Mathematical modelling of immune response in infectious diseases. Transl. from Russian by G. Kontarev a. I. Sidorov.

*(English)*Zbl 0876.92015
Mathematics and its Applications (Dordrecht). 395. Dordrecht: Kluwer Academic Publishers. x, 347 p. Dfl 280.00; $ 174.00; £104.00 (1997).

The monograph describes in two main parts fundamental problems in the mathematical modelling of immun response in infectious diseases. Understanding the regularities in immune response can researchers and clinicians help to increase the procedures against antigen invasions. Models of immun response to antigens can help to formulate and to verify hypothesises with ”mathematical experiments”.

In the chapters of the first part of the book basic aspects are considered like components of immun response, immun stimulation, cellular immun response or antiviral and antibacterial immun response. The chapters of the second part discuss particular models of viral and bacterial infections, such as viral hepatitis B, infections of respiratory organs or influenca. The mathematical models are formulated in the form of systems of differential equations or delay differential equations. The treatment of related problems like parameter identification, optimal control of the spread of an infection or the sensitivity analysis of the mathematical model are also discussed. Two sections of the book are devoted to the numerical solutions of the corresponding problems, as initial value problems for delay differential equations or systems of adjoint equations. The monograph gives several hints to the mathematical approach to optimizing the treatment of chronic and hypertoxic forms of diseases.

In the chapters of the first part of the book basic aspects are considered like components of immun response, immun stimulation, cellular immun response or antiviral and antibacterial immun response. The chapters of the second part discuss particular models of viral and bacterial infections, such as viral hepatitis B, infections of respiratory organs or influenca. The mathematical models are formulated in the form of systems of differential equations or delay differential equations. The treatment of related problems like parameter identification, optimal control of the spread of an infection or the sensitivity analysis of the mathematical model are also discussed. Two sections of the book are devoted to the numerical solutions of the corresponding problems, as initial value problems for delay differential equations or systems of adjoint equations. The monograph gives several hints to the mathematical approach to optimizing the treatment of chronic and hypertoxic forms of diseases.

Reviewer: H.-P.Altenburg (Mannheim)