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Articles

A stochastic SACR epidemic model for HBV transmission

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Pages 788-801 | Received 29 Jan 2020, Accepted 29 Sep 2020, Published online: 19 Oct 2020

References

  • L.J.S. Allen, An introduction to stochastic epidemic models, in Mathematical Epidemiology, F. Brauer, P. van den Driessche, J. Wu, eds., Springer, Berlin, Heidelberg, 2008, pp. 81–130
  • J.R. Beddington and R.M. May, Harvesting natural populations in a randomly fluctuating environment, Science 197 (1977), pp. 463–465. doi: 10.1126/science.197.4302.463
  • T. Britton and D. Lindenstrand, Epidemic modelling: aspects where stochastic epidemic models: a survey, Math. Biosci. 222 (2010), pp. 109–116. doi: 10.1016/j.mbs.2009.10.001
  • Y. Cai, Y. Kang, M. Banerjee, and W. Wang, A stochastic epidemic model incorporating media coverage, Commun. Math. Sci. 14 (2016), pp. 892–910. doi: 10.4310/CMS.2016.v14.n4.a1
  • N. Dalal, D. Greenhalgh, and X. Mao, A stochastic model for internal HIV dynamics, J. Math. Anal. Appl. 341 (2008), pp. 1084–1101. doi: 10.1016/j.jmaa.2007.11.005
  • W.J. Edmunds, G.F. Medley, and D.J. Nokes, The transmission dynamics and control of hepatitis B virus in the Gambia, Stat. Medic 15 (1996), pp. 2215–2233. doi: 10.1002/(SICI)1097-0258(19961030)15:20<2215::AID-SIM369>3.0.CO;2-2
  • A. Gray, D. Greenhalgh, L. Hu, X. Mao, and J. Pan, A stochastic differential equation SIS epidemic model, SIAM J. Appl. Math. 71 (2011), pp. 876–902. doi: 10.1137/10081856X
  • Q. Han, L. Chen, and D. Jiang, A note on the stationary distribution of stochastic SEIR epidemic model with saturated incidence rate, Sci. Rep. 7(1) (2017), p. 3996. doi: 10.1038/s41598-017-03858-8
  • C. Ji and D. Jiang, Threshold behaviour of a stochastic SIR model, Appl. Math. Model. 38 (2014), pp. 5067–5079. doi: 10.1016/j.apm.2014.03.037
  • T. Khan, I.H. Jung, and G. Zaman, A stochastic model for the transmission dynamics of hepatitis B virus, J. Biol. Dyn. 13(1) (2019), pp. 328–344. doi: 10.1080/17513758.2019.1600750
  • T. Khan, A. Khan, and G. Zaman, The extinction and persisitence of the stochastic hepatitis B epidemic model, Chaos. Sol. Fractals 108 (2018), pp. 123–128. doi: 10.1016/j.chaos.2018.01.036
  • T. Khan and G. Zaman, Classification of different hepatitis B infected individuals with saturated incidence rate, SpringerPlus. 5 (2016), pp. 1082. doi: 10.1186/s40064-016-2706-3
  • T. Khan, G. Zaman, and M.I. Chohan, The transmission dynamic and optimal control of acute and chronic hepatitis B, J. Biol. Dyn. 11 (2017), pp. 172–189. doi: 10.1080/17513758.2016.1256441
  • A. Lahrouz and L. Omari, Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence, Stat. Prob. Lett. 83 (2013), pp. 960–968. doi: 10.1016/j.spl.2012.12.021
  • Q. Lu, Stability of SIRS system with random perturbations, Phys. A Stat. Mech. Appl. 388 (2009), pp. 3677–3686. doi: 10.1016/j.physa.2009.05.036
  • J. Mann and M. Roberts, Modelling the epidemiology of hepatitis B in New Zealand, J. Theor. Biol. 269 (2011), pp. 266–272. doi: 10.1016/j.jtbi.2010.10.028
  • A. Mwasa and J.M. Tchuenche, Mathematical analysis of a cholera model with public health interventions, Biosystems 105 (2011), pp. 190–200. doi: 10.1016/j.biosystems.2011.04.001
  • B. Øksendal, Stochastic Differential Equations, Springer, Berlin, Heidelberg, 2003.
  • J. Pang, J.A. Cui, and X. Zhou, Dynamical behavior of a hepatitis B virus transmission model with vaccination, J. Theor. Biol. 265 (2010), pp. 572–578. doi: 10.1016/j.jtbi.2010.05.038
  • S. Thornley, C. Bullen, and M. Roberts, Hepatitis B in a high prevalence New Zealand population: a mathematical model applied to infection control policy, J. Theor. Biol. 254 (2008), pp. 599–603 doi: 10.1016/j.jtbi.2008.06.022
  • J.E. Truscott and C.A. Gilligan, Response of a deterministic epidemiological system to a stochastically varying environment, Proc. Nat. Acad. Sci. 100 (2003), pp. 9067–9072. doi: 10.1073/pnas.1436273100
  • F. Wei and C. Fangxiang, Stochastic permanence of an SIQS epidemic model with saturated incidence and independent random perturbations, Phys. A Stat. Mech. Appl. 453 (2016), pp. 99–107. doi: 10.1016/j.physa.2016.01.059
  • M. Zahri, Multidimensional Milstein scheme for solving a stochastic model for prebiotic evolution, Jou. Tai. Uni. Sci. 8(2) (2014), pp. 186–198. doi: 10.1016/j.jtusci.2013.12.002
  • M. Zahri, Barycentric interpolation of interface-solution for solving SPDEs on non-overlapping subdomains with additive multi-noises, Inter. J. Comp. Math. 95(4) (2018), pp. 645–685. doi: 10.1080/00207160.2017.1297429
  • G. Zaman, Y.H. Kang, and I.H. Jung, Stability analysis and optimal vaccination of an SIR epidemic model, BioSystems 93(3) (2008), pp. 240–249. doi: 10.1016/j.biosystems.2008.05.004
  • T. Zhang, K. Wang, and X. Zhang, Modeling and analyzing the transmission dynamics of HBV epidemic in Xinjiang, China, PLoS One 10 (2015), p. e0138765. doi: 10.1371/journal.pone.0138765
  • Y. Zhao, D. Jiang, and D. O'Regan, The extinction and persistence of the stochastic SIS epidemic model with vaccination, Phys. A Stat. Mech. Appl. 392 (2013), pp. 4916–4927. doi: 10.1016/j.physa.2013.06.009
  • S. Zhao, Z. Xu, and Y. Lu, A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in China, Int. J. Epidemiol. 29 (2000), pp. 744–752. doi: 10.1093/ije/29.4.744
  • Y. Zhao, Q. Zhang, and D. Jiang, The asymptotic behavior of a stochastic SIS epidemic model with vaccination, Adv. Diff. Equ. 2015(1) (2015), pp. 328. doi: 10.1186/s13662-015-0592-6
  • Y. Zhou, W. Zhang, and S. Yuan, Survival and stationary distribution of a SIR epidemic model with stochastic perturbations, Appl. Math. Comput. 244 (2014), pp. 118–131.
  • L. Zou, W. Zhang, and S. Ruan, Modeling the transmission dynamics and control of hepatitis B virus in China, J. Theor. Biol. 262 (20100), pp. 330–338. doi: 10.1016/j.jtbi.2009.09.035
  • L. Zou, W. Zhang, and S. Ruan, Modeling the transmission dynamics and control of hepatitis B virus in China, J. Theor. Biol. 262 (2010), pp. 330–338. doi: 10.1016/j.jtbi.2009.09.035