Dynamics of an infectious disease where media coverage influences transmission.

*(English)*Zbl 1269.92052Summary: There is significant current interest in the application of media/psychosocial effects to problems in epidemiology. News reporting has the potential to reach and to modify the knowledge, attitudes, and behavior of a large proportion of the community. A susceptible-infected-hospitalized-recovered model with vital dynamics, where media coverage of disease incidence and disease prevalence can influence people to reduce their contact rates is formulated. The media function is incorporated into the model using an exponentially decreasing function. Qualitative analysis of the model reveals that the disease-free equilibrium is locally asymptotically stable when a certain threshold is less than unity. Numerical results show the potential short-term beneficial effect of media coverage.

##### MSC:

92C60 | Medical epidemiology |

92-08 | Computational methods for problems pertaining to biology |

34C60 | Qualitative investigation and simulation of ordinary differential equation models |

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\textit{J. M. Tchuenche} and \textit{C. T. Bauch}, ISRN Biomath. 2012, Article ID 581274, 10 p. (2012; Zbl 1269.92052)

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##### References:

[1] | Bonanni, P., Demographic impact of vaccination: a review, Vaccine, 17, S120-S125, (1999) |

[2] | Brinn, M. P.; Carson, K. V.; Esterman, A. J.; Chang, A. B.; Smith, B. J., Mass media interventions for preventing smoking in Young people, Cochrane Database of Systematic Reviews, 11, (2010) |

[3] | Young, M. E.; Norman, G. R.; Humphreys, K. R., Medicine in the popular press: the influence of the media on perceptions of disease, PLoS One, 3, 10, (2008) |

[4] | Jaramillo, E., The impact of media-based health education on tuberculosis diagnosis in cali, Colombia, Health Policy and Planning, 16, 1, 68-73, (2001) |

[5] | Grilli, R.; Ramsay, C.; Minozzi, S., Mass media interventions: effects on health services utilisation, Cochrane Database of Systematic Reviews, 1, (2002) |

[6] | Schwitzer, G.; Mudur, G.; Henry, D.; Wilson, A.; Goozner, M.; Simbra, M.; Sweet, M.; Baverstock, K. A., What are the roles and responsibilities of the media in disseminating health information?, PLoS Medicine, 2, 7, article e215, (2005) |

[7] | Brownstein, J. S.; Freifeld, C. C.; Madoff, L. C., Influenza A (H1N1) virus, 2009—online monitoring, The New England journal of medicine, 360, 21, 2156, (2009) |

[8] | Mykhalovskiy, E.; Weir, L., The global public health intelligence network and early warning outbreak detection: a Canadian contribution to global public health, Canadian Journal of Public Health, 97, 1, 42-44, (2006) |

[9] | Bauman, A.; Smith, B. J.; Maibach, E. W.; Reger-Nash, B., Evaluation of mass media campaigns for physical activity, Evaluation and Program Planning, 29, 3, 312-322, (2006) |

[10] | Brewer, N. T.; Weinstein, N. D.; Cuite, C. L.; Herrington, J. E., Risk perceptions and their relation to risk behavior, Annals of Behavioral Medicine, 27, 2, 125-130, (2004) |

[11] | Brewer, N. T.; Hallman, W. K., Subjective and objective risk as predictors of influenza vaccination during the vaccine shortage of 2004-2005, Clinical Infectious Diseases, 43, 11, 1379-1386, (2006) |

[12] | Bala, M.; Strzeszynski, L.; Cahill, K., Mass media interventions for smoking cessation in adults, Cochrane Database of Systematic Reviews, 1, (2008) |

[13] | Jepson, R.; Harris, F.; Rowa-Dewar, N., A review of the effectiveness of mass media interventions which both encourage quit attempts and reinforce current and recent attempts to quit smoking (report) |

[14] | US Department of Health and Human Services, Preventing tobacco use among Young people: a report of the surgeon general |

