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 Dynamics -- 3.1 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 Equation -- 4.1.1 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 Theorem -- 5.1.5 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 Type -- 7.1.3 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 -- 8.1.3 Motivating Application: Pattern Control in Hydra -- 8.1.4 Diffusive Morphogens and Turing Patterns -- 8.1.5 Receptor-based Models -- 8.1.6 Multistability -- 8.1.7 Discussion -- 9 Modeling the Dynamics of Genetic Mechanism, Pattern Formation, and the Genetics of "Geometry" -- 9.1 Modeling the Positioning of Trichomes on the Leaves of Plants -- 9.1.1 Introduction.

9.1.2 Activator-inhibitor Reaction-diffusion Modeling of the Trichome Positioning -- 9.1.3 Hexagonal Recursion -- 9.1.4 Conclusions -- 10 Statistical Modeling in Life Sciences and Direct Measurements -- 10.1 Error Estimation for Direct Measurements in May-June 1986 of 131I Radioactivity in Thyroid Gland of Children and Adolescents and Their Registration in Risk Analysis -- 10.1.1 Introduction -- 10.1.2 Materials and Methods -- 10.1.3 Conclusion and Discussion -- 10.1.4 Appendix. Approximation of Conditional Expectations -- 11 Design and Development of Experiments for Life Science Applications -- 11.1 Physiological Effects of Static Magnetic Field Exposure in an in vivo Acute Visceral Pain Model in Mice -- 11.1.1 Introduction -- 11.1.2 Methods -- 11.1.3 Results -- 11.1.4 Discussion -- 11.1.5 Conclusions -- 12 Mathematical Biomedicine and Modeling Avascular Tumor Growth -- 12.1 Continuum Models of Avascular Tumor Growth -- 12.1.1 Introduction -- 12.1.2 Diffusion-limited Models of Avascular Tumor Growth -- 12.1.3 Tumor Invasion -- 12.1.4 Multiphase Models of Avascular Tumor Growth -- 12.1.5 Conclusions -- Index.