Mathematical Models in Medical and Health Sciences

Mary Ann Horn, Gieri Simonett, and Glenn Webb, eds.

Vanderbilt University Press, 1998

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . xi

Cancer Treatment Strategies and Mathematical Modeling Evans K. Afenya . . . . . . . . . . . . . . . . . . . . . . . . 1

A Flow Reactor with Wall Growth Mary M. Ballyk and Hal L. Smith . . . . . . . . . . . . . . . 17

Controlling the S-I-S Age-Structured Epidemics Viorel Barbu and Mimmo Iannelli . . . . . . . . . . . . . . . . 29

Cluster Form Analysis Techniques for Diabetic Retinopathy Michael W. Berry and Dax M. Westerman . . . . . . . . . . . . 35

Tuberculosis: The Evolution of Antibiotic Resistance and the Design of Epidemic Control Strategies

Sally Blower, Travis Porco and Tom Lietman . . . . . . . . . . 51

Skew Brownian Motion: A Model for Diffusion with Interfaces?

R. S. Cantrell and C. Cosner . . . . . . . . . . . . . . . . . . 73

Spatio-Temporal Dynamics of the Immune System Response to Cancer M. A. J. Chaplain, V. A. Kuznetsov, Z. H. James

and L. A. Stepanova . . . . . . . . . . . . . . . . . . . . 79

An Age and Maturity Structured Model of Cell Population Dynamics Janet Dyson, Rosanna Villella-Bressan and Glenn Webb . . . . . . 99

A New Mathematical Model of Schistosomiasis Zhilan Feng and Fabio Augusto Milner . . . . . . . . . . . . . 117

Positive Profit in a Predator-Prey Situation K. Renee Fister and Suzanne Lenhart . . . . . . . . . . . . . . 129

Analysis of a Two Component Reaction Diffusioni Model on a Heterogeneous Domain

William E. Fitzgibbon and Jeff Morgan . . . . . . . . . . . . 139

Branch Tree Models of Muscle Sensory Receptors J. P. A. Foweraker, D. P. Bashor, M. Hulliger and E. Otten …. 145 Key Dynamics from a Simple Model of HIV Infection Faustino Sánchez Garduño, Denise Kirschner

and Janelle Reynolds . . . . . . . . . . . . . . . . . . . . 161

Optimal Control of a PDE/ODE System Modeling a Gas-Phase Bioreactor

Naresh Handagama and Suzanne Lenhart . . . . . . . . . . . . 197

Mathematical Analysis for an Evolutionary Epidemic Model Hisashi Inaba . . . . . . . . . . . . . . . . . . . . . . . . . 213

A Mathematical Model of the Time Course of Myelosuppression Resulting from Cancer Chemotherapy

Paul B. Laub . . . . . . . . . . . . . . . . . . . . . . . . 237

Modeling the Effects of Angiogenic Factors on Tumor-related Angiogenesis and Vascularization: A Review

Sophia A. Maggelakis . . . . . . . . . . . . . . . . . . . . 247

Remarks on an Environmental Control Problem Natalia Navarova and Horst R. Thieme . . . . . . . . . . . . . 267

The Mathematical Modelling of Cancer: A Review John Carl Panetta, Mark A. J. Chaplain and John A. Adam …. 281

The Hodgkin-Huxley Equations of Nerve Impulse Propagation Mary E. Parrott . . . . . . . . . . . . . . . . . . . . . . . 311

The Effect of Anisotropy on the Meandering of Spiral Waves in Cardiac Tissue

Bradley J. Roth . . . . . . . . . . . . . . . . . . . . . . . 327

Sister, Mother-Daughter and Cousin Cell Generation Time Correlations and Cell Cycle Progression

Roland Sennerstam and Jan-Olof Strömberg . . . . . . . . . . 337

Some State Space Models of HIV Pathogenesis Wai-Yuan Tan and Zhihua Xiang . . . . . . . . . . . . . . . . 351

Cell Cycle Checkpoints and the Overall Dynamics of Cell Cycle Control

C. D. Thron . . . . . . . . . . . . . . . . . . . . . . . . 369

Modeling the Probability of Tumor Cure after Fractionated Radiotherapy

Susan L. Tucker . . . . . . . . . . . . . . . . . . . . . . . 381