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Interaction of media and disease dynamics and its impact on emerging infection management
1.  College of Transport & Communications, Shanghai Maritime University, Shanghai, 201306, China 
2.  SinoUS Global Logistics Institute, Shanghai Jiao Tong University, Shanghai, 200030, China 
3.  School of Administrative Studies, York University, Toronto, M3J 1P3, Canada 
4.  School of Mathematics, Shandong Normal University, Jiannan, 250014, China 
5.  Center for Disease Modeling, Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada 
References:
[1] 
J. Arino and C. C. McCluskey, Effect of a sharp change of the incidence function on the dynamics of a simple disease, Journal of Biological Dynamics, 4 (2010), 490505. doi: 10.1080/17513751003793017. 
[2] 
M. Arydah and R. Smith, Controlling malaria with indoor residual spraying in spatially heterogenous environments, Mathematical Biosciences and Engineering, 8 (2011), 889914. doi: 10.3934/mbe.2011.8.889. 
[3] 
F. B. Agusto and A. B. Gumel, Theoretical assessment of avian influenza vaccine, Discrete and Continuous Dynamical Systems  Series B, 13 (2010), 125. doi: 10.3934/dcdsb.2010.13.1. 
[4] 
S. Bansal, B. T. Grenfell and L. A. Meyers, When individual behaviour matters: Homogeneous and network models in epidemiology, Journal of the Royal Society Interface, 4 (2007), 879891. doi: 10.1098/rsif.2007.1100. 
[5] 
J. A. Cui, Y. H. Sun and H. P. Zhu, The impact of media on the control of infectious diseases, Journal of Dynamics and Differential Equations, 20 (2007), 3153. doi: 10.1007/s1088400790750. 
[6] 
J. A. Cui, X. Tao and H. P. Zhu, An sis infection mode incorporating media coverage, The Rocky Mountain Journal of Mathematics, 38 (2008), 13231334. doi: 10.1216/RMJ20083851323. 
[7] 
D. Drache and S. Feldman, Media Coverage of the 2003 Toronto SARS Outbreak, Robarts Centre Research Paper, York University, (2003), 118. 
[8] 
N. Ferguson, Capturing human behaviour, Nature, 446 (2007), 733733. doi: 10.1038/446733a. 
[9] 
S. Funk, E. Gilad and V. A. A. Jansen, Endemic disease, awareness, and local behavioural response, Journal of Theoretical Biology, 264 (2010), 501509. doi: 10.1016/j.jtbi.2010.02.032. 
[10] 
S. Funk, E. Gilad and V. A. A. Jansen, The spread of awareness and its impact on epidemic outbreaks, Proceedings of the National Academy of Sciences of the United States of America, 106 (2009), 68726877. doi: 10.1073/pnas.0810762106. 
[11] 
A. B. Gumel, C. C. McCluskey and J. Watmough, An sveir model for assessing potential impact of an imperfect antiSARS vaccine, Mathematical Biosciences and Engineering, 3 (2006), 485512. doi: 10.3934/mbe.2006.3.485. 
[12] 
D. Z. Gao and S. G. Ruan, An SIS patch model with variable transmission coefficients, Mathematical Biosciences, 232 (2011), 110115. doi: 10.1016/j.mbs.2011.05.001. 
[13] 
J. Gu, Z. M. Gao and W. Li, Modeling of epidemic spreading with white Gaussian noise, Chinese Science Bull., 56 (2011), 36833688. doi: 10.1007/s114340114753z. 
[14] 
Z. M. Gao, J. Gu and W. Li, Epidemic spreading in a multicompartment system, Chinese Physics Letter, 29 (2012), 028902. doi: 10.1088/0256307X/29/2/028902. 
[15] 
J. H. Huang and X. F. Zou, Avian influenza dynamics in wild birds with bird mobility and spatial heterogeneous environment, Discrete and Continuous Dynamical Systems  Series B, 17 (2012), 28292848. doi: 10.3934/dcdsb.2012.17.2829. 
