Mathematical models with time delays are widely used to analyze the mechanisms of the immune response to viral infections and predict various therapeutic effects. Using the LCMV infection model as an example, this work describes an original computational technology for searching the bistable regimes of such models. This technology includes numerical methods for finding all possible steady states at fixed values of parameters, for tracing these states along the parameters and for analyzing their stability.

delay differential equations, virus infection models, treatment strategies, steady states, bistability, optimal disturbances

Mathematical modelling in actual problems of science and technics

Nechepurenko Yuri Mikhailovich,  ,  ИВМ РАН

Khristichenko Michael Yurievich,  ,  KIAM RAS

Grebennikov Dmitry Sergeevich,  ,  ИВМ РАН

Bocharov Gennady Alekseevich,  ,  ИВМ РАН