A stochastic nutrient-phytoplankton model with viral infection and Markov switching

Abstract

Abstract 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.