[16] 
Z. X. Hu, W. B. Ma and S. G. Ruan, Analysis of SIR epidemic models with nonlinear incidence rate and treatment, Mathematical Biosciences, 238 (2012), 1220. doi: 10.1016/j.mbs.2012.03.010. 
[17] 
J. H. Jones and M. Salathe, Early assessment of anxiety and behavioral response to novel swineorigin influenza A (H1N1), Plos One, 4 (2009), e8032. doi: 10.1371/journal.pone.0008032. 
[18] 
W. Li, Z. M. Gao and J. Gu, Effects of variant rates and noise on epidemic spreading, Chinese Physics Letter, 28 (2011), 058903. doi: 10.1088/0256307X/28/5/058903. 
[19] 
Y. F. Li, C. Q. Ma and J. A. Cui, The effect of constant and mixed impulsive vaccination on sis epidemic models incorporating media coverage, Rocky Mountain Journal of Mathematics, 38 (2008), 14371455. doi: 10.1216/RMJ20083851437. 
[20] 
R. S. Liu, J. P. Shuai, J. Wu and H. P. Zhu, Modeling spatial spread of west nile virus and impact of directional dispersal of birds, Mathematical Biosciences and Engineering, 3 (2006), 145160. 
[21] 
R. S. Liu, J. H. Wu and H. P. Zhu, Media/Psychological impact on multiple outbreaks of emerging infectious diseases, Computational and Mathematical Methods in Medicine, 8 (2007), 153164. doi: 10.1080/17486700701425870. 
[22] 
E. Liz and G. Rost, On the global attractor of delay differential equations with unimodal feedback, Discrete and Continuous Dynamical Systems, 24 (2009), 12151224. doi: 10.3934/dcds.2009.24.1215. 
[23] 
A. K. Misra, A. Sharma and J. B. Shukla, Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases, Mathematical and Computer Modelling, 53 (2011), 12211228. doi: 10.1016/j.mcm.2010.12.005. 
[24] 
G. A. Ngwa, Modelling the dynamics of endemic malaria in growing populations, Discrete and Continuous Dynamical Systems  Series B, 4 (2004), 11731202. doi: 10.3934/dcdsb.2004.4.1173. 
[25] 
M. A. Safi and A. B. Gumel, Global asymptotic dynamics of a model for quarantine and isolation, Discrete and Continuous Dynamical Systems  Series B, 14 (2010), 209231. doi: 10.3934/dcdsb.2010.14.209. 
[26] 
M. Salathle and S. Khandelwal, Assessing vaccination sentiments with online social media: Implications for infectious disease dynamics and control, PLoS Computational Biology, 7 (2011), 127. 
[27] 
S. Samanta, S. Rana, A. Sharma, A. K. Misra and J. Chattopadhyay, Effect of awareness programs by media on the epidemic outbreaks: A mathematical model, Applied Mathematics and Computation, 219 (2013), 69656977. doi: 10.1016/j.amc.2013.01.009. 
[28] 
C. J. Sun, W. Yang, J. Arino and K. Khan, Effect of mediainduced social distancing on disease transmission in a two patch setting, Mathematical Biosciences, 230 (2011), 8795. doi: 10.1016/j.mbs.2011.01.005. 
[29] 
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. 
[30] 
P. Van den Driessche and J. Watmough, Reproductive numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 2948. doi: 10.1016/S00255564(02)001086. 
[31] 
A. Wang and Y. N. Xiao, Filippov system describing media effects on the spread of infectious diseases, Nonlinear Analysis: Hybrid Systems, 11 (2014), 8497. doi: 10.1016/j.nahs.2013.06.005. 
[32] 
D. M. Xiao and S. G. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate, Mathematical Biosciences, 208 (2007), 419429. doi: 10.1016/j.mbs.2006.09.025. 
[33] 
M. E. Young, G. R. Norman and K. R. Humphreys, Medicine in the popular press: The influence of the media on perceptions of disease, PLoS One, 3 (2008), e3552. doi: 10.1371/journal.pone.0003552. 
