Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates

Physica A: Statistical Mechanics and its Applications

Volumn 472, Issue , 2017, Pages 103-116

  Chang, Zhengbo ^a   Meng, Xinzhu ^a   Lu, Xiao ^a  

^a SHANDONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Ito's formula; Nonlinear incidence rate; Persistence in mean; Stochastic dynamics; Stochastic epidemic model

Indexed keywords

EPIDEMIOLOGY; STOCHASTIC SYSTEMS;

ITO'S FORMULA; NON-LINEAR INCIDENCE RATES; PERSISTENCE IN MEANS; STOCHASTIC DYNAMICS; STOCHASTIC EPIDEMIC MODELS;

STOCHASTIC MODELS;

EID: 85009106521     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2017.01.015     Document Type: Article

References (19)

1. [1] Priplata, A.A, Patritti, B.L., Niemi, J.B., Noise-enhanced balance control in patients with diabetes and patients with stroke. Ann. Neurology 59 (2006), 4–12.
2. [2] Bao, J., Hou, Z., Yuan, C., Stability in distribution of neutral stochastic differential delay equations with Markovian switching. Statist. Probab. Lett. 79 (2009), 1663–1673.
3. [3] Meng, X.Z., Zhao, S.N., Feng, T., Zhang, T.H., Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis. J. Math. Anal. Appl. 433 (2016), 227–242.
4. [4] Muroya, Y., Enatsu, Y., Kuniya, T., Global stability for a multi-group SIRS epidemic model with varying population sizes. Nonlinear Anal. RWA 14 (2013), 1693–1704.
5. [5] Zhao, Y.N., Jiang, D.Q., ORegan, Donal, The extinction and persistence of the stochastic SIS epidemic model with vaccination. Physica A 392 (2013), 1135–1143.
6. [6] Zhou, Y.L., Yuan, S.L., Zhao, D.L., Threshold behavior of a stochastic SIS model with levy jumps. Appl. Math. Comput. 275 (2016), 255–267.
7. [7] Kermazk, W.O., Mckendrick, A.G., A contribution to the mathematical theory of epidemic. Proc. R. Soc. Lond. All. 5 (1927), 700–721.
8. [8] Liu, Q., Chen, Q.M., Jiang, D.Q., The threshold of a stochastic delayed SIR epidemic model with temporary immunity. Physica A 450 (2016), 115–125.
9. [9] Han, L.T., Ma, Zhien, Shi, T., An SIRS epidemic model of two competitive species. Math. Comput. Modelling 37 (2003), 87–108.
10. [10] Muroya, Y., Kuniya, T., Further stability analysis for a multi-group SIRS epidemic model with varying total population size. Appl. Math. Lett. 38 (2014), 73–78.
11. [11] Song, Z.G., Xu, J., Li, Q.H., Local and global bifurcations in an SIRS epidemic model. Appl. Math. Comput. 214 (2009), 534–547.
12. [12] Liu, W.M., Levin, S.A., Iwasa, Y., Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J. Math. Biol. 23 (1986), 187–204.
13. [13] Zhao, Y.N., Jiang, D.Q., The threshold of a stochastic SIRS epidemic model with saturated incidence. Appl. Math. Lett. 34 (2014), 90–93.
14. [14] Liu, Q., Chen, Q.M., Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence. Physica A 428 (2015), 140–153.
15. [15] Meng, X.Z., Stability of a novel stochastic epidemic model with double epidemic hypothesis. Appl. Math. Comput. 217 (2010), 506–515.
16. [16] Meng, X.Z., Li, Z.Q., Wang, X.L., Dynamics of a novel nonlinear SIR model with double epidemic hypothesis and impulsive effects. Nonlinear Dynam. 59 (2010), 503–513.
17. [17] Kuniya, T., Global stability of a multi-group SVIR epidemic model. Nonlinear Anal. RWA 14 (2013), 1135–1143.
18. [18] Mao, X., Stochastic Differential Equations and Applications, second ed., 2008, Horwood, Chichester, UK.
19. [19] Xu, C.Q., Yuan, S.L., An analogue of break-even concentration in a simple stochastic chemostat model. Appl. Math. Lett. 48 (2015), 62–68.