Abstract
In this paper, we develop a mathematical model of viral infection of monocytes population by dengue virus with immune response which is perturbed by both white and telegraph noises. By constructing a suitable stochastic Lyapunov function with regime switching, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. The existence of a stationary distribution implies stochastic weak stability.
•A stochastic dengue infection model with immune response and regime switching is studied.•We establish sufficient conditions for the existence of a unique ergodic stationary distribution.•The existence of a stationary distribution implies stochastic weak stability.