematical Forecasting in Ecology. Wiley, 1984.
  • Poole. An Introduction to Quantitative Ecology. McGraw-Hill, 1974.
  • Rose. Quantitative Ecological Theory - An Introduction to Basic Models. Johns Hopkins University Press, 1987.
  • Roughgarden. Perspectives in Ecological Theory. Princeton, 1989.
  • Roughgarden. Primer of Ecological Theory. Prentice Hall, 1998.
  • Schneider. Qualitative Ecology: Spatial and Temporal Scaling. Academic Press, 1994.
  • Scudo and Ziegler. The Golden Age of Theoretical Ecology. Springer-Verlag, 1978.
  • Segel. Quantitative Ecology: Spatial and Temporal Scaling. Academic Press, 1984.
  • Seuront and Strutton, eds. Handbook of Scaling Methods in Aquatic Ecology. CRC, 2003.
  • Smitalova and Sujan. A Mathematical Treatment of Dynamical Models in Biological Science. Ellis Horwood, 1991.
  • Smith and Waltman. The Theory of the Chemostat: Dynamics of Microbial Competition. Cambridge University Press, 1995.
  • Starfield and Bleloch. Building Models for Conservation and Wildlife Management. MacMillan, 1986.
  • Suter, ed. Ecological Risk Assessment. Lewis Publishers, 1993.
  • Thornley and Johnson. Plant and Crop Modeling. Clarendon Press, 1990.
  • Tuchinsky. Man in Competition with the Spruce Budworm - An Application of Differential Equations. Birkhauser, 1981.
  • Turner and Gardner, eds. Quantitative Methods in Landscape Ecology: The Analysis and Interpretation of Landscape Heterogeneity. Springer-Verlag, 1991.
  • Vandermeer. Elementary Mathematical Ecology. Wiley and Sons, 1981.
  • Watt. Ecology and Resource Management: A Quantitative Approach. McGraw-Hill, 1968.
  • Whittaker. Communities and Ecosystems. Macmillan, 1970.
  • Whittaker and Levin. Niche: Theory and Application. Dowden, Hutchinson and Ross, 1975.
  • Williams. Patterns in the Balance of Nature and Related Problems in Quantitative Ecology. Academic Press, 1964.
  • Wilson. Simulating Ecological and Evolutionary Systems in C. Cambridge, 2000.
  • Yodzis. Competition for Space and the Structure of Ecological Communities. Springer-Verlag, 1978.
  • Yodzis. Introduction to Theoretical Ecology. Harper and Row, 1989.




  • Anderson, ed. Population Dynamics of Infectious Diseases: Theory and Applications. Chapman & Hall, 1982.
  • Anderson and May, eds. Population Biology of Infectious Diseases. Springer-Verlag, 1982.
  • Asachenkov et al. Disease Dynamics. Birkhäuser Boston, 1984.
  • Bailey. The Mathematical Theory of Infectious Diseases and Its Applications. Macmillan, 1975.
  • Brauer and Castillo-Chavez. Mathematical Models in Population Biology and Epidemiology. Springer, 2001.
  • Busenberg and Cooke. Vertically Transmitted Diseases: Models and Dynamics. Springer-Verlag, 1993.
  • Castillo-Chavez et al., eds. Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory. Springer, 2002.
  • Castillo-Chavez, ed. Mathematical and Statistical Approaches to AIDS Epidemiology. Springer-Verlag, 1989.
  • Daley and Gani. Epidemic Modelling: An Introduction. Cambridge, 1999.
  • Diekmann and Heesterbeek. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis, and Interpretation. Wiley, 2000.
  • Frauenthal. Mathematical Modeling in Epidemiology. Springer-Verlag, 1980.
  • Hethcote and Yorke. Gonorrhea, Transmission Dynamics, and Control. Springer-Verlag, 1984.
  • Hoffman and Hraba, eds. Immunology and Epidemiology. Springer-Verlag, 1986.
  • Kleinbaum, Kupper, and Morgenstern. Epidemiological Research: Principles and Quantitative Methods. Lifetime Learning, 1982.
  • Kranz, ed. Epidemics of Plant Diseases: Mathematical Analysis and Modeling. Springer-Verlag, 1990.
  • Lauwerier. Mathematical Models of Epidemics. Mathematisch Centrum, 1981.
  • Mollison, ed. Epidemic Models: Their Structure and Relation to Data. Cambridge University Press, 1995.
  • Morabia, ed. A History of Epidemiologic Methods and Concepts. Birkh&user, 2006.
  • Nasell. Hybrid Models of Tropical Infections. Springer-Verlag, 1985.
  • Prentice and Whittemore, eds. Environmental Epidemiology: Risk Assessment. Society for Industrial and Applied Mathematics, 1982.
  • Smith. Veterinary Clinical Epidemiology, 3rd ed. CRC, 2005.
  • Emilia Vynnycky and Richard White. An Introduction to Infectious Disease Modelling. Oxford University Press, 2010.




