Mathematical Modelling of Immune Response in Infectious Diseases

Abstract

This is the first monograph to present a unified approach to using mathematical models in the study of qualitative and quantitative regularities of immune response dynamics in infectious diseases within individual organisms. These mathematical models are formulated as systems of delay- differential equations. Simple mathematical models of infectious diseases, antiviral immune response and antibacterial response were developed and applied to the study of hepatitis B, influenza A, infectious bacterial pneumonia, and mixed infections. Particular attention was paid to the development of efficient computational procedures for solving the initial value problem for stiff delay-differential equations and to the parameter identification problem. Adjoint equations and the perturbation theory were used for the sensitivity analysis. Audience: This book will be of interest to a wide range of mathematicians and specialists in immunology and infectious diseases. It can also be recommended as a textbook for postgraduate students, bridging the gap between mathematics, immunology and infectious diseases research. 1. General Knowledge, Hypotheses, and Problems -- 2. Survey of Mathematical Models in Immunology -- 3. Simple Mathematical Model of Infectious Disease -- 4. Mathematical Modeling of Antiviral and Antibacterial Immune Responses -- 5. Identification of Parameters of Models -- 6. Numerical Realization Algorithms for Mathematical Models -- 7. Viral Hepatitis B -- 8. Viral and Bacterial Infections of Respiratory Organs -- 9. Model of Experimental Influenza Infection -- 10. Adjoint Equations and Sensitivity Study for Mathematical Models of Infectious Diseases.