Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 243, Issue -, Pages 546-558Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2014.05.136
Keywords
Lyapunov function; Random perturbations; Non-linear incidence; It(o)over-cap's formula; Stationary distribution
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Funding
- Hongliu Young Teachers of Lanzhou University of Technology [Q201313]
- NNSF of China [10961018]
- NSF for Distinguished Young Scholars of Gansu Province of China [1111RJDA003]
- Special Fund for the Basic Requirements in the Research of University of Gansu Province of China
- Development Program for HongLiu Distinguished Young Scholars in Lanzhou University of Technology
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The deterministic and stochastic SIQS models with non-linear incidence are introduced. For deterministic model, the basic reproductive rate R-0 is derived. Moreover, if R-0 <= 1, the disease-free equilibrium is globally asymptotically stable and if R-0 > 1, there exists a unique endemic equilibrium which is globally asymptotically stable. For stochastic model, sufficient condition for extinction of the disease that is regardless of the value of R-0 is presented. In addition, if the intensities of the white noises are sufficiently small and R-0 > 1, then there exists a unique stationary distribution to stochastic model. Numerical simulations are also carried out to confirm the analytical results. (C) 2014 Elsevier Inc. All rights reserved.
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