Global analysis of marchukʹs model in a case of weak immune system

Some special cases of Marchukʹs simplest model of an infectious disease are considered. We assume that damage to the target organ is not too large so a paralysis effect is neglected and the model reduces to three ordinary differential equations with time delay. The initial condition corresponds to a healthy organism infected by some dose of an antigen at time 0. proved that if the immune system is weak and the antigen reproduction rate is large, then the end of every infection is lethal. This means that the antigen concentration increases to infinity in time. me is true if the antigen reproduction rate is small but the initial dose of antigen is sufficiently large.