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Dynamics of an infectious diseases with media/psychology induced non-smooth incidence
1. | Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049 |
2. | Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, 710049, China |
3. | College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China |
References:
[1] |
R. M. Anderson and R. M. May, "Infectious Diseases of Humans, Dynamics and Control," Oxford University, Oxford, 1991. |
[2] |
J. Aubin and A. Cellina, "Differential Inclusion," Springer-Verlag, Berlin, 1984. |
[3] |
A. Banaszuk, On the existence and uniqueness of solutions for implicit linear systems on finite interval, Circ. Syst. Signal. Pr., 12 (1993), 375-390.
doi: 10.1007/BF01223316. |
[4] |
S. Banerjee and G. Verghese, "Nonlinear Phenomena in Power Electronics," IEEE Press, New York, 2001. |
[5] |
M. D. Bernardo, C. J. Budd, A. R. Champneys, et al., Bifurcations in nonsmooth dynamical systems, SIAM Review, 50 (2008), 629-701.
doi: 10.1137/050625060. |
[6] |
M. di Bernardo, K. H. Johansson and F. Vasca, Self-oscillations and sliding in relay feedback systems: Symmetry and bifurcations, Int. J. Bifurcat. Chaos, 11 (2001), 1121-1140. |
[7] |
M. P. Brinn, K. V. Carson, A. J. Esterman, A. B. Chang and B. J. Smith, Mass media interventions for preventing smoking in young people, Cochrane Db. Syst. Rev., 11 (2010) , 1-47. |
[8] |
B. Brogliato, "Nonsmooth Mechanics: Models, Dynamics and Control," Springer-Verlag, London, 1999. |
[9] |
R. M. Corless, G. H. Gonnet, et al., On the Lambert W function, Adv. Comput. Math., 5 (1996), 329-359.
doi: 10.1007/BF02124750. |
[10] |
J. Cui, Y. Sun and H. Zhu, The impact of media on the spreading and control of infectious disease. J. Dynam. Diff. Eqns., 20 (2008), 31-53.
doi: 10.1007/s10884-007-9075-0. |
[11] |
J. Cui, X. Tao and H. Zhu, An SIS infection model incorporating media coverage, Rocky Mt. J. Math., 38 (2008), 1323-1334.
doi: 10.1216/RMJ-2008-38-5-1323. |
[12] |
K. Deimling, "Multivalued Differential Equations," Walter De Gruyter, Berlin, 1992.
doi: 10.1515/9783110874228. |
[13] |
A. F. Filippov, "Differential Equations with Discontinuous Right-Hand Sides," Kluwer Academic, Dordrecht, The Netherlands, 1988. |
[14] |
S. Funk, M. Salathe and V. A. A. Jansen, Modelling the influence of human behaviour on the spread of infectious diseases: A review, J. R. Soc. Interface, 7 (2010), 1247-1256 |
[15] |
S. Funk, E. Gilad, C. Watkins and V. A. A. Jansen, The spread of awareness and its impact on epidemic outbreaks, PNAS, 106 (2009), 6872-6877. |
[16] |
A. Handel, Jr I. M. Longini and R. Antia, What is the best control strategy for multiple infectious disease outbreaks?, Proc. R. Soc. B., 274 (2007), 833-837. |
[17] |
W. Heemels and B. Brogliato, The complementarity class of hybrid dynamical systems, European J. Control., 9 (2003), 311-319. |
[18] |
J. H. Jones and M. Salathé, Early assessment of anxiety and behavioral response to novel swine-origin influenza A(H1N1), PLoS ONE, 4 (2009), e8032.
doi: 10.1371/journal.pone.0008032. |
[19] |
R. Liu, J. Wu and H. Zhu, Media/psychological impact on multiple outbreaks of emerging infectious diseases, Comput. Math. Methods Med., 8 (2007), 153-164.
doi: 10.1080/17486700701425870. |
[20] |
Y. Liu and J. Cui, The impact of media coverage on the dynamics of infectious disease, Int. J. Biomath., 1 (2008), 65-74.
doi: 10.1142/S1793524508000023. |
[21] |
J. Melin, Does distribution theory contain means for extending Poincaré-Bendixson theory, J. Math. Anal. Appl., 303 (2004), 81-89.
doi: 10.1016/j.jmaa.2004.06.069. |
[22] |
G. J. Rubin, H. W. W. Potts and S. Michie, The impact of communications about swine flu (influenza A H1N1v) on public responses to the outbreak: Results from 36 national telephone surveys in the UK, Health Technol. Assess., 14 (2010), 183-266. |
[23] |
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), 87-95.
doi: 10.1016/j.mbs.2011.01.005. |
[24] |
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), S5. |
[25] |
J. M. Tchuenche and C. T. Bauch, Dynamics of an infectious disease where media coverage influences transmission, ISRN Biomathematics, (2012).
doi: 10.5402/2012/581274. |
[26] |
W. Wang, Backward bifurcation of an epidemic model with treatment, Math. Biosci., 201 (2006), 58-71.
doi: 10.1016/j.mbs.2005.12.022. |
[27] |
Y. Xiao, Y. Zhou and S. Tang, Modelling disease spread in dispersal networks at two levels, IMA. J. Math. appl. Med. Biol., 28 (2010), 227-244.
doi: 10.1093/imammb/dqq007. |
[28] |
Y. Xiao and S. Tang, Dynamics of infection with nonlinear incidence in a simple vaccination model, Nonl. Anal. RWA., 11 (2010), 4154-4163.