  • Charlesworth. Evolution in Age-Structured Populations. Cambridge University Press, 1994.
  • Charnov. The Theory of Sex Allocation. Princeton University Press, 1982.
  • Christiansen and Fenchel, eds. Measuring Selection in Natural Populations. Springer-Verlag, 1977.
  • Feldman, ed. Mathematical Evolutionary Theory. Princeton University Press, 1989.
  • Galton. Natural Inheritance. Macmillan and Co., 1889.
  • Hofbauer and Sigmund. The Theory of Evolution and Dynamical Systems: Mathematical Aspects of Selection. Cambridge University Press, 1988.
  • Hofbauer and Sigmund. Evolutionary Games and Population Dynamics. Cambridge University Press, 1998.
  • Karlin and Lessard. Theoretical Studies on Sex Ratio Evolution. Princeton University Press, 1986.
  • Kirkpatrick, ed. The Evolution of Haploid-Diploid Life Cycles. American Mathematical Society, 1994.
  • Mangel, ed. Some Mathematical Questions in Biology: Sex Allocation and Sex Change. American Mathematical Society, 1990.
  • Mani. Evolutionary Dynamics of Genetic Diversity. Springer-Verlag, 1984.
  • Maynard Smith. Mathematical Ideas in Biology. Cambridge, 1968.
  • Michod and Levin, eds. The Evolution of Sex. Sinauer Associates, 1988.
  • Nagylaki. Selection in One- and Two-Locus Systems. Springer-Verlag, 1977.
  • Nielsen. Statistical Methods in Molecular Evolution. Springer, 2005.
  • Ohta. Evolution and Variation of Multigene Families. .




  • Akin. Geometry of Population Genetics. Springer-Verlag, 1979.
  • Boorman and Levitt. The Genetics of Altruism. Academic Press, 1980.
  • Bulmer. The Mathematical Theory of Quantitative Genetics. Oxford University Press, 1985.
  • Bower and Bolouri. Computational Modeling of Genetic and Biochemical Networks. MIT Press, 2001.
  • Cannings and Thompson. Genealogical and Genetic Structure. Cambridge University Press, 1981.
  • Chen. Extending the Scalability of Linkage Learning Genetic Algorithms: Theory & Practice. Springer, 2005.
  • Crow and Kimura. An Introduction to Population Genetics Theory. Harper & Row, 1970.
  • Dunn and Everitt. Introduction to Mathematical Taxonomy. Dover, 2004.
  • Ewens. Mathematical Population Genetics. Springer, 2004.
  • Findley, McGlynn, and Findley. The Geometry of Genetics. John Wiley, 1989.
  • Gale. Theoretical Population Genetics. Unwin Hyman, 1990.
  • Gregorius. Population Genetics in Forestry. Springer-Verlag, 1985.
  • Jacquard. The Genetic Structure of Populations. Springer-Verlag, 1974.
  • Kingman. Mathematics of Genetic Diversity. Society for Industrial and Applied Mathematics, 1980.
  • Lange. Mathematical and Statistical Methods for Genetic Analysis. Springer-Verlag, 1997.
  • Martin-Vide and Mitrana. Grammars and Automata for String Processing; From Mathematics and Computer Science to Biology, and Back. CRC, 2003.
  • Mather and Links. Biometrical Genetics. Chapman & Hall, 1982.
  • Mirkin and Rodin. Graphs and Genes. Springer-Verlag, 1984.
  • Provine. The Origins of Theoretical Population Genetics. University of Chicago Press, 1971.
  • Roughgarden. Theory of Population Genetics and Evolutionary Ecology: An Introduction. MacMillan Publishing Company, 1979.
  • Svirezhev and Passekov. Fundamentals of Mathematical Evolutionary Genetics. Kluwer Academic, 1990.
  • Whorz-Busekros. Algebras in Genetics. Springer-Verlag, 1980.




