The ACE2 receptor protein-mediated SARS-CoV-2 infection: dynamic properties of a novel delayed stochastic system

We investigated the dynamic effect of stochastic environmental fluctuations on the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus infection system with time delay and mediations by the angiotensin-converting enzyme 2 (ACE2) receptor protein. First, we discussed the existence and uniqueness of global positive solutions as well as the stochastic ultimate boundedness of the stochastic SARS-CoV-2 model. Second, the asymptotic properties of stochastic time-delay system were investigated by constructing a number of appropriate Lyapunov functions and applying differential inequality techniques. These properties indicated a positive relationship between the strength of oscillations and the intensity of environmental fluctuations, and this launched the properties of a deterministic system. When the random disturbance was relatively large, the disease went extinct. When the random disturbance was relatively small and $R_0<1$, the disease could become extinct. Conversely, when the random disturbance was smaller and $R_0>1$, then it would oscillate around the disease enduring equilibrium. At last, a series of numerical simulations were carried out to show how the SARS-CoV-2 system was affected by the intensity of environmental fluctuations and time delay.