[34] 
X. P. Yuan, Y. K. Xue and M. X. Liu, Analysis of an epidemic model with awareness programs by media on complex networks, Chaos, Solitons & Fractals, 48 (2013), 111. doi: 10.1016/j.chaos.2012.12.001. 
show all references
References:
[1] 
J. Arino and C. C. McCluskey, Effect of a sharp change of the incidence function on the dynamics of a simple disease, Journal of Biological Dynamics, 4 (2010), 490505. doi: 10.1080/17513751003793017. 
[2] 
M. Arydah and R. Smith, Controlling malaria with indoor residual spraying in spatially heterogenous environments, Mathematical Biosciences and Engineering, 8 (2011), 889914. doi: 10.3934/mbe.2011.8.889. 
[3] 
F. B. Agusto and A. B. Gumel, Theoretical assessment of avian influenza vaccine, Discrete and Continuous Dynamical Systems  Series B, 13 (2010), 125. doi: 10.3934/dcdsb.2010.13.1. 
[4] 
S. Bansal, B. T. Grenfell and L. A. Meyers, When individual behaviour matters: Homogeneous and network models in epidemiology, Journal of the Royal Society Interface, 4 (2007), 879891. doi: 10.1098/rsif.2007.1100. 
[5] 
J. A. Cui, Y. H. Sun and H. P. Zhu, The impact of media on the control of infectious diseases, Journal of Dynamics and Differential Equations, 20 (2007), 3153. doi: 10.1007/s1088400790750. 
[6] 
J. A. Cui, X. Tao and H. P. Zhu, An sis infection mode incorporating media coverage, The Rocky Mountain Journal of Mathematics, 38 (2008), 13231334. doi: 10.1216/RMJ20083851323. 
[7] 
D. Drache and S. Feldman, Media Coverage of the 2003 Toronto SARS Outbreak, Robarts Centre Research Paper, York University, (2003), 118. 
[8] 
N. Ferguson, Capturing human behaviour, Nature, 446 (2007), 733733. doi: 10.1038/446733a. 
[9] 
S. Funk, E. Gilad and V. A. A. Jansen, Endemic disease, awareness, and local behavioural response, Journal of Theoretical Biology, 264 (2010), 501509. doi: 10.1016/j.jtbi.2010.02.032. 
[10] 
S. Funk, E. Gilad and V. A. A. Jansen, The spread of awareness and its impact on epidemic outbreaks, Proceedings of the National Academy of Sciences of the United States of America, 106 (2009), 68726877. doi: 10.1073/pnas.0810762106. 
[11] 
A. B. Gumel, C. C. McCluskey and J. Watmough, An sveir model for assessing potential impact of an imperfect antiSARS vaccine, Mathematical Biosciences and Engineering, 3 (2006), 485512. doi: 10.3934/mbe.2006.3.485. 
[12] 
D. Z. Gao and S. G. Ruan, An SIS patch model with variable transmission coefficients, Mathematical Biosciences, 232 (2011), 110115. doi: 10.1016/j.mbs.2011.05.001. 
[13] 
J. Gu, Z. M. Gao and W. Li, Modeling of epidemic spreading with white Gaussian noise, Chinese Science Bull., 56 (2011), 36833688. doi: 10.1007/s114340114753z. 
[14] 
Z. M. Gao, J. Gu and W. Li, Epidemic spreading in a multicompartment system, Chinese Physics Letter, 29 (2012), 028902. doi: 10.1088/0256307X/29/2/028902. 
[15] 
J. H. Huang and X. F. Zou, Avian influenza dynamics in wild birds with bird mobility and spatial heterogeneous environment, Discrete and Continuous Dynamical Systems  Series B, 17 (2012), 28292848. doi: 10.3934/dcdsb.2012.17.2829. 
[16] 
Z. X. Hu, W. B. Ma and S. G. Ruan, Analysis of SIR epidemic models with nonlinear incidence rate and treatment, Mathematical Biosciences, 238 (2012), 1220. doi: 10.1016/j.mbs.2012.03.010. 
