Mathematical Modeling of Antiviral and Antibacterial Immune Responses

Abstract

We shall construct in this chapter the model of viral disease developed by Marchuk and Petrov [200] on the basis of recent advances in immunology. The cytotoxic action of T-lymphocytes against infected cells has been used as the main point of the model that describes pathological changes in an organism. The destruction of an organism’s cells is the essential mechanism of recovery from infection. As for a viral population which gets into lymph and blood plasma from infected cells, it seems to be largely neutralized by the immunoglobulins with further elimination of viruses from organism. Severity of the course of disease, in the context of this model, depends on the degree of damage to target organ caused by viruses, and on the effectiveness of immune response. A modification of the mathematical model of antiviral response will also be considered. This model takes into account local immunophysiological mechanisms of action of cytotoxic T-cells and antibodies in a target organ affected by a virus, which are connected with the oedema development and changes in the circulation of blood in the organ. This modification of the model has been developed by Marchuk in collaboration with Petrov [201].