Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number \({\mathcal{R}}_{0}^{s}\) for the stochastic model which is smaller than \({\mathcal{R}}_{0}\) of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. Our findings show that white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can occur due to the existence of feedback time-delay (or memory) in the transmission terms.

湿度、降水和温度等环境因素对新毒株冠状病毒 COVID-19 在人类中的传播具有重大影响。在本文中，我们使用随机流行病 SIRC 模型来计算 COVID-19 的传播，该模型具有交叉免疫类别和传播时间延迟。我们分析了模型并证明了全局正解的存在性和唯一性。我们推导出随机模型的基本再生数\({\mathcal{R}}_{0}^{s}\)，该再生数小于\({\mathcal{R}}_{0}\)相应的确定性模型。使用随机李亚普诺夫函数，获得了保证唯一遍历平稳分布存在的充分条件，以及疾病灭绝的条件。我们的研究结果表明，白噪声在控制疾病传播方面发挥着重要作用。当白噪声较大时，传染病就会灭绝；当白噪声较大时，传染病就会灭绝；由于传播条件中反馈时间延迟（或记忆）的存在，可能会发生再次感染和周期性爆发。