[17] 
J. H. Jones and M. Salathe, Early assessment of anxiety and behavioral response to novel swineorigin influenza A (H1N1), Plos One, 4 (2009), e8032. doi: 10.1371/journal.pone.0008032. 
[18] 
W. Li, Z. M. Gao and J. Gu, Effects of variant rates and noise on epidemic spreading, Chinese Physics Letter, 28 (2011), 058903. doi: 10.1088/0256307X/28/5/058903. 
[19] 
Y. F. Li, C. Q. Ma and J. A. Cui, The effect of constant and mixed impulsive vaccination on sis epidemic models incorporating media coverage, Rocky Mountain Journal of Mathematics, 38 (2008), 14371455. doi: 10.1216/RMJ20083851437. 
[20] 
R. S. Liu, J. P. Shuai, J. Wu and H. P. Zhu, Modeling spatial spread of west nile virus and impact of directional dispersal of birds, Mathematical Biosciences and Engineering, 3 (2006), 145160. 
[21] 
R. S. Liu, J. H. Wu and H. P. Zhu, Media/Psychological impact on multiple outbreaks of emerging infectious diseases, Computational and Mathematical Methods in Medicine, 8 (2007), 153164. doi: 10.1080/17486700701425870. 
[22] 
E. Liz and G. Rost, On the global attractor of delay differential equations with unimodal feedback, Discrete and Continuous Dynamical Systems, 24 (2009), 12151224. doi: 10.3934/dcds.2009.24.1215. 
[23] 
A. K. Misra, A. Sharma and J. B. Shukla, Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases, Mathematical and Computer Modelling, 53 (2011), 12211228. doi: 10.1016/j.mcm.2010.12.005. 
[24] 
G. A. Ngwa, Modelling the dynamics of endemic malaria in growing populations, Discrete and Continuous Dynamical Systems  Series B, 4 (2004), 11731202. doi: 10.3934/dcdsb.2004.4.1173. 
[25] 
M. A. Safi and A. B. Gumel, Global asymptotic dynamics of a model for quarantine and isolation, Discrete and Continuous Dynamical Systems  Series B, 14 (2010), 209231. doi: 10.3934/dcdsb.2010.14.209. 
[26] 
M. Salathle and S. Khandelwal, Assessing vaccination sentiments with online social media: Implications for infectious disease dynamics and control, PLoS Computational Biology, 7 (2011), 127. 
[27] 
S. Samanta, S. Rana, A. Sharma, A. K. Misra and J. Chattopadhyay, Effect of awareness programs by media on the epidemic outbreaks: A mathematical model, Applied Mathematics and Computation, 219 (2013), 69656977. doi: 10.1016/j.amc.2013.01.009. 
[28] 
C. J. Sun, W. Yang, J. Arino and K. Khan, Effect of mediainduced social distancing on disease transmission in a two patch setting, Mathematical Biosciences, 230 (2011), 8795. doi: 10.1016/j.mbs.2011.01.005. 
[29] 
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. 
[30] 
P. Van den Driessche and J. Watmough, Reproductive numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 2948. doi: 10.1016/S00255564(02)001086. 
[31] 
A. Wang and Y. N. Xiao, Filippov system describing media effects on the spread of infectious diseases, Nonlinear Analysis: Hybrid Systems, 11 (2014), 8497. doi: 10.1016/j.nahs.2013.06.005. 
[32] 
D. M. Xiao and S. G. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate, Mathematical Biosciences, 208 (2007), 419429. doi: 10.1016/j.mbs.2006.09.025. 
[33] 
M. E. Young, G. R. Norman and K. R. Humphreys, Medicine in the popular press: The influence of the media on perceptions of disease, PLoS One, 3 (2008), e3552. doi: 10.1371/journal.pone.0003552. 
[34] 
X. P. Yuan, Y. K. Xue and M. X. Liu, Analysis of an epidemic model with awareness programs by media on complex networks, Chaos, Solitons & Fractals, 48 (2013), 111. doi: 10.1016/j.chaos.2012.12.001. 
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