Narrow Results

Some special cases of Marchuk's model of an infectious disease are studied. A paralysis effect is neglected, and the model reduces to 3 ordinary differential equations with time delay and initial data corresponding to a healthy organism infected by some dose of the antigen at time 0. It is proved that, if the immune system is very strong and the antigen reproduction rate is not too large, then every solution has a finite limit, which is equal to the stationary state describing the healthy organism. If the antigen reproduction rate is large, then all solutions have average values equal to the values corresponding to the chronic form of the disease.

Some generalizations of Marchuk's model of an infectious disease with respect to the role of interleukins are presented in this paper. Basic properties of the models are studied. Results of numerical simulations with different coefficients corresponding to the different forms of the disease are shown.