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Original Articles

Media alert in an SIS epidemic model with logistic growth

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Pages 120-137 | Received 10 Aug 2015, Accepted 18 Apr 2016, Published online: 04 May 2016

References

  • R.M. Anderson, H.C. Jackson, R.M. May, and A.D.M. Smith, Population dynamics of fox rabies in Europe, Nature 289 (1981), pp. 765–771. doi: 10.1038/289765a0
  • F. Brauer, Models for the spread of universally fatal diseases, J. Math. Biol. 28 (1990), pp. 451–462. doi: 10.1007/BF00178328
  • F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, New York, 2001.
  • S. Broder and R.C. Gallo, A pathogenic retrovirus (HTLV-III) linked to AIDS, New Engl. J. Med. 311 (1984), pp. 1292–1297. doi: 10.1056/NEJM198411153112006
  • S. Busenberg and P. van den Driessche, Analysis of a disease transmission model in a population with varying size, J. Math. Biol. 28 (1990), pp. 257–270. doi: 10.1007/BF00178776
  • CDC, H1N1 Flu, Center for Disease Control and Prevention Website. Available at http://www.cdc.gov/h1n1flu/.
  • N.S. Chong and R.J. Smith, Modeling avian influenza using Filippov systems to determine culling of infected birds and quarantine, Nonlinear Anal. Real World Appl. 24 (2015), pp. 196–218. doi: 10.1016/j.nonrwa.2015.02.007
  • S. Collinson and J.M. Heffernan, Modelling the effects of media during an influenza epidemic, BMC Public Health 14 (2014), pp. 1–10. doi: 10.1186/1471-2458-14-376
  • J. Cui, Y. Sun, and H. Zhu, The impact of media on the control of infectious diseases, J. Dynam. Differential Equations 20 (2008), pp. 31–53. doi: 10.1007/s10884-007-9075-0
  • J-A. Cui, X. Tao, and H. Zhu, An SIS infection model incorporating media coverage, Rocky Mountain J. Math. 38 (2008), pp. 1323–1334. doi: 10.1216/RMJ-2008-38-5-1323
  • H.W. Hethcote, A thousand and one epidemic models, in Frontiers in Mathematical Biology, S.A. Levin, ed., Lecture Notes in Biomathematics, Vol. 100, Springer, Berlin, 1994, pp. 504–515.
  • S. Leekha, N.L. Zitterkopf, M.J. Espy, T.F. Smith, R.L. Thompson, and P. Sampathkumar, Duration of influenza: A virus shedding in hospitalized patients and implications for infection control, Infect. Control Hosp. Epidemiol. 28 (2007), pp. 1071–1076. doi: 10.1086/520101
  • Y. Liu and J-A. Cui, The impact of media coverage on the dynamics of infectious disease, Int. J. Biomath. 1 (2008), pp. 65–74. doi: 10.1142/S1793524508000023
  • R. Liu, J. Wu, and H. Zhu, Media/psychological impact on multiple outbreaks of emerging infectious diseases, Comput. Math. Methods Med. 8 (2007), pp. 153–164. doi: 10.1080/17486700701425870
  • Y. Li and J. Cui, The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), pp. 2353–2365. doi: 10.1016/j.cnsns.2008.06.024
  • Y. Li, C. Ma, and J. Cui, The effect of constant and mixed impulsive vaccination on SIS epidemic models incorporating media coverage, Rocky Mountain J. Math. 38 (2008), pp. 1437–1455. doi: 10.1216/RMJ-2008-38-5-1437
  • J. Pang and J. Cui, An SIRS epidemiological model with nonlinear incidence rate incorporating media coverage, Second International Conference on Information and Computing Science, USA, IEEE, 2009, pp. 116–119.
  • L. Perko, Differential Equations and Dynamical Systems, Springer-Verlag, New York, 1996.
  • M.S. Rahman and M.L. Rahman, Media and education play a tremendous role in mounting AIDS awareness among married couples in Bangladesh, AIDS Res. Therapy 4 (2007), pp. 1–7. doi: 10.1016/0005-7967(66)90037-4