  • Aldroubi and Unser, eds. Wavelets in Medicine and Biology. CRC Press, 1996.
  • Bailar and Mosteller, eds. Medical Uses of Statistics. New England Journal of Medicine Books, 1986.
  • Banks. Modeling and Control in the Biomedical Sciences. Springer-Verlag, 1975.
  • Bélair et al., eds. Dynamical Disease: Mathematical Analysis of Human Illness. American Institute of Physics Press, 1995.
  • Bellman. Mathematical Methods in Medicine. World Scientific, 1983.
  • Bithell and Coppi, eds. Perspectives in Medical Statistics. Academic Press, 1981.
  • Borgers and Natterer. Computational Radiology and Imaging. Springer, 1999.
  • Bruni et al. Systems Theory in Immunology. Springer-Verlag, 1979.
  • Capasso, Grosso, and Paveri-Fontana, eds. Mathematics in Biology and Medicine. Springer-Verlag, 1985.
  • Cherruault. Mathematical Modelling in Biomedicine: Optimal Control of Biomedical Systems. D. Reidel Publishers, 1985.
  • Deisboeck and Kresh, eds. Complex Systems Science in Biomedicine. Springer, 2006.
  • DeLisi. Antigen Antibody Interactions. Springer-Verlag, 1976.
  • Diekmann and Heesterbeek. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Wiley, 2000.
  • Eisen. Mathematical Models in Cell Biology and Cancer Chemotherapy. Springer-Verlag, 1979.
  • Glantz. Mathematics for Biomedical Applications. University of California Press, 1979.
  • Höhne, ed. Pictorial Information Systems in Medicine. Springer-Verlag, 1986.
  • Hoppensteadt and Peskin. Mathematics in Medicine and the Life Sciences. Springer-Verlag, 1992.
  • Ingram and Bloch, eds. Mathematical Methods in Medicine (two volumes). John Wiley, 1984, 1986.
  • Iosifescu and Tautu. Stochastic Processes and Applications in Biology and Medicine. Springer-Verlag, 1973.
  • Jacquez. Compartmental Analysis in Biology and Medicine. University of Michigan Press, 1985.
  • Macheras and Iliadis. Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics: Homogeneous and Heterogeneous Approaches. Springer, 2005.
  • Manton and Stallard. Chronic Disease Modeling. Oxford, 1988.
  • Marchuk. Mathematical Modelling of Immune Response in Infectious Diseases. Kluwer Academic, 1997.
  • Miké and Stanley, eds. Statistics in Medical Research: Methods and Issues, with Applications in Cancer Research. John Wiley, 1982.
  • Nonnenmacher, Losa, and Weibel, eds. Fractals in Biology and Medicine. Birkhäuser Boston, 1994.
  • Quarteroni, Formaggia, and Veneziani, eds. Complex Systems in Biomedicine. Springer, 2006.
  • Swan. Applications of Optimal Control Theory in Biomedicine. Marcel Dekker, 1984.
  • Umar, Kapetanovic, and Khan, eds. The Applications of Bioinformatics in Cancer Detection. National Institutes of Health, 2002.




