Mathematical Modeling of Biological Systems Geometry, Symmetry and Conservation Laws

• Other Authors: Papa, Federico (Editor), Sinisgalli, Carmela (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2022
• Subjects: Information technology industries; COVID-19 seasonality; S.I.R. models; mathematical modeling; forced seasonality; confounding variables; uncertainty; Atangana-Baleanu; Caputo; eco-epidemiology; Rosenzweig-MacArthur; epidemic ODE model; COVID-19 spread in Italy; system control and identification; blood microcirculation; ultrafiltration process; vasomotion; Fårhæus-Lindquist effect; type-1 diabetes mellitus; global analysis; β cells; regulatory system; dynamical systems; network optimization; stability analysis; global attractor; relative entropy; information geometry; Voronoi diagram; diffusion process; bivariate probability density function; diameter; polygon area; stand density; predictive microbiology; lactic acid bacteria; batch fermentation; primary mathematical model; bacterial growth; bounded noises; kinetic theory; active particles; statistical mechanics; population dynamics; Fokker-Planck equation; mathematical oncology; ecology; noise induced transitions; systems biology; enzymatic reactions; quadratization; ODE integration
• Online Access: DOAB: download the publication; DOAB: description of the publication

Mathematical modeling is a powerful approach supporting the investigation of open problems in natural sciences, in particular physics, biology and medicine. Applied mathematics allows to translate the available information about real-world phenomena into mathematical objects and concepts. Mathematical models are useful descriptive tools that allow to gather the salient aspects of complex biological systems along with their fundamental governing laws, by elucidating the system behavior in time and space, also evidencing symmetry, or symmetry breaking, in geometry and morphology. Additionally, mathematical models are useful predictive tools able to reliably forecast the future system evolution or its response to specific inputs. More importantly, concerning biomedical systems, such models can even become prescriptive tools, allowing effective, sometimes optimal, intervention strategies for the treatment and control of pathological states to be planned. The application of mathematical physics, nonlinear analysis, systems and control theory to the study of biological and medical systems results in the formulation of new challenging problems for the scientific community. This Special Issue includes innovative contributions of experienced researchers in the field of mathematical modelling applied to biology and medicine.