The study of infectious diseases in humans has become increasingly important in public health. This paper extends the SEIR model to include unreported COVID-19 cases (U) and environmental white noise. Dynamic analysis is conducted based on the variation of the environment. The ergodicity and stationary distribution criteria are discussed. Using a Lyapunov function, we write down some sufficient conditions for disease extinction. With different intensities of stochastic noises, we calculate the threshold of extinction for the stochastic epidemic system. In order to control the spread of disease, the stochastic noise plays an important role. A numerical simulation and a fit to real data have shown that the model and theoretical results are valid.
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Rihan et al. (2024) studied this question.
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