In this paper, we extend a nutrient-phytoplankton model with viral infection from a deterministic model to a stochastic model by introducing white noise and color noise. We analyze this model mainly from the perspectives of mathematics and biology. Mathematically, we get a critical value. In the case of low white noise intensity, if this critical value is less than one, the infected phytoplankton tend to die out exponentially. If this critical value is greater than one, the infected phytoplankton is persistent in mean and the solution of system is positive recurrent. From a biological standpoint, we show that white noise may have negative effect on population survival, while Markov chain can balance the different survival states of the population and increase its survival probability, which can provide effective measures to control the infected phytoplankton and ensure the stationary distribution of the population in reality.

在本文中，我们通过引入白噪声和色噪声将具有病毒感染的营养性浮游植物模型从确定性模型扩展到随机模型。我们主要从数学和生物学的角度分析此模型。从数学上讲，我们获得了至关重要的价值。在低白噪声强度的情况下，如果该临界值小于1，则受感染的浮游植物趋向于指数灭绝。如果该临界值大于1，则受感染的浮游植物的平均值将持续存在，并且系统的求解将是正循环的。从生物学的角度来看，我们表明白噪声可能会对种群生存产生负面影响，而马尔可夫链可以平衡种群的不同生存状态并增加其生存概率，