The objective of this study is to investigate a stochastic SIR epidemic model incorporating a mean-reverting Ornstein–Uhlenbeck process and individual heterogeneity. Initially, we establish the global existence and positivity of a solution within the model through the application of Lyapunov functions. Subsequently, we delve into the dynamical behavior of the SIR model. Our research reveals that increased noise intensity, a slower reversion rate, and positive individual behavior collaboratively contribute to the mitigation of infection outbreaks.
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Song et al. (2024) studied this question.
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