doi: 10.1016/j.nonrwa.2010.05.002. |
[29] |
Y. Xiao, X. Xu and S. Tang, Sliding mode control of outbreaks of emerging infectious diseases, Bull. Math. Biol., 74 (2012), 2403-2422. |
show all references
References:
[1] |
R. M. Anderson and R. M. May, "Infectious Diseases of Humans, Dynamics and Control," Oxford University, Oxford, 1991. |
[2] |
J. Aubin and A. Cellina, "Differential Inclusion," Springer-Verlag, Berlin, 1984. |
[3] |
A. Banaszuk, On the existence and uniqueness of solutions for implicit linear systems on finite interval, Circ. Syst. Signal. Pr., 12 (1993), 375-390.
doi: 10.1007/BF01223316. |
[4] |
S. Banerjee and G. Verghese, "Nonlinear Phenomena in Power Electronics," IEEE Press, New York, 2001. |
[5] |
M. D. Bernardo, C. J. Budd, A. R. Champneys, et al., Bifurcations in nonsmooth dynamical systems, SIAM Review, 50 (2008), 629-701.
doi: 10.1137/050625060. |
[6] |
M. di Bernardo, K. H. Johansson and F. Vasca, Self-oscillations and sliding in relay feedback systems: Symmetry and bifurcations, Int. J. Bifurcat. Chaos, 11 (2001), 1121-1140. |
[7] |
M. P. Brinn, K. V. Carson, A. J. Esterman, A. B. Chang and B. J. Smith, Mass media interventions for preventing smoking in young people, Cochrane Db. Syst. Rev., 11 (2010) , 1-47. |
[8] |
B. Brogliato, "Nonsmooth Mechanics: Models, Dynamics and Control," Springer-Verlag, London, 1999. |
[9] |
R. M. Corless, G. H. Gonnet, et al., On the Lambert W function, Adv. Comput. Math., 5 (1996), 329-359.
doi: 10.1007/BF02124750. |
[10] |
J. Cui, Y. Sun and H. Zhu, The impact of media on the spreading and control of infectious disease. J. Dynam. Diff. Eqns., 20 (2008), 31-53.
doi: 10.1007/s10884-007-9075-0. |
[11] |
J. Cui, X. Tao and H. Zhu, An SIS infection model incorporating media coverage, Rocky Mt. J. Math., 38 (2008), 1323-1334.
doi: 10.1216/RMJ-2008-38-5-1323. |
[12] |
K. Deimling, "Multivalued Differential Equations," Walter De Gruyter, Berlin, 1992.
doi: 10.1515/9783110874228. |
[13] |
A. F. Filippov, "Differential Equations with Discontinuous Right-Hand Sides," Kluwer Academic, Dordrecht, The Netherlands, 1988. |
[14] |
S. Funk, M. Salathe and V. A. A. Jansen, Modelling the influence of human behaviour on the spread of infectious diseases: A review, J. R. Soc. Interface, 7 (2010), 1247-1256 |
[15] |
S. Funk, E. Gilad, C. Watkins and V. A. A. Jansen, The spread of awareness and its impact on epidemic outbreaks, PNAS, 106 (2009), 6872-6877. |
[16] |
A. Handel, Jr I. M. Longini and R. Antia, What is the best control strategy for multiple infectious disease outbreaks?, Proc. R. Soc. B., 274 (2007), 833-837. |
[17] |
W. Heemels and B. Brogliato, The complementarity class of hybrid dynamical systems, European J. Control., 9 (2003), 311-319. |
[18] |
J. H. Jones and M. Salathé, Early assessment of anxiety and behavioral response to novel swine-origin influenza A(H1N1), PLoS ONE, 4 (2009), e8032.
doi: 10.1371/journal.pone.0008032. |
[19] |
R. Liu, J. Wu and H. Zhu, Media/psychological impact on multiple outbreaks of emerging infectious diseases, Comput. Math. Methods Med., 8 (2007), 153-164.
doi: 10.1080/17486700701425870. |
[20] |
Y. Liu and J. Cui, The impact of media coverage on the dynamics of infectious disease, Int. J. Biomath., 1 (2008), 65-74.
doi: 10.1142/S1793524508000023. |
[21] |
J. Melin, Does distribution theory contain means for extending Poincaré-Bendixson theory, J. Math. Anal. Appl., 303 (2004), 81-89.
doi: 10.1016/j.jmaa.2004.06.069. |
[22] |
G. J. Rubin, H. W. W. Potts and S. Michie, The impact of communications about swine flu (influenza A H1N1v) on public responses to the outbreak: Results from 36 national telephone surveys in the UK, Health Technol. Assess., 14 (2010), 183-266. |
[23] |
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), 87-95.
doi: 10.1016/j.mbs.2011.01.005. |
[24] |
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), S5. |
[25] |
J. M. Tchuenche and C. T. Bauch, Dynamics of an infectious disease where media coverage influences transmission, ISRN Biomathematics, (2012).
doi: 10.5402/2012/581274. |
[26] |
W. Wang, Backward bifurcation of an epidemic model with treatment, Math. Biosci., 201 (2006), 58-71.
doi: 10.1016/j.mbs.2005.12.022. |
[27] |
Y. Xiao, Y. Zhou and S. Tang, Modelling disease spread in dispersal networks at two levels, IMA. J. Math. appl. Med. Biol., 28 (2010), 227-244.
doi: 10.1093/imammb/dqq007. |
[28] |
Y. Xiao and S. Tang, Dynamics of infection with nonlinear incidence in a simple vaccination model, Nonl. Anal. RWA., 11 (2010), 4154-4163.
doi: 10.1016/j.nonrwa.2010.05.002. |
[29] |
Y. Xiao, X. Xu and S. Tang, Sliding mode control of outbreaks of emerging infectious diseases, Bull. Math. Biol., 74 (2012), 2403-2422. |
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