Effects of two types of noise and switching on the asymptotic dynamics of an epidemic model

This paper mainly investigates dynamics behavior of HIV (human immunodeficiency virus) infectious disease model with switching parameters, and combined bounded noise and Gaussian white noise. This model is different from existing HIV models. Based on stochastic Itô lemma and Razumikhin-type approach, some threshold conditions are established to guarantee the disease eradication or persistence. Results show that the smaller amplitude of bounded noise and R¯₀ < 1 can cause the disease to die out; the disease becomes persistent if R₀ > 1. Moreover, it is found that larger noise intensity suppresses the prevalence of the disease even if R₀ > 1. Some numerical examples are given to verify the obtained results.