Mathematics and life sciences
The book provides a unique collection of in-depth mathematical, statistical, and modeling methods and techniques for life sciences, as well as their applications in a number of areas within life sciences. It also includes a range of new ideas that represent emerging frontiers in life sciences where...
Saved in:
Table of Contents:
- 1 Introduction; 1.1 Scientific Frontiers at the Interface of Mathematics and Life Sciences; 1.1.1 Developing the Language of Science and Its Interdisciplinary Character; 1.1.2 Challenges at the Interface: Mathematics and Life Sciences; 1.1.3 What This Book Is About; 1.1.4 Concluding Remarks; 2 Mathematical and Statistical Modeling of Biological Systems; 2.1 Ensemble Modeling of Biological Systems; 2.1.1 Introduction; 2.1.2 Background; 2.1.3 Ensemble Model; 2.1.4 Computational Techniques; 2.1.5 Application to Viral Infection Dynamics; 2.1.6 Ensemble Models in Biology; 2.1.7 Conclusions
- 3 Probabilistic Models for Nonlinear Processes and Biological Dynamics3.1 Nonlinear Lévy and Nonlinear Feller Processes: an Analytic Introduction; 3.1.1 Introduction; 3.1.2 Dual Propagators; 3.1.3 Perturbation Theory for Weak Propagators; 3.1.4 T-Products; 3.1.5 Nonlinear Propagators; 3.1.6 Linearized Evolution Around a Path of a Nonlinear Semigroup; 3.1.7 Sensitivity Analysis for Nonlinear Propagators; 3.1.8 Back to Nonlinear Markov Semigroups; 3.1.9 Concluding Remarks; 4 New Results in Mathematical Epidemiology and Modeling Dynamics of Infectious Diseases
- 4.1 Formal Solutions of Epidemic Equation4.1.1 Introduction; 4.1.2 Epidemic Models; 4.1.3 Formal Solutions; 4.1.4 Separation of Variables; 4.1.5 Solvability of General Equations; 4.1.6 Concluding Remarks; 5 Mathematical Analysis of PDE-based Models and Applications in Cell Biology; 5.1 Asymptotic Analysis of the Dirichlet Spectral Problems in Thin Perforated Domains with Rapidly Varying Thickness and Different Limit Dimensions; 5.1.1 Introduction; 5.1.2 Description of a Thin Perforated Domain with Quickly Oscillating Thickness and Statement of the Problem; 5.1.3 Equivalent Problem
- 5.1.4 The Homogenized Theorem5.1.5 Asymptotic Expansions for the Eigenvalues and Eigenfunctions; 5.1.6 Conclusions; 6 Axiomatic Modeling in Life Sciences with Case Studies for Virus-immune System and Oncolytic Virus Dynamics; 6.1 Axiomatic Modeling in Life Sciences; 6.1.1 Introduction; 6.1.2 Boosting Immunity by Anti-viral Drug Therapy: Timing, Efficacy and Success; 6.1.3 Predictive Modeling of Oncolytic Virus Dynamics; 6.1.4 Conclusions; 7 Theory, Applications, and Control of Nonlinear PDEs in Life Sciences; 7.1 On One Semilinear Parabolic Equation of Normal Type; 7.1.1 Introduction
- 7.1.2 Semilinear Parabolic Equation of Normal Type7.1.3 The Structure of NPE Dynamics; 7.1.4 Stabilization of Solution for NPE by Start Control; 7.1.5 Concluding Remarks; 7.2 On some Classes of Nonlinear Equations with L1 -Data; 7.2.1 Nonlinear Elliptic Second-order Equations with L1-data; 7.2.2 Nonlinear Fourth-order Equations with Strengthened Coercivity and L1-Data; 7.2.3 Concluding Remarks; 8 Mathematical Models of Pattern Formation and Their Applications in Developmental Biology; 8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology; 8.1.1 Introduction
- 8.1.2 Mechanisms of Developmental Pattern Formation