Dynamical behavior of a stochastic cholera model with differential
infectivity and regime switching
AbstractIn this paper, we study a stochastic cholera model with differential
infectivity which is disturbed by both white noise and telegraph noise.
Firstly, we prove that there exists a unique global positive solution to
the system with any positive initial value. Then we obtain sufficient
criteria for extinction of the diseases. Finally, we establish
sufficient criteria for the existence and uniqueness of an ergodic
stationary distribution of the positive solutions to the model by
constructing a suitable stochastic Lyapunov function with regime
switching. The stationary distribution implies that all the individuals
can coexist and persist in the long term.