About the Authors
- Tianyu Zhang
- Department of Mathematical Sciences, Montana State University, Bozeman, Montana, United States of America
- Breana Pabst, Philip S. Stewart
- Department of Chemical and Biological Engineering, Montana State University, Bozeman, Montana, United States of America
- Isaac Klapper
- Department of Mathematics, Temple University, Philadelphia, Pennsylvania, United States of America
- Philip S. Stewart
- Center for Biofilm Engineering, Montana State University, Bozeman, Montana, United States of America
The authors have declared that no competing interests exist.
Conceived and designed the experiments: PS. Performed the experiments: BP. Analyzed the data: PS BP. Contributed reagents/materials/analysis tools: BP. Wrote the paper: TZ PS. Conceived the basic model structure and identified case studies: PS. Formulated the mathematical model: TZ IK PS. Implemented numerical solution of the model case studies: TZ.