Geodesic
Numerical analysis of stationary solutions of systems with delayed argument in mathematical immunology
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 68 (2022) no. 4, pp. 686-703

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This work is devoted to the technology developed by the authors that allows one for fixed values of parameters and tracing by parameters to calculate stationary solutions of systems with delay and analyze their stability. We discuss the results of applying this technology to Marchuk–Petrov's antiviral immune response model with parameter values corresponding to hepatitis B infection. The presence of bistability and hysteresis properties in this model is shown for the first time.
Keywords: Marchuk–Petrov’s antiviral immune response model, delayed argument, stationary solutions, tracing by parameters, numerical experiment, hepatitis B infection, bistability, hysteresis. 
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     author = {M. Yu. Khristichenko and Yu. M. Nechepurenko and D. S. Grebennikov and G. A. Bocharov},
     title = {Numerical analysis of stationary solutions of systems with delayed argument in mathematical immunology},
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M. Yu. Khristichenko; Yu. M. Nechepurenko; D. S. Grebennikov; G. A. Bocharov. Numerical analysis of stationary solutions of systems with delayed argument in mathematical immunology. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 68 (2022) no. 4, pp. 686-703. http://geodesic.mathdoc.fr/item/CMFD_2022_68_4_a8/