  • S. Ruan and W. Wang, Dynamical behavior of an epidemic model with a nonlinear incidence rate, J. Differential Equations 188 (2003), pp. 135–163. doi: 10.1016/S0022-0396(02)00089-X
  • F. Schweitzer and R. Mach, The epidemics of donations: Logistic growth and power-laws, PLoS One 3 (2008), p. e1458. doi: 10.1371/journal.pone.0001458
  • A.M. Spagnuolo, M. Shillor, L. Kingsland, A. Thatcher, M. Toeniskoetter, and B. Wood, A logistic delay differential equation model for Chagas disease with interrupted spraying schedules, J. Biol. Dynam. 6 (2012), pp. 377–394. doi: 10.1080/17513758.2011.587896
  • C. Sun, W. Yang, J. Arino, and K. Khan, Effect of media-induced social distancing on disease transmission in a two patch setting, Math. Biosci. 230 (2011), pp. 87–95. doi: 10.1016/j.mbs.2011.01.005
  • J.M. Tchuenche, N. Dube, C.P. Bhunu, R.J. Smith, and C.T. Bauch, The impact of media coverage on the transmission dynamics of human influenza, BMC Public Health 11 (2011), pp. 1–16. doi: 10.1186/1471-2458-11-1
  • S.M. Tracht, S.Y. Del Valle, J.M. Hyman, and D.A. Carter, Mathematical modeling of the effectiveness of facemasks in reducing the spread of novel influenza A (H1N1), PLoS One 5 (2010), p. e9018. doi: 10.1371/journal.pone.0009018
  • V.I. Utkin, Sliding Modes in Control and Optimization, Springer-Verlag, Berlin, 1992.
  • W. Wang, Backward bifurcation of an epidemic model with treatment, Math. Biosci. 201 (2006), pp. 58–71. doi: 10.1016/j.mbs.2005.12.022
  • A. Wang and Y. Xiao, A Filippov system describing media effects on the spread of infectious diseases, Nonlinear Anal. Hybr. Syst. 11 (2014), pp. 84–97. doi: 10.1016/j.nahs.2013.06.005
  • J-J. Wang, J-Z. Zhang, and Z. Jin, Analysis of an SIR model with bilinear incidence rate, Nonlinear Anal. Real World Appl. 11 (2010), pp. 2390–2402. doi: 10.1016/j.nonrwa.2009.07.012
  • L.F. White, J. Wallinga, L. Finelli, C. Reed, S. Riley, M. Lipsitch, and M. Pagano, Estimation of the reproductive number and the serial interval in early phase of the 2009 influenza A/H1N1 pandemic in the USA, Influenza Other Respir. Viruses 3 (2009), pp. 267–276. doi: 10.1111/j.1750-2659.2009.00106.x
  • WHO, Avian influenza A(H7N9) overview, 2013. Available at http://www.who.int/influenza/human_animal_interface/influenza_h7n9/WHA_H7N9_update_KeijiFukuda_21May13.pdf?ua=1.
  • WHO, Situation Report 1 Ebola virus disease, Guinea, 2014. Available at http://www.afro.who.int/en/clusters-a-programmes/dpc/epidemic-a-pandemic-alert-and-response/sitreps/4070-sitrep-1-ebola-guinea-28-march-2014.html.
  • D. Xiao and S. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate, Math. Biosci. 208 (2007), pp. 419–429. doi: 10.1016/j.mbs.2006.09.025
  • Y. Xiao, X. Xu, and S. Tang, Sliding mode control of outbreaks of emerging infectious diseases, Bull. Math. Biol. 74 (2012), pp. 2403–2422. doi: 10.1007/s11538-012-9758-5
  • Y. Xiao, S. Tang, and J. Wu, Media impact switching surface during an infectious disease outbreak, Scientific Reports, 5 (2015), article 7838.
  • X. Zhang and L. Chen, The periodic solution of a class of epidemic models, Comput. Math. Appl. 38 (1999), pp. 61–71. doi: 10.1016/S0898-1221(99)00206-0
  • Z. Zhang, T. Ding, W. Huang, and Z. Dong, Qualitative Theory of Differential Equations, Vol. 101, Amer. Math. Soc., Providence, 1992.
  • J. Zu and L. Wang, Periodic solutions for a seasonally forced SIR model with impact of media coverage, Adv. Difference Equ. 2015 (2015), pp. 1–10. doi:10.1186/s13662-015-0477-8.