Abstract <p>This work is devoted to optimal disturbances of stationary and periodic solutions to systems of delay differential equations, their computation, and use in mathematical immunology. Original methods for computing the stationary and periodic solutions themselves and tracing them along the system parameters, as well as methods for computing optimal disturbances for these solutions are briefly described. The performance of the described methods is demonstrated using the example of the well-known Marchuk–Petrov model of the antiviral immune response with parameter values corresponding to the infection caused by hepatitis B viruses.</p>