Most probable trajectories in a two-dimensional tumor-immune system under stochastic perturbation

This paper investigates the most probable trajectories of the stochastic two-dimensional tumor-immune system. It is worth mentioning that the most probable trajectories are a deterministic indicator for researching stochastic systems, and its role is analogous to the phase diagram and time history diagram of deterministic systems. Firstly, the effects of system parameters on dynamical behavior of the deterministic system are analyzed. Next, the stochastic system is introduced to explore the most probable trajectories under the known initial conditions and boundary conditions. Finally, given initial conditions, we can conclude that the tumor growth rate and the immune cell death rate (greater than 0.1) suppress the extinction of tumor cells, while the source rate of the immune cell and the stochastic parameters facilitate tumor cells apoptosis, which is beneficial to host health. Further, the stochastic parameters are also conducive to health under the known boundary conditions, which is exactly what we expect.