Generalization of the Antiviral Immune Response Model for Complex Consideration of Diffusion Perturbations, Body Temperature Response, and Logistic Antigen Population Dynamics

The Marchuk–Petrov mathematical model of antiviral immune response is generalized for complex consideration of diffusion perturbations, concentrated influences, body temperature response, and logistic population dynamics of viral elements and antibodies to the development of infectious disease. A step-by-step procedure for numerically asymptotic solution to the corresponding singularly perturbed problems with delays is developed. The authors present the results of computer simulation that illustrate the “model” reduction of the maximum level of antigens in the epicenter of infection due to their diffusion “scattering,” body temperature response, and logistic population dynamics of viruses on the nature of infectious disease, including the presence of concentrated sources of antigens. It is emphasized that such a systemic effect of these factors can reduce the initial supercritical concentration of antigens to a level after which their neutralization and excretion are provided by the existing level of immune protection, which is important in deciding whether to use external “therapeutic” effects.