by Livio Triolo (Università di Roma Tor Vergata, Italy)

This book takes an in-depth look into the great interdisciplinary mainstream of mathematical modeling in the life sciences. The various topics reflect the author's experience in statistical mechanics and in multiscale biomathematical analysis. One of the main issues is the multiscale aspect — the microscopic, subcellular level is linked, through the growth process, to the emerging macroscopic organization. Detailed attention is paid to the interplay between different descriptions — deterministic and stochastic, spatial and non-spatial. The exposition is not formal, details are referred to the Bibliography and some topics are critically reviewed.

• Mathematical Modeling of Many-Component Systems
• Examples from Ecology, Epidemiology and Cell Biology
• Birth-Death Processes: Initial and Asymptotic Behavior
• From Microscale to Macroscale: Stochastic Dynamics and Scaling Limits
• Mean-Field Approximation and Nonlocal Behavior
• An Intermediate, Mesoscopic Scale: The Kinetic Theory Approach
• More Examples from Current Research: Chemotaxis, Tumor Growth and Viral Infections
• Appendix on Qualitative Analysis of Differential and Integral Equations and on the Limit Behavior of Stochastic Processes