  • Amari and Arbib, eds. Competition and Cooperation in Neural Nets. Springer-Verlag, 1982.
  • Arbib. Brains, Machines, and Mathematics. Springer-Verlag, 1987.
  • Borisyuk, Ermentrout, Freidman, and Terman. Tutorials in Mathematical Biosciences I: Mathematical Neuroscience. Springer, 2005.
  • Coombes and Bressloff, eds. Bursting: The Genesis of Rhythm in the Nervous System. World Scientific Publishing Company, 2005.
  • Cronin. Mathematical Aspects of Hodgkin-Huxley Neural Theory. Cambridge University Press, 1987.
  • Dario, ed. Sensors and Sensory Systems for Advanced Robots. Springer-Verlag, 1988.
  • De Schutter. Computational Neuroscience: Realistic Modeling for Experimentalists. CRC, 2000.
  • Grossberg, ed. Neural Networks and Natural Intelligence. MIT Press, 1988.
  • Heiden. Analysis of Neural Networks. Springer-Verlag, 1980.
  • Hoppensteadt. An Introduction to the Mathematics of Neurons. Cambridge University Press, 1997.
  • Hoppensteadt and Izhikevich. Weakly Connected Neural Networks. Springer-Verlag, 1997.
  • House. Depth Perception in Frogs and Toads: A Study in Neural Computing. Springer-Verlag, 1989.
  • Kent. The Brains of Men and Machines. BYTE/McGraw-Hill, 1981.
  • MacGregor. Theoretical Mechanics of Biological Neural Networks. Academic Press, 1993.
  • Miura, ed. Some Mathematical Questions in Biology: Neurobiology. American Mathematical Society, 1982.
  • Peretto. An Introduction to the Modeling of Neural Networks. Cambridge University Press, 1992.
  • Reeke et al., eds. Modeling in the Neurosciences. CRC, 2005.
  • Rumehlart and McClelland. Parallel Distributed Processing: Explorations in the Microstructure of Cognition. MIT Press, 1986.
  • Scott. Neurophysics. John Wiley, 1977.
  • Tahib. Branching Process and Neutral Evolution. Springer-Verlag, 1992.
  • Torras. Temporal-Pattern Learning in Neural Models. Springer-Verlag, 1985.
  • Tuckwell. Introduction to Theoretical Neurobiology. Cambridge University Press, 1988.
  • Tuckwell. Stochastic Processes in the Neurosciences. Society for Industrial and Applied Mathematics, 1989.
  • Wu. Introduction to Neural Dynamics and Signal Transmission Delay. Walter de Gruyter, 2001.




  • Alt and Hoffman, eds. Biological Motion. Springer-Verlag, 1991.
  • Beuter, Glass, Mackey, and Titcombe. Nonlinear Dynamics in Physiology and Medicine. Springer, 2003.
  • Carson, Cobelli, and Finkelstein. The Mathematical Modeling of Metabolic and Endocrine Systems. John Wiley, 1983.
  • Childress. Mechanics of Swimming and Flying. Cambridge University Press, 1981.
  • Collins and Van der Werff. Mathematical Models of the Dynamics of the Human Eye. Springer-Verlag, 1980.
  • Dallos et al., eds. Mechanics and Biophysics of Hearing. Springer-Verlag, 1990.
  • Feng. Computational Neuroscience. CRC, 2003.
  • Glass and Hunter et al. Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function. Springer-Verlag, 1991.
  • Glass and Mackey. From Clocks to Chaos. Princeton, 1988.
  • Holmes and Rubenfeld, eds. Mathematical Modeling of the Hearing Process. Springer-Verlag, 1981.
  • Hoppensteadt, ed. Mathematical Aspects of Physiology. American Mathematical Society, 1981.
  • Hoppensteadt and Peskin. Modeling and Simulation in Medicine and the Life Sciences. Springer, 2001.
  • Keener and Sneyd. Mathematical Physiology. Springer, 1998.
  • Lambrecht and Rescigno, eds. Tracer Kinetics and Physiologic Modeling. Springer-Verlag, 1983.
  • Layton and Weinstein. Membrane Transport and Renal Physiology. Springer, 2002.
  • Lighthill. Mathematical Biofluiddynamics. Society for Industrial and Applied Mathematics, 1975.
  • Mazumdar ed. An Introduction to Mathematical Physiology and Biology. Cambridge, 1989.
  • McMahon. Muscles, Reflexes, and Locomotion. Princeton University Press, 1984.
  • Miura, ed. Some Mathematical Questions in Biology: Muscle Physiology. American Mathematical Society, 1986.
  • Mulquiney and Kuchel. Modelling Metabolism with Mathematica. CRC, 2003.
  • Nobel. Biophysical Plant Physiology and Ecology. W. H. Freeman, 1983.
  • Ottesen, Olufsen, and Larsen. Applied Mathematical Models in Human Physiology. Cambridge University Press, 2004.
  • Panfilov and Holden, eds. Computational Biology of the Heart. John Wiley, 1997.
  • Pedley, ed. Scale Effects in Animal Locomotion. Academic Press, 1977.
  • Scott. Neuroscience: A Mathematical Primer. Springer, 2002.
  • Strogatz. The Mathematical Structure of the Human Sleep-Wake Cycle. Springer-Verlag, 1986.
  • Thornley. Mathematical Models in Plant Physiology. Academic Press, 1976.
  • Vogel and Defarrari. Comparative Biomechanics. Princeton, 2003.
  • Winfree. The Timing of Biological Clocks. Scientific American Library, 1987.

