Ergodicity & dynamical aspects of a stochastic childhood disease model

摘要

The purpose of the present article is to explore dynamical aspects of a stochastic childhood diseases model. For any initial value it is shown that the Markov process of proposed model is V-geometrically ergodic. Moreover, it is found that the solutions of the underlying model are stochastically ultimately bounded and permanent for any initial conditions. Some sufficient conditions are established to show the extinction of the diseases. Also, it is shown that under some subsidiary conditions the system of stochastic differential equations is ergodic. Lastly, the effect of noise on the dynamics of model is also shown while the obtained result is illustrated graphically.