Mathematical Modelling of Immune Response in Infectious Diseases

This monograph aims 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 are developed and applied to the study of hepatitis B, influenza A, infectious bacterial pneumonia, and mixed infections. Particular attention is 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 are used for the sensitivity analysis. This book is aimed at mathematicians and specialists in immunology and infectious diseases. It can also be used as a textbook for postgraduate students, bridging the gap between mathematics, immunology and infectious diseases research.