Abstract
In this paper, we introduce two perturbations in the classical deterministic susceptible–infected–susceptible epidemic model. Greenhalgh and Gray [4] in 2011 use a perturbation on β in SIS model. Based on their previous work, we consider another perturbation on the parameter μ+γ and formulate the original model as a stochastic differential equation (SDE) with two independent Brownian Motions for the number of infected population. We then prove that our Model has a unique and bounded global solution I(t). Also we establish conditions for extinction and persistence of the infected population I(t). Under the conditions of persistence, we show that there is a unique stationary distribution and derive its mean and variance. Computer simulations illustrate our results and provide evidence to back up our theory.
Original language | English |
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Pages (from-to) | 1536-1550 |
Number of pages | 15 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 474 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Jun 2019 |
Externally published | Yes |
Keywords
- Extinction
- Independent Brownian motion
- Persistence
- SIS model
- Stationary distribution
ASJC Scopus subject areas
- Analysis
- Applied Mathematics