Abstract
In this paper, the dynamic behavior of a class of hybrid SIRS model with nonlinear incidence is studied. Firstly, we provide the condition under which the positive recurrence exists and then give the threshold R 0 S for disease extinction, that is, when R 0 S < 1 , the disease will die out. Finally, some examples are constructed to verify the conclusion.
Highlights
Disease is one of the most dangerous enemies of human beings
White noise depicted by Brownian motion and telegraph noise characterized by continuous time Markov chain are two important types of noise
Some scholars have studied the effect of Le vy noise on epidemic models [20, 21]
Summary
Disease is one of the most dangerous enemies of human beings. COVID-19 has spread throughout the world since the end of 2019 and brought great harm to people’s life and global economy. Because of its importance and rich research content, different scholars have used various methods to study dynamical behavior and properties of epidemic models, such as persistence and extinction [1,2,3,4,5,6,7], stationary distribution and ergodicity [5, 8,9,10,11,12], stability [13, 14], bifurcation [15, 16], and optimal control of disease [17]. Many scholars have studied the different properties of epidemic models with white noise and Markovian switching [22,23,24,25,26], there are few studies on the positive recurrence and extinction of SIRS models with the abovementioned general incidence rate.
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