An integer-order SIS epidemic model having variable population and fear effect: comparing the stability with fractional order
Tóm tắt
Từ khóa
Tài liệu tham khảo
Hamer, W.: Epidemic diseases in England- the evidence of variability and of persistency of type. Lancet 1, 733–739 (1906)
Ross, R.: The Prevention of Malaria. John Murray, London (1911)
Kermack, W., McKendric, A.: A contribution to the mathematical theory of epidemics. P. Roy. Soc. Long A Mat. 115, 700–721 (1927)
Hethcote, H.W., Yorke, J.A.: Gonorrhea-1 transmission dynamics and control. Lecture Notes in Biomathematics, Springer-Verlag, Berlin, 56 (1984)
Busenberg, S., Cooke, K.L.: Vertically Transmitted Diseases, Biomathematics, vol. 23. Springer-Verlag, Berlin (1993)
Zhang, J., Sun, J.: Stability analysis of an SIS epidemic model with feedback mechanism on networks. Phys. A 39, 24–32 (2014)
El-Saka, H. A. A.: The fractional-order SIS epidemic model with variable population. J. Egypt. Math. Soc. 22(1), 50–54 (2014)
Zhang, X., Jiang, D., Hayat, T., Ahmad, B.: Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps. Phys. A Stat. Mech. Appl. 471, 767–777 (2017)
Liu, N., Fang, J., Deng, W., Sun, J.W.: Stability analysis of a fractional-order SIS model on complex networks with linear treatment function. Adv. Differ. Equ. 1-10 (2019)
Wang, Y., Cao, J., Alofi, A., Al-Mazrooei, A., Elaiw, A.: Revisiting node-based SIR models in complex networks with degree correlations. Phys. A 437, 75–88 (2015)
Huo, J.-J., Zhao, H.-Y.: Dynamical analysis of a fractional SIR model with birth and death on heterogeneous complex networks. Phys. A 448, 41–45 (2016)
Zhou, J. S.: An SIS disease transmission model with recruitment-birth-death emographics. Math. Compzlt. Model. 21(11), 1–11 (1995)
Li, J., Ma, Z.: Qualitative analyses of SIS epidemic model with vaccination and varying total population size. Math. Comput. Model. 20, 1235–43 (2002)
Funk, S., Marcel, S., Vincent, A.A.J.: Modelling the influence of human behaviour on the spread of infectious diseases a review. J. Royal Soc. Interface 7, 1247–56 (2010)
Polgar, S.: Health and human behavior : areas of interest common to the social and medical sciences. Curr. Anthropol. 3(2), 159–205 (1962)
Morse, S.S.: Factors in the emergence of infectious diseases. In: Plagues and pol- itics, pp. 8-26. Palgrave Macmillan (2001)
World Heath Organization Severe acute respiratory syndrome. Accessed 27 Jan 2010
Johnston, A.C., Warkentin, M.: Fear appeals and information security behaviour: an empirical study. MIS Q. 34, 549–66 (2010)
Wang, X., Zanette, L., Zou, X.: Modelling the fear effect in predator-prey interactions. J. Math. Biol. 73(5), 1–26 (2016)
Wang, X., Zou, X.: Modeling the fear effect in predator-prey interactions with adaptive avoidance of predators. Bull. Math. Biol. 79(6), 1–35 (2017)
Zhang, J., Song, X., Saka, El.: Analysis of an SEIR epidemic model with saturated incidence and saturated treatment function. Sci. World J. 1-11(2014)
Capasso, V., Serio, G.: A generalization of the Kermack-Mckendrick deterministic epidemic model. Math. Biosci. 42(1–2), 43–61 (1978)
El.Saka, H. A. A.: Backward bifurcations in fractional order vaccination models. J. Egypt. Math. Soc. 23(1), 49–55 (2015)
Ameen, P.: Novati, The solution of fractional order epidemic model by implicit Adams methods. J. Appl. Math. Model. 43, 78–84 (2017)
Banerjee, S.K.: Analysis of fractional order SIS epidemic with constant recruitment rate and variable population size. ASIO-JCPMAS 1(2), 1–4 (2016)
Chen, C., Kang, Y.: Dynamics of a Stochastic SIS epidemic model with saturated incidence. Abstr. Appl. Anal. (2014). https://doi.org/10.1155/2014/723825
Diethelm, K., Ford, N.J.: Analysis of fractional differential equation. J. Math. Anal. Appl. 265, 229–248 (2002)
Jing, H.Z., Yan, C.H., Zhidong, T.: Dynamical analysis of a fractional-order predator-prey model incorporating a prey refuge. J. Appl. Math. comput. 54, 435–449 (2015)
Odibat, Z., Shawagfeh, N.: Generalised Taylors formula. Appl. Math. comput. 186, 286–293 (2007)
Matington, D.: Stability result on fractional differential equations with application to control processing, In: IMACS-SMC proceeding, Lille, France, 963–968 (1996)
Petras, I.: Fractional-Order Nonlinear Systems: Modelling, Analysis and Simulation. Springer, Beijing (2011)
Birkhoff, G., Rota, G.C.: Ordinary Differential Equation. Ginn, Boston (1982)