Control of models of virus infections with delayed variables, based on optimal disturbances

Abstract

Control of models of virus infections with delayed variables, based on optimal disturbances Abstract. A new method for constructing the multi-modal impacts on the immune system in the chronic phase of a viral infection, based on the mathematical models with delayed argument, was proposed. So called, optimal disturbances, widely used in the aerodynamic stability theory with models without delays, were proposed for perturbing the steady states of the system for maximizing the perturbation-induced response. The concept of optimal disturbances was generalized on the systems with delayed argument. An algorithm for computing the optimal disturbances was proposed for such systems. The developed technolo gy was tested using a system of four nonlinear delay-differential equations with delayed time which represents the model of experimental infection in mice caused by lymphocytic choriomeningitis virus. Steady-state perturbations causing the maximum response were computed with the proposed algorithm for two types of steady states: with low and with high level of viral load. The possibility of correction of the infection dynamics and restoration of function of virus specific lymphocytes of immune system by perturbing the steady states was demonstrated.