Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence

Physica A: Statistical Mechanics and its Applications

Volumn 462, Issue , 2016, Pages 870-882

  Liu, Qun ^a,b   Jiang, Daqing ^a,c,d   Shi, Ningzhong ^a   Hayat, Tasawar ^c,e   Alsaedi, Ahmed ^c  

^a NORTHEAST NORMAL UNIVERSITY   (China)

^b YULIN NORMAL UNIVERSITY   (China)

^c KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^d CHINA UNIVERSITY OF PETROLEUM   (China)

^e QUAID I AZAM UNIVERSITY   (Pakistan)

Author keywords

Lyapunov function; Nonlinear incidence; Stochastic SEIR epidemic model; Time delays

Indexed keywords

ASYMPTOTIC ANALYSIS; LYAPUNOV FUNCTIONS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; TIME DELAY;

ASYMPTOTIC BEHAVIORS; DISEASE-FREE EQUILIBRIUM; ENDEMIC EQUILIBRIUM; NONLINEAR INCIDENCE; POSITIVE SOLUTION; SEIR EPIDEMIC MODELS;

EPIDEMIOLOGY;

EID: 84978863550     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2016.06.095     Document Type: Article

References (36)

1. [1] Anderson, R., May, R., Population biology of infectious diseases: Part I. Nature 280 (1979), 361–367.
2. [2] Capasso, V., Mathematical Structure of Epidemic Systems Lect. Notes in Biomath., vol. 97, 1993, Springer, Berlin.
3. [3] Hethcote, H., Tudor, D., Integral equation models for endemic infectious diseases. J. Math. Biol. 9 (1980), 37–47.
4. [4] Huo, H., Ma, Z., Dynamics of a delayed epidemic model with non-monotonic incidence rate. Commun. Nonlinear Sci. Numer. Simul. 15 (2010), 459–468.
5. [5] McCluskey, C., Complete global stability for an SIR epidemic model with delay-Distributed or discrete. Nonlinear Anal. RWA 11 (2010), 55–59.
6. [6] Xiao, D., Ruan, S., Global analysis of an epidemic model with nonmonotone incidence rate. Math. Biosci. 208 (2007), 419–429.
7. [7] Xu, R., Ma, Z., Stability of a delayed SIRS epidemic model with a nonlinear incidence rate. Chaos Solitons Fractals 41 (2009), 2319–2325.
8. [8] Xu, R., Ma, Z., Global stability of a SIR epidemic model with nonlinear incidence rate and time delay. Nonlinear Anal. RWA 10 (2009), 3175–3189.
9. [9] Muroya, Y., Enatsu, Y., Nakata, Y., Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate. J. Math. Anal. Appl. 377 (2011), 1–14.
10. [10] Enatsu, Y., Messina, E., Muroya, Y., Nakata, Y., Russo, E., Vecchio, A., Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates. Appl. Math. Comput. 218 (2012), 5327–5336.
11. [11] Ma, W., Song, M., Global stability of an SIR Epidemic Model with Time Delay. Appl. Math. Lett. 17 (2004), 1141–1145.
12. [12] Zhang, T., Teng, Z., Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence. Chaos Solitons Fractals 37 (2008), 1456–1468.
13. [13] Cooke, K., Van Den Driessche, P., Analysis of an SEIRS epidemic model with two delays. J. Math. Biol. 35 (1996), 240–260.
14. [14] Kyrychko, Y., Blyuss, K., Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate. Nonlinear Anal. 6 (2005), 495–507.
15. [15] Kuang, Y., Delay Differential Equations with Applications in Population Dynamics. 1993, Academic Press, New York.
16. [16] Beretta, E., Takeuchi, Y., Global stability of an SIR epidemic model with time delays. J. Math. Biol. 33 (1995), 250–260.
17. [17] Cooke, K., Stability analysis for a vector disease model. Rocky Mountain J. Math. 9 (1979), 31–42.
18. [18] Capasso, V., Serio, G., A generalization of the Kermack–Mckendrick deterministic epidemic model. Math. Biosci. 42 (1978), 43–61.
19. [19] Korobeinikov, A., Global properties of infectious disease models with nonlinear incidence. Bull. Math. Biol. 69 (2007), 1871–1886.
20. [20] Artalejo, J., Economou, A., Lopez-Herrero, M., The stochastic SEIR model before extinction: Computational approaches. Appl. Math. Comput. 265 (2015), 1026–1043.
21. [21] Witbooi, P., Stability of an SEIR epidemic model with independent stochastic perturbations. Physica A 392 (2013), 4928–4936.
22. [22] Yang, Q., Jiang, D., Shi, N., Ji, C., The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence. J. Math. Anal. Appl. 388 (2012), 248–271.
23. [23] Zhang, X., Wang, K., Stochastic SEIR model with jumps. Appl. Math. Comput. 239 (2014), 133–143.
24. [24] Zhou, Y., Zhang, W., Yuan, S., Survival and stationary distribution of a SIR epidemic model with stochastic perturbations. Appl. Math. Comput. 244 (2014), 118–131.
25. [25] Lahrouz, A., Settati, A., Necessary and sufficient condition for extinction and persistence of SIRS system with random perturbation. Appl. Math. Comput. 233 (2014), 10–19.
26. [26] Yang, Q., Mao, X., Extinction and recurrence of multi-group SEIR epidemic models with stochastic perturbations. Nonlinear Anal. RWA 14 (2013), 1434–1456.
27. [27] Liu, Q., Chen, Q., Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence. Physica A 428 (2015), 140–153.
28. [28] Liu, M., Bai, C., Wang, K., Asymptotic stability of a two-group stochastic SEIR model with infinite delays. Commun. Nonlinear Sci. Numer. Simul. 19 (2014), 3444–3453.
29. [29] Yuan, C., Jiang, D., O'Regan, D., Agarwal, R., Stochastically asymptotically stability of the multi-group SEIR and SIR models with random perturbation. Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 2501–2516.
30. [30] Arnold, L., Horsthemke, W., Stucki, J., The influence of external real and white noise on the Lotka–Volterra model. J. Biomed. 21 (1979), 451–471.
31. [31] Lahrouz, A., Omari, L., Kiouach, D., Belmaâti, A., Complete global stability for an SIRS epidemic model with generalized non-linear incidence and vaccination. Appl. Math. Comput. 218 (2012), 6519–6525.
32. [32] Zhu, C., Yin, G., Asymptotic properties of hybrid diffusion systems. SIAM J. Control Optim. 46 (2007), 1155–1179.
33. [33] Lin, Y., Jiang, D., Wang, S., Stationary distribution of a stochastic SIS epidemic model with vaccination. Physica A 394 (2014), 187–197.
34. [34] Zhao, Y., Jiang, D., The threshold of a stochastic SIS epidemic model with vaccination. Appl. Math. Comput. 243 (2014), 718–727.
35. [35] Jiang, D., Yu, J., Ji, C., Shi, N., Asymptotic behavior of global positive solution to a stochastic SIR model. Math. Comput. Modelling 54 (2011), 221–232.
36. [36] Mao, X., Stochastic Differential Equations and Applications. 1997, Horwood Publishing, Chichester.