Abstract 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 are illustrated graphically.

中文翻译：

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随机儿童疾病模型的遍历性和动力学方面

摘要 本文的目的是探索随机儿童疾病模型的动力学方面。对于任何初始值，表明所提出模型的马尔可夫过程是 V 几何遍历的。此外，发现基础模型的解对于任何初始条件都是随机最终有界和永久的。建立了一些充分条件来表明疾病已经灭绝。还表明，在一些附属条件下，随机微分方程组是遍历的。最后，还显示了噪声对模型动力学的影响，同时以图形方式说明了所获得的结果。