Understanding Complex Biological Systems with Mathematics

1. Front Matter

   Pages i-xiv

   PDF

2. Searching for Superspreaders: Identifying Epidemic Patterns Associated with Superspreading Events in Stochastic Models

   • Christina J. Edholm, Blessing O. Emerenini, Anarina L. Murillo, Omar Saucedo, Nika Shakiba, Xueying Wang et al.

   Pages 1-29

3. How Disease Risks Can Impact the Evolution of Social Behaviors and Emergent Population Organization

   • Nakeya D. Williams, Heather Z. Brooks, Maryann E. Hohn, Candice R. Price, Ami E. Radunskaya, Suzanne S. Sindi et al.

   Pages 31-46

4. Mathematical Analysis of the Impact of Social Structure on Ectoparasite Load in Allogrooming Populations

   • Heather Z. Brooks, Maryann E. Hohn, Candice R. Price, Ami E. Radunskaya, Suzanne S. Sindi, Nakeya D. Williams et al.

   Pages 47-61

5. Modeling the Argasid Tick (Ornithodoros moubata) Life Cycle

   • Sara M. Clifton, Courtney L. Davis, Samantha Erwin, Gabriela Hamerlinck, Amy Veprauskas, Yangyang Wang et al.

   Pages 63-87

6. A Mathematical Model for Tumor–Immune Dynamics in Multiple Myeloma

   • Jill Gallaher, Kamila Larripa, Urszula Ledzewicz, Marissa Renardy, Blerta Shtylla, Nessy Tania et al.

   Pages 89-122

7. Fluid Dynamics of Nematocyst Prey Capture

   • Wanda Strychalski, Sarah Bryant, Baasansuren Jadamba, Eirini Kilikian, Xiulan Lai, Leili Shahriyari et al.

   Pages 123-144

8. Simulations of the Vascular Network Growth Process for Studying Placenta Structure and Function Associated with Autism

   • Catalina Anghel, Kellie Archer, Jen-Mei Chang, Amy Cochran, Anca Radulescu, Carolyn M. Salafia et al.

   Pages 145-169

9. Placental Vessel Extraction with Shearlets, Laplacian Eigenmaps, and a Conditional Generative Adversarial Network

   • Catalina Anghel, Kellie Archer, Jen-Mei Chang, Amy Cochran, Anca Radulescu, Carolyn M. Salafia et al.

   Pages 171-196

10. Back Matter

    Pages 197-198

    PDF

This volume examines a variety of biological and medical problems using mathematical models to understand complex system dynamics. Featured topics include autism spectrum disorder, ectoparasites and allogrooming, argasid ticks dynamics, super-fast nematocyst firing, cancer-immune population dynamics, and the spread of disease through populations. Applications are investigated with mathematical models using a variety of techniques in ordinary and partial differential equations, difference equations, Markov-chain models, Monte-Carlo simulations, network theory, image analysis, and immersed boundary method. Each article offers a thorough explanation of the methodologies used and numerous tables and color illustrations to explain key results. This volume is suitable for graduate students and researchers interested in current applications of mathematical models in the biosciences.

The research featured in this volume began among newly-formed collaborative groups at the 2017 Women Advancing Mathematical Biology Workshop that took place at the Mathematical Biosciences Institute in Columbus, Ohio. The groups spent one intensive week working at MBI and continued their collaborations after the workshop, resulting in the work presented in this volume.

• Dynamical Systems
• Stochastic models
• Image analysis
• Complex biological systems
• Association for Women in Mathematics
• superspreaders
• tumor-immune dynamics

• Mathematics Department, Pomona College, Claremont, USA

  Ami Radunskaya, Blerta Shtylla

• Department of Mathematics, Virginia Commonwealth University, Richmond, USA

  Rebecca Segal

Ami Radunskaya is a professor of mathematics at Pomona College, the President of the Association for Women in Mathematics (2017-2018), and a Fellow of the American Mathematical Society. 

Rebecca Segal is an associate professor of mathematics at Virginia Commonwealth University.


Blerta Shtylla is an assistant professor of mathematics at Pomona College. 

Policies and ethics