Population Biology



  • Barigozzi, ed. Vito Volterra Symposium on Mathematical Models in Biology. Springer-Verlag, 1980.
  • Bartlett. Stochastic Population Models in Ecology and Epidemiology. Methuen, 1960.
  • Bartlett and Hiorns, eds. The Mathematical Theory of the Dynamics of Biological Populations. Academic Press, 1973.
  • Chapman and Gallucci, eds. Quantitative Population Dynamics. International Cooperative Publishers, 1981.
  • Christiansen and Fenchel. Theories of Populations in Biological Communities. Springer-Verlag, 1977.
  • Costantino and Desharnais. Population Dynamics and the Tribolium Model: Genetics and Demography. Springer-Verlag, 1991.
  • Frauenthal. Introduction to Population Modeling. Birkhäuser Boston, 1980.
  • Freedman and Strobeck, eds. Population Biology. Springer-Verlag, 1983.
  • Ginzburg and Golenberg. Lectures in Theoretical Population Biology. Prentice Hall, 1985.
  • Hassell. The Dynamics of Arthropod Predator-Prey Systems. Princeton University Press, 1978.
  • Hastings. Population Biology: Concepts and Models. Springer, 1997.
  • Hastings, ed. Some Mathematical Questions in Biology: Models in Population Biology. American Mathematical Society, 1989.
  • Hoppensteadt. Mathematical Methods of Population Biology. Cambridge, 1982.
  • Hoppensteadt. Mathematical Theories of Populations: Demographics, Genetics, and Epidemics. Society for Industrial and Applied Mathematics, 1975.
  • Hutchinson. An Introduction to Population Ecology. Yale University Press, 1978.
  • Iannelli, Martcheva, and Milner. Gender-structured Population Modeling: Mathematical Methods, Numerics, and Simulations. Cambridge University Press, 2005.
  • Keyfitz. Introduction to the Mathematics of Population. Addison-Wesley, 1968.
  • Kingsland. Modeling Nature: Episodes in the History of Population Ecology. University of Chicago Press, 1985.
  • Lewis. Network Models in Population Biology. Springer-Verlag, 1977.
  • Ludwig. Stochastic Population Theories. Springer-Verlag, 1974.
  • Malthus. An Essay on the Principle of Population. J. Johnson, 1798.
  • McDonald et al., eds. Estimation and Analysis of Insect Populations. Springer-Verlag, 1989.
  • Metz and Diekmann, eds. The Dynamics of Physiologically Structured Populations. Springer-Verlag, 1986.
  • Nisbet and Gurney. Modelling Fluctuating Populations. The Blackburn Press (reprint), 1982.
  • Pollard. Mathematical Models for the Growth of Human Populations. Cambridge University Press, 1973.
  • Renshaw. Modelling Biological Populations in Space and Time. Cambridge, 1991.
  • Renshaw. Population and Community Ecology: Principles and Methods. Gordon & Breach, 1991.
  • Smith and Waltman. The Theory of the Chemostat: Dynamics of Microbial Competition. Cambridge University Press, 1994.
  • Song and Yu. Population System Control. Springer-Verlag, 1988.
  • Teramoto and Yamaguti, eds. Mathematical Topics in Population Biology, Morphogenesis and Neurosciences. Springer-Verlag, 1987.
  • Therneau and Grambsch. Modeling Survival Data: Extending the Cox Model. Springer-Verlag, 2000.
  • Thieme. Mathematics in Population Biology. Princeton, 2003.
  • Turchin. Complex Population Dynamics. Princeton, 2003.
  • Vandermeer and Goldberg. Population Biology. Princeton, 2003.
  • Waltman. Competition Models in Population Biology. Society for Industrial and Applied Mathematics, 1984.
  • Wilson and Bossert. A Primer of Population Biology. Sinauer Associates, 1971.

