Global threshold dynamics of a stochastic epidemic model incorporating media coverage

• Published in: Advances in difference equations Vol. 2018; no. 1; pp. 1 - 14
• Main Authors: Yang, Bin, Cai, Yongli, Wang, Kai, Wang, Weiming
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 12.12.2018; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Basic reproduction number; Computer simulation; Difference and Functional Equations; Disease control; Epidemics; Feller’s test; Fokker–Planck equations; Functional Analysis; Invariant density; Mathematical models; Mathematics; Mathematics and Statistics; Media coverage; Noise intensity; Ordinary Differential Equations; Partial Differential Equations; Stochastic models; Fokker–Planck equations; Basic reproduction number; Invariant density; 92D30; 60H10; 93E15; Feller’s test
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-018-1925-z

In this paper, we investigate the global threshold dynamics of a stochastic SIS epidemic model incorporating media coverage. We give the basic reproduction number R 0 s and establish a global threshold theorem by Feller’s test: if R 0 s ≤ 1 , the disease will die out a.s.; if R 0 s > 1 , the disease will persist a.s. In the case of R 0 s > 1 , we prove the existence, uniqueness, and global asymptotic stability of the invariant density of the Fokker–Planck equations associated with the stochastic model. Via numerical simulations, we find that the average extinction time decreases with the increase of noise intensity σ , and also find that the increasing σ will be beneficial to control the disease spread. Thus, in order to control the spread of the disease, we must increase the intensity of noise σ .