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The impact of information transmission on epidemic outbreaks. (English) Zbl 1188.92033
Summary: For many diseases (e.g., sexually transmitted infections, STIs), most individuals are aware of the potential risks of becoming infected, but choose not to take action (‘respond’) despite the information that aims to raise awareness and to increases the responsiveness or alertness of the population. We propose a simple mathematical model that accounts for the diffusion of health information disseminated as a result of the presence of a disease and an ‘active’ host population that can respond to it by taking measures to avoid infection or if infected by seeking treatment early. We assume that the whole population is potentially aware of the risk but only a certain proportion chooses to respond appropriately by trying to limit their probability of becoming infectious or seeking treatment early. The model also incorporates a level of responsiveness that decays over time. We show that if the dissemination of information is fast enough, infection can be eradicated. When this is not possible, information transmission has an important effect in reducing the prevalence of the infection. We derive the full characterisation of the global behaviour of the model, and we show that the parameter space can be divided into three parts according to the global attractor of the system which is one of the two disease-free steady states or the endemic equilibrium.

MSC:
92D30 Epidemiology
34D20 Stability of solutions to ordinary differential equations
93A30 Mathematical modelling of systems (MSC2010)
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[1] Andersen, B.; Ostergaard, L.; Moller, J.K.; Olesen, F., Effectiveness of a mass media campaign to recruit Young adults for testing of chlamydia trachomatis by use of home obtained and mailed samples, Sex. transm. infect., 77, 416, (2001)
[2] Anderson, R.M.; May, R.M., Infectious diseases of humans: dynamics and control, (1991), Oxford University Press
[3] Buonomo, B.; D’Onofrio, A.; Lacitignola, D., Global stability of ans SIR epidemic model with information dependent vaccination, Math. biosci., 216, 9, (2008) · Zbl 1152.92019
[4] Chen, F.H., Modeling the effect of information quality on risk behaviour change and the transmission of infectious diseases, Math. biosci., 217, 125, (2009) · Zbl 1157.92026
[5] Castillo-Chavez, C.; Feng, Z., To treat or not to treat: the case of tuberculosis, J. math. biol., 35, 629, (1997) · Zbl 0895.92024
[6] Derrick, W.R.; van den Driessche, P., A disease transmission model in a nonconstant population, J. math. biol., 31, 495, (1993) · Zbl 0772.92015
[7] Diekmann, O.; Heesterbeek, J.A.P., Mathematical epidemiology of infectious diseases: model building, analysis and interpretation, (2000), John Wiley & Sons Ltd. Chichester, UK · Zbl 0997.92505
[8] Ferguson, N.M.; Cummings, D.A.T.; Fraser, C.; Cajka, J.C.; Cooley, P.C.; Burke, D.S., Strategies for mitigating an influenza pandemic, Nature, 442, 228, (2006)
[9] S. Funk, E. Gilad, V.A.A. Jansen, Endemic disease, awareness, and local behavioural response. J. Theor. Biol. (2010), in press. doi:10.1016/j.jtbi.2010.02.032. · Zbl 1406.92567
[10] S. Funk, E. Gilad, C. Watkins, V.A.A. Jansen, The spread of awareness and its impact on epidemic outbreaks, PNAS, early edition, Available from <www.pnas.org/cgi/doi/10.1073/pnas.0810762106, 2009>. · Zbl 1203.91242
[11] Gross, T.; Dommar DĹima, C.J.; Blasius, B., Epidemic dynamics on an adaptive network, Phys. rev. lett., 96, 208701, (2006)
[12] Hethcote, H.W.; van den Driessche, P., Some epidemiological models with nonlinear incidence, J. math. biol., 29, 271, (1991) · Zbl 0722.92015
[13] Hethcote, H.W.; Yorke, J.A., Gonorrhea transmission dynamics and control, Lecture notes in biomathematics, vol. 56, (1984), Springer-Verlag New York · Zbl 0542.92026
[14] Korobeinikov, A.; Maini, P.K., Non-linear incidence and stability of infectious disease models, Math. med. biol., 22, 113, (2005) · Zbl 1076.92048
[15] N. Low, N. Bender, L. Nartey, S. Redmond, A. Shang, J. Stephenson, Revised rapid review of evidence for the effectiveness of screening for genital chlamydia infection in sexually active young women and men, Review 2, National Institute of Clinical Excellence. Ref Type: Report, 2006.
[16] Nicoll, A.; Hughes, G.; Donnelly, M.; Livingstone, S.; De Angelis, D.; Fenton, K.; Evans, B.; Nöel Gill, O.; Catchpole, M., Assessing the impact of national anti-HIV health campaigns: trends in the transmission of HIV and other sexually transmitted infections in england, Sex. transm. inf., 77, 242, (2001)
[17] Oh, M.K.; Grimley, D.M.; Merchant, J.S.; Brown, P.R.; Cecil, H.; Hook, E.W., Mass media as a population-level intervention tool for chlamydia trachomatis screening: report of a pilot study, J. adoles. health, 31, 40, (2002)
[18] Risau-Gusman, S.; Zanette, D.H., Contact switching as a control startegy for epidemic outbreaks, J. theor. biol., 257, 52-60, (2009), online · Zbl 1400.92534
[19] van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. biosci., 180, 29, (2002) · Zbl 1015.92036
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