Abstract
In this paper, a novel influenza SINIRR model with white noise is investigated. According to the research, white noise has a significant impact on the disease. First, we explain that there is global existence and positivity to the solution. Then we show that the stochastic basic reproduction <(R) under dot>(r) is a threshold that determines whether the disease is cured or persists. When the noise intensity is high, we get <(R) under dot>(r) < 1 and the disease goes away; when the white noise intensity is low, we get <(R) under dot>(r) > 1, and a sufficient condition for the existence of a stationary distribution is obtained, which suggests that the disease is still there. However, the main objective of the study is to produce a stochastic analogue of the deterministic model that we analyze using numerical simulations to get views on the infection dynamics in a stochastic environment that we can relate to the deterministic context.