Bioinformatics, Genomics and Proteomics

Population Growth and Decay

(1) Population based on generation number:

Nn = N0Qn

This equation shows the population Nn as a function of n generations, when N0 is the initial population and Q is the number of offspring per parent in one generation. Does not include time.
(2) Population based on time and rate of doubling:
Nt = N02t/d

This equation shows the population Nn after a given time t, depending on the doubling time d. The units of t and d must be the same.
Does NOT include the actual number of offspring per parent. The "generation" is defined arbitrarily as 2. This is the way populations are usually measured. It avoids complications arising from variable family size.


Hardy Weinberg Law

p + q = 1

p2 + 2pq + q2 = 1

Description: This law predicts how gene frequencies will be transmitted from generation to generation.
Assumptions necessary: an infinitely large, random mating population that is free from outside evolutionary forces (i.e. mutation, migration and natural selection), individuals survive equally.

Definitions: p = frequency of allele 'A'; q = frequency of allele 'a'; p2 = AA genotype frequency; 2pq = Aa genotype frequency; and q2 = aa genotype frequency.

Consequences: genetic variability can be maintained in a population; gene frequencies will remain unchanged from one generation to the next unless selection pressure is exerted; frequencies of heterozygous carriers can be calculated.

Basic Wave Equation

λ = c/f

Description: This equation shows the relation between wavelength and frequency. Quantities: c is the speed of light (3.00 x 108 meter/sec); λ is the wavelength; and f is the frequency of the light wave (sometimes written as Greek nu). Units: Wavelength should be in meters and frequency in Hertz (1 Hz = 1 cycle/second).

Photon Energy

E = hc/λ


Description: This equation relates the photon energy to the wavelength of the light wave. Quantities: E is the photon energy; λ is the wavelength; h is Planck's constant (6.626 x 10-34 Joules sec); c is the speed of light.

Energy relationships

Watt = Joule per second
W = J/sec

Measuring Evolution Time with a Molecular Clock

A "molecular clock" is a gene that evolves at a steady rate and is present in many related species.

The percent similarity of this gene between any pair of species is given by the number of base positions in the gene that are the same between two species.

The time that has passed since the point when two species diverged varies approximately with the percent difference between the two; that is:

Time since divergence of two species is given by
(100 - X% sequence similarity) / (% change / years).

[Note: This simple equation only approximates real biology. Actual animals and plants show different molecular clock rates for different genes and species; thus it takes a supercomputer with complex analysis to work it out.]


pH = -log[H+] or pH = -log[H3O+]

Description: pH is a measure of the acidity (also basicity) of a solution

Quantities: [H+] is the concentration of the hydronium ion. Units: concentrations should be in the units moles/liter.

Ionization of Water

Kw = 1.0 x 10-14 for the reaction: 2H2O <=> H3O+ + OH-

Kw = 1.0 x 10-14 = [H3O+] [OH-]

Taking the negative log of both sides of the equation gives you: pH + pOH = 14

Description: Water ionizes to form the hydronium ion (H3O+) and the hydroxide ion (OH-).

Quantities: Kw is the equilibrium constant for this reaction. [H3O+] is the hydronium ion concentration and [OH-] is the hydroxide ion concentration.

Units: Ion concentrations are in moles per liter (moles/liter = M).

Weak Acid Dissociation

Ka for the reaction: HA + H2O <=> H3O+ + A-

Ka = [H3O+] [A-] / [HA]

% dissociation = {[H3O+] / original [HA]} x 100 or {[A-] / original [HA]} x 100

Description: Weak acids dissociate only partially in water to form the hydronium ion (H3O+) and the conjugate base of the weak acid (A-). Ka is the equilibrium constant that mathematically describes the concentration of all chemical species at equilibrium.

Quantities: Ka is the dissociation constant for a weak acid. Values for individual acids are either supplied in the question or located in reference tables. [H3O+] is the hydronium ion concentration and [A-] is the concentration of the conjugate base. [HA] is the concentration of the acid that remains undissociated.

Units: Concentrations are in moles per liter (moles/liter = M).
















Last Updated on 09-01-2015 at 10:38:46 PM
This page is designed and maintained by Dr. Willson Kwok