Stochastic HIV-1 infection model with time delay: case study of clinical data

This paper proposes an immunosuppressive infection model with time delay and stochastic perturbation. A stochastic threshold <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mi>s</mml:mi></mml:msubsup></mml:math> is constructed, and the sufficient conditions for virus extinction and weak persistence are given. Subsequently, we respectively fit the SDDE and ODE models to the real data, and conduct a sensitivity analysis of the equilibrium. The greater the noise intensity, the more obvious the oscillation amplitude of the solution curve around the immune-free equilibrium, the larger noise intensity can cause the originally persistent virus in ODE to go extinct in the SDDE model. The greater the time delay, the longer it takes for the virus and immune cells to reach their first peaks. The viral replication rate significantly affects the virus-immune system, and the reproduction of HIV-1 can be inhibited by modulating it. A relatively high viral inhibition rate will lead to the extinction of immune cells while the virus persists.