Abstract
AbstractWe propose a unified stochastic SIR model driven by Lévy noise. The model is structural enough to allow for time-dependency, nonlinearity, discontinuity, demography, and environmental disturbances. We present concise results on the existence and uniqueness of positive global solutions and investigate the extinction and persistence of the novel model. Examples and simulations are provided to illustrate the main results.
Funder
Natural Sciences and Engineering Research Council of Canada
Publisher
Springer Science and Business Media LLC
Reference27 articles.
1. Applebaum, D.: Lévy Processes and Stochastic Calculus, 2nd edn. Cambridge University Press, Cambridge (2009)
2. Bailey, N.: The Mathematical Theory of Infectious Diseases and Its Applications, 2nd edn. Griffin, London (1975)
3. Bao, J., Yuan, C.: Stochastic population dynamics driven by Lévy noise. J. Math. Anal. Appl. 391, 363–375 (2012)
4. Bezanson, J., Edelman, A., Karpinski, S., Shah Julia, V.B.: A fresh approach to numerical computing. SIAM Rev. 59, 65–98 (2017)
5. Brauer, F.: Mathematical epidemiology: past, present, and future. Infect. Dis. Model. 2, 113–127 (2017)