# American Institute of Mathematical Sciences

January  2015, 20(1): 215-230. doi: 10.3934/dcdsb.2015.20.215

## 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 Sino-US 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

Received  November 2012 Revised  January 2014 Published  November 2014

The 2002-2003 SARS outbreaks exhibited some distinct features such as rapid spatial spread, massive media reports, and fast self-control. These features were shared by the 2009 pandemic influenza and will be experienced by other emerging infectious diseases. We focus on the dynamic interaction of media reports, epidemic outbreak and behavior change in the population and formulate a compartmental model, that tracks the evolution of the human population. Such population is characterized by the disease progression (susceptible, infected, hospitalized, and recovered) and by the extent to which the media has impacted, so individuals have modified their behaviors to reduce their transmissibility and infectivity. The model also describes the dynamics of media reports by considering how media is influenced by the disease statistics (numbers of infected and hospitalized individuals, for example). We then conduct linear stability analysis and numerical simulations to study how interaction of media reports and disease progress affects the disease transmission dynamics, so as to shed light on what type of media will be the most effective for the control of an epidemic.
Citation: Qin Wang, Laijun Zhao, Rongbing Huang, Youping Yang, Jianhong Wu. Interaction of media and disease dynamics and its impact on emerging infection management. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 215-230. doi: 10.3934/dcdsb.2015.20.215
##### 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), 490-505. 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), 889-914. 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), 1-25. 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), 879-891. 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), 31-53. doi: 10.1007/s10884-007-9075-0. [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), 1323-1334. doi: 10.1216/RMJ-2008-38-5-1323. [7] D. Drache and S. Feldman, Media Coverage of the 2003 Toronto SARS Outbreak, Robarts Centre Research Paper, York University, (2003), 1-18. [8] N. Ferguson, Capturing human behaviour, Nature, 446 (2007), 733-733. 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), 501-509. 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), 6872-6877. 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 anti-SARS vaccine, Mathematical Biosciences and Engineering, 3 (2006), 485-512. 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), 110-115. 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), 3683-3688. doi: 10.1007/s11434-011-4753-z. [14] Z. M. Gao, J. Gu and W. Li, Epidemic spreading in a multi-compartment system, Chinese Physics Letter, 29 (2012), 028902. doi: 10.1088/0256-307X/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), 2829-2848. 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), 12-20. doi: 10.1016/j.mbs.2012.03.010. [17] J. H. Jones and M. Salathe, 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. [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: 10.1088/0256-307X/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), 1437-1455. doi: 10.1216/RMJ-2008-38-5-1437. [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), 145-160. [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), 153-164. 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), 1215-1224. 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), 1221-1228. 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), 1173-1202. 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), 209-231. 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), 1-27. [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), 6965-6977. doi: 10.1016/j.amc.2013.01.009. [28] C. J. Sun, W. Yang, J. Arino and K. Khan, Effect of media-induced social distancing on disease transmission in a two patch setting, Mathematical Biosciences, 230 (2011), 87-95. 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), 29-48. doi: 10.1016/S0025-5564(02)00108-6. [31] A. Wang and Y. N. Xiao, Filippov system describing media effects on the spread of infectious diseases, Nonlinear Analysis: Hybrid Systems, 11 (2014), 84-97. 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), 419-429. 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), 1-11. 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), 490-505. 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), 889-914. 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), 1-25. 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), 879-891. 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), 31-53. doi: 10.1007/s10884-007-9075-0. [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), 1323-1334. doi: 10.1216/RMJ-2008-38-5-1323. [7] D. Drache and S. Feldman, Media Coverage of the 2003 Toronto SARS Outbreak, Robarts Centre Research Paper, York University, (2003), 1-18. [8] N. Ferguson, Capturing human behaviour, Nature, 446 (2007), 733-733. 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), 501-509. 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), 6872-6877. 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 anti-SARS vaccine, Mathematical Biosciences and Engineering, 3 (2006), 485-512. 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), 110-115. 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), 3683-3688. doi: 10.1007/s11434-011-4753-z. [14] Z. M. Gao, J. Gu and W. Li, Epidemic spreading in a multi-compartment system, Chinese Physics Letter, 29 (2012), 028902. doi: 10.1088/0256-307X/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), 2829-2848. 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), 12-20. doi: 10.1016/j.mbs.2012.03.010. [17] J. H. Jones and M. Salathe, 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. [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: 10.1088/0256-307X/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), 1437-1455. doi: 10.1216/RMJ-2008-38-5-1437. [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), 145-160. [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), 153-164. 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), 1215-1224. 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), 1221-1228. 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), 1173-1202. 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), 209-231. 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), 1-27. [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), 6965-6977. doi: 10.1016/j.amc.2013.01.009. [28] C. J. Sun, W. Yang, J. Arino and K. Khan, Effect of media-induced social distancing on disease transmission in a two patch setting, Mathematical Biosciences, 230 (2011), 87-95. 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), 29-48. doi: 10.1016/S0025-5564(02)00108-6. [31] A. Wang and Y. N. Xiao, Filippov system describing media effects on the spread of infectious diseases, Nonlinear Analysis: Hybrid Systems, 11 (2014), 84-97. 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), 419-429. 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), 1-11. doi: 10.1016/j.chaos.2012.12.001.
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