Dynamic Behavior and State Feedback Control of Hybrid Stochastic Infectious Disease System with Virus Concentration Perturbation

A stochastic hybrid dynamic system with infectious diseases in prey population was constructed, where the influence of random disturbances on virus concentration in the environment is considered. The uniqueness and boundedness of the global positive solution of the system were discussed, and the bifurcation behavior of the system around the positive equilibrium point was studied. A state feedback controller was designed to eliminate singular induced bifurcation. By solving the basic regeneration number and conducting sensitivity analysis, the combined influence of parameters on the basic regeneration number is studied. The asymptotic dynamical behavior around the interior equilibrium under stochastic perturbations are investigated. Numerical simulations are carried out to show consistency with theoretical analysis.