Some results connected with a simple mathematical model of infectious disease are discussed in order to demonstrate the approach to the modelling of such real processes. A more complicated model of antiviral immune response is presented. A new modification of this model in which targets for the viruses are immunocompetent ceils is suggested.
I. A Simple Model and Some Results
Here we would like to demonstrate our approach to the modeling of infectious diseases and use for this aim the simple mathematical model advanced by G.I. Marchuk [2]. And at first let us define the term 'infectious disease'. What does it mean? How do we understand it?
According to medical literature the infectious disease is regarded as expression of the relationship between two members of a biocenosis, one of which (stimulant) being capable of existing in the other owing to pathogenic mechanisms, and this other organism being capable of counteracting this pathogenic action. It is also well known that the immune system plays an important role in the defense of organisms from the infections. Based on these two points we consider the infectious disease as a conflict between multiplying pathogenic antigen and the immune system, and as a first step we distinguish the following main characteristics of a disease. 1 Concentration of viruses V(t). By viruses we mean multiplying pathogenic antigen. 2 Concentrations of antibodies F(t). By antibodies we mean the substrates of the immune system, neutralizing viruses (immunoglobulins, cell receptor, killers).