Laboratory Manual of Biomathematics

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Academic Press, Aug 28, 2007 - Mathematics - 192 pages
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Laboratory Manual of Biomathematics is a companion to the textbook An Invitation to Biomathematics. This laboratory manual expertly aids students who wish to gain a deeper understanding of solving biological issues with computer programs.

It provides hands-on exploration of model development, model validation, and model refinement, enabling students to truly experience advancements made in biology by mathematical models. Each of the projects offered can be used as individual module in traditional biology or mathematics courses such as calculus, ordinary differential equations, elementary probability, statistics, and genetics. Biological topics include: Ecology, Toxicology, Microbiology, Epidemiology, Genetics, Biostatistics, Physiology, Cell Biology, and Molecular Biology .

Mathematical topics include Discrete and continuous dynamical systems, difference equations, differential equations, probability distributions, statistics, data transformation, risk function, statistics, approximate entropy, periodic components, and pulse-detection algorithms. It includes more than 120 exercises derived from ongoing research studies.

This text is designed for courses in mathematical biology, undergraduate biology majors, as well as general mathematics. The reader is not expected to have any extensive background in either math or biology.



* Can be used as a computer lab component of a course in biomathematics or as homework projects for independent student work
* Biological topics include: Ecology, Toxicology, Microbiology, Epidemiology, Genetics, Biostatistics, Physiology, Cell Biology, and Molecular Biology
* Mathematical topics include: Discrete and continuous dynamical systems, difference equations, differential equations, probability distributions, statistics, data transformation, risk function, statistics, approximate entropy, periodic components, and pulse-detection algorithms
* Includes more than 120 exercises derived from ongoing research studies
 

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Contents

Exploring BERKELEY MADONNA in the Context of SingleSpecies Population Dynamics
1
Logistic Models of SingleSpecies Population Dynamics Equilibrium States and LongTerm Behavior
19
Physiological Mechanisms of Drug Elimination from the Bloodstream and Optimal Drug Intake Regimens
29
Epidemic Models
43
PredatorPrey Models
57
Selection in Genetics The Effect of A Maladaptive or Lethal Gene
71
Quantitative Genetics and Statistics
79
Blood Glucose Fluctuation Characteristics in Type I versus Type II Diabetes Mellitus
99
Using Heartbeat Characteristics and Patterns to Predict Sepsis in Neonates
113
Hormone Pulsatility in Reproductive Endocrinology
131
Endocrine Oscillators Modeling and Analysis of the Growth Hormone Network
143
Chemical Perturbation on the Operations of Circadian Clocks
159
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About the author (2007)

Raina Robeva was born in Sofia, Bulgaria. She has a PhD in Mathematics from the University of Virginia and has led multiple NSF-funded curriculum development projects at the interface of mathematics and biology. She is the lead author of the textbook An Invitation to Biomathematics (2008) and the lead editor of the volume Mathematical Concepts and Methods in Modern Biology: Using Modern Discrete Models (2013), both published by Academic Press. Robeva is the founding Chief Editor of the research journal Frontiers in Systems Biology. She is a professor of Mathematical Sciences at Sweet Briar College and lives in Charlottesville, Virginia.

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