[15] | Rahman, M. S.; Rahman, M. L., Media and education play a tremendous role in mounting AIDS awareness among married couples in bangladesh, AIDS Research and Therapy, 4, article no. 10, (2007) |

[16] | Ramalingaswami, V., Psychosocial effects of the 1994 plague outbreak in surat, India, Military Medicine, 166, 12, 29-30, (2001) |

[17] | D’Onofrio, A.; Manfredi, P.; Manfredi, P., Bifurcation thresholds in an SIR model with information-dependent vaccination, Mathematical Modelling of Natural Phenomena, 2, 1, 26-43, (2007) · Zbl 1337.92223 |

[18] | Mukandavire, Z.; Garira, W., Effects of public health educational campaigns and the role of sex workers on the spread of HIV/AIDS among heterosexuals, Theoretical Population Biology, 72, 3, 346-365, (2007) · Zbl 1147.92317 |

[19] | Mukandavire, Z.; Garira, W.; Tchuenche, J. M., Modelling effects of public health educational campaigns on HIV/AIDS transmission dynamics, Applied Mathematical Modelling, 33, 4, 2084-2095, (2009) · Zbl 1205.34092 |

[20] | Redman, S.; Spencer, E. A.; Sanson-Fisher, R. W., The role of mass media in changing health-related behaviour: a critical appraisal of two models, Health Promotion International, 5, 1, 85-101, (1990) |

[21] | Chen, F. H., Modeling the effect of information quality on risk behavior change and the transmission of infectious diseases, Mathematical Biosciences, 217, 2, 125-133, (2009) · Zbl 1157.92026 |

[22] | Capasso, V.; Serio, G., A generalization of the kermack-mckendrick deterministic epidemic model, Mathematical Biosciences, 42, 1-2, 43-61, (1978) · Zbl 0398.92026 |

[23] | Liu, R.; Wu, J.; Zhu, H., Media/psychological impact on multiple outbreaks of emerging infectious diseases, Computational and Mathematical Methods in Medicine, 8, 3, 153-164, (2007) · Zbl 1121.92060 |

[24] | Liu, Y.; Cui, J., The impact of media coverage on the dynamics of infectious disease, International Journal of Biomathematics, 1, 1, 65-74, (2008) · Zbl 1155.92343 |

[25] | Cai, L. M.; Li, X. Z., Analysis of a SEIV epidemic model with a nonlinear incidence rate, Applied Mathematical Modelling, 33, 7, 2919-2926, (2009) · Zbl 1205.34049 |

[26] | Cui, J. A.; Tao, X.; Zhu, H., An SIS infection model incorporating media coverage, Rocky Mountain Journal of Mathematics, 38, 5, 1323-1334, (2008) · Zbl 1170.92024 |

[27] | Sun, C.; Yang, W.; Arino, J.; Khan, K., Effect of media-induced social distancing on disease transmission in a two patch setting, Mathematical Biosciences, 230, 2, 87-95, (2011) · Zbl 1211.92051 |

[28] | Cui, J.; Sun, Y.; Zhu, H., The impact of media on the control of infectious diseases, Journal of Dynamics and Differential Equations, 20, 1, 31-53, (2008) · Zbl 1160.34045 |

[29] | Li, Y.; Cui, J., The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage, Communications in Nonlinear Science and Numerical Simulation, 14, 5, 2353-2365, (2009) · Zbl 1221.34034 |

[30] | Joshi, H.; Lenhart, S.; Albright, K.; Gipson, K., Modeling the effect of information campaigns on the hiv epidemic in uganda, Mathematical Biosciences and Engineering, 5, 4, 757-770, (2008) · Zbl 1154.92037 |

[31] | Mummert, A.; Weiss, H., Get the news out loudly and quickly: modeling the influence of the media on limiting infectious disease outbreaks |

[32] | Tchuenche, J. M.; Dube, N.; Bhunu, C. P.; Smith, R. J.; Bauch, C. T., The impact of media coverage on the transmission dynamics of human influenza, BMC Public Health, 11, (2011) |

[33] | Perlman, G. Y., The influence of an event in the israeli media on the compliance of patients with influenza vaccinations in the winter of 2006-2007, Harefuah, 148, 12, 811-856, (2009) |

[34] | Yoo, B. K.; Holland, M. L.; Bhattacharya, J.; Phelps, C. E.; Szilagyi, P. G., Effects of mass media coverage on timing and annual receipt of influenza vaccination among medicare elderly, Health Services Research, 45, 5, 1287-1309, (2010) |

[35] | Anderson, R. M.; May, R. M., Infectious Diseases of Humans: Dynamics and Control, (1992), Oxford University Press |

[36] | Rubin, G. J.; Potts, H. W. W.; Michie, S., The impact of communications about swine flu (influenza A hiniv) on public responses to the outbreak: results from 36 national telephone surveys in the UK, Health Technology Assessment, 14, 34, 183-266, (2010) |

[37] | Funk, S.; Gilad, E.; Watkins, C.; Jansen, V. A. A., The spread of awareness and its impact on epidemic outbreaks, Proceedings of the National Academy of Sciences of the United States of America, 106, 16, 6872-6877, (2009) · Zbl 1203.91242 |

[38] | Banaszuk, A., On the existence and uniqueness of solutions for implicit linear systems on finite interval, Circuits, Systems, and Signal Processing, 12, 3, 375-390, (1993) · Zbl 0780.93040 |

[39] | Zhang, Z.; Suo, Y.; Peng, J.; Lin, W., Singular perturbation approach to stability of a SIRS epidemic system, Nonlinear Analysis: Real World Applications, 10, 5, 2688-2699, (2009) · Zbl 1162.92039 |

[40] | Van Den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180, 29-48, (2002) · Zbl 1015.92036 |

[41] | Feng, Z.; Huang, W.; Castillo-Chavez, C., On the role of variable latent periods in mathematical models for tuberculosis, Journal of Dynamics and Differential Equations, 13, 2, 425-452, (2001) · Zbl 1012.34045 |

[42] | Fan, Y. H.; Li, W. T., Permanence in delayed ratio-dependent predator-prey models with monotonic functional responses, Nonlinear Analysis: Real World Applications, 8, 2, 424-434, (2007) · Zbl 1152.34368 |

[43] | Korobeinikov, A.; Maini, P. K., A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence, Mathematical Bioscience and Engineering, 1, 1, 57-60, (2004) · Zbl 1062.92061 |

[44] | Barbalat, I., Système d’équation différentielle d’oscillation nonlinéaires, Revue Roumaine de Mathématique Pures et Appliquées, 4, 267-270, (1959) |

[45] | Jefferson, T., Real or perceived adverse effects of vaccines and the media—a tale of our times, Journal of Epidemiology and Community Health, 54, 6, 402-403, (2000) |

[46] | Brauer, F., A simple model for behaviour change in epidemics, BMC Public Health, 11, (2011) |

[47] | Evensen, D. T. N.; Clarke, C., Efficacy information in media coverage of infectious disease risks: an ill predicament? |

[48] | Goffman, W.; Newill, V. A., Generalization of epidemic theory: an application to the transmission of ideas, Nature, 204, 4955, 225-228, (1964) |

[49] | Agliari, E.; Burioni, R.; Cassi, D.; Neri, F. M., Efficiency of information spreading in a population of diffusing agents, Physical Review E, 73, 4, (2006) · Zbl 1189.82044 |

[50] | Ferguson, N., Capturing human behaviour, Nature, 446, 7137, 733, (2007) |

[51] | Nekovee, M.; Moreno, Y.; Bianconi, G.; Marsili, M., Theory of rumour spreading in complex social networks, Physica A, 374, 1, 457-470, (2007) |

[52] | Lynch, A., Thoaught contagion as abstract evolution, Journal of Ideas, 2, 3-10, (1991) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.