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Spontaneous behavioural changes in response to epidemics. (English) Zbl 1402.92404

Summary: We study how spontaneous reduction in the number of contacts could develop, as a defensive response, during an epidemic and affect the course of infection events. A model is proposed which couples an SIR model with selection of behaviours driven by imitation dynamics. Therefore, infection transmission and population behaviour become dynamical variables that influence each other. In particular, time scales of behavioural changes and epidemic transmission can be different. We provide a full qualitative characterization of the solutions when the dynamics of behavioural changes is either much faster or much slower than that of epidemic transmission. The model accounts for multiple outbreaks occurring within the same epidemic episode. Moreover, the model can explain “asymmetric waves”, i.e., infection waves whose rising and decaying phases differ in slope. Finally, we prove that introduction of behavioural dynamics results in the reduction of the final attack rate.

MSC:

92D30 Epidemiology
92D50 Animal behavior
91A22 Evolutionary games
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[1] Adler, F.R., Losada, J.M., 2002. Super- and coinfection: filling the range. In: Adaptive Dynamics of Infectious Diseases: In Pursuit of Virulence Management, Cambridge University Press, Cambridge.; Adler, F.R., Losada, J.M., 2002. Super- and coinfection: filling the range. In: Adaptive Dynamics of Infectious Diseases: In Pursuit of Virulence Management, Cambridge University Press, Cambridge.
[2] Andreasen, V.; Lin, J.; Levin, S., The dynamics of cocirculating influenza strains conferring partial cross-immunity, Journal of mathematical biology, 35, 7, 825-842, (1997) · Zbl 0874.92023
[3] Bagnoli, F.; Lio, P.; Sguanci, L., Risk perception in epidemic modeling, Physical review E, 76, 6, 061904(7), (2007)
[4] Bauch, C.T., Imitation dynamics predict vaccinating behaviour, Proceedings of the royal society B: biological sciences, 272, 1669-1675, (2005)
[5] Bauch, C.T.; Earn, D.J.D., Vaccination and the theory of games, Proceedings of the national Academy of sciences, 101, 36, 13391-13394, (2004) · Zbl 1064.91029
[6] Boni, M.; Gog, J.; Andreasen, V.; Christiansen, F., Influenza drift and epidemic size: the race between generating and escaping immunity, Theoretical population biology, 65, 179-191, (2004) · Zbl 1106.92048
[7] Bootsma, M.C.J.; Ferguson, N.M., The effect of public health measures on the 1918 influenza pandemic in U.S. cities, Proceedings of the national Academy of sciences, 104, 18, 7588-7593, (2007)
[8] Castillo-Chavez, C.; Hethcote, H.; Andreasen, V.; Levin, S.A.; Liu, W.M., Epidemiological models with age structure, proportionate mixing, and cross-immunity, Journal of mathematical biology, 89, 27, 233-258, (1989) · Zbl 0715.92028
[9] Chowell, G.; Ammon, C.E.; Hengartner, N.W.; Hyman, J.M., Estimation of the reproductive number of the Spanish flu epidemic in Geneva, Switzerland, Vaccine, 24, 6747-6750, (2006)
[10] Chowell, G.; Ammon, C.E.; Hengartner, N.W.; Hyman, J.M., Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: assessing the effects of hypothetical interventions, Journal of theoretical biology, 241, 193-204, (2006) · Zbl 1447.92408
[11] Ciofi degli Atti, M.; Merler, S.; Rizzo, C.; Ajelli, M.; Massari, M.; Manfredi, P.; Furlanello, C.; Scalia Tomba, G.; Iannelli, M., Mitigation measures for pandemic influenza in Italy: an individual based model considering different scenarios, Plos one, 3, 3, e1790, (2008)
[12] Colizza, V.; Barrat, A.; Barthélemy, M.; Vespignani, A., The role of the airline transportation network in the prediction and predictability of global epidemics, Proceedings of the national Academy of sciences, 103, 7, 2015-2020, (2006) · Zbl 1296.92225
[13] Colizza, V.; Barrat, A.; Barthélemy, M.; Valleron, A.-J.; Vespignani, A., Modeling the worldwide spread of pandemic influenza: baseline case and containment interventions, Plos medicine, 4, 1, e13, (2007)
[14] D’Onofrio, A.; Manfredi, P.; Salinelli, E., Vaccinating behaviour, information, and the dynamics of SIR vaccine preventable diseases, Theoretical population biology, 71, 301-317, (2007) · Zbl 1124.92029
[15] Edwards, D.; Man, J.C.; Brand, P.; Katsra, J.P.; Sommerer, K.; Stone, H.A.; Nardell, E.; Scheuch, G., Inhaling to mitigate exhaled bioaerosols, Proceedings of the national Academy of sciences, 101, 50, 17383-17388, (2004)
[16] Ferguson, N.M., Capturing human behaviour, Nature, 446, 733, (2007)
[17] Ferguson, N.M.; Cummings, D.A.; Fraser, C.; Cajka, J.C.; Cooley, P.C., Strategies for mitigating an influenza pandemic, Nature, 442, 448-452, (2006)
[18] Hofbauer, J.; Sigmund, K., Evolutionary games and population dynamics, (1998), Cambridge University Press Cambridge · Zbl 0914.90287
[19] Hoppensteadt, F., Singular perturbations on the infinite interval, Transactions of the American mathematical society, 123, 521-535, (1966) · Zbl 0151.12502
[20] Lloyd-Smith, J.O.; Schreiber, S.J.; Koop, P.E.; Getz, W.M., Superspreading and the effect of individual variation on disease emergence, Nature, 438, 355-359, (2005)
[21] May, R.M.; Nowak, M.A., Coinfection and the evolution of parasite virulence, Proceedings of the royal society B: biological sciences, 261, 1361, 209-215, (1995)
[22] Merler, S.; Poletti, P.; Ajelli, M.; Caprile, B.; Manfredi, P., Coinfection can trigger multiple pandemic waves, Journal of theoretical biology, 254, 2, 499-507, (2008) · Zbl 1400.92526
[23] Mills, C.E.; Robins, J.M.; Lipsitch, M., Transmissibility of 1918 pandemic influenza, Nature, 432, 904-906, (2004)
[24] Moneim, I.A., The effect of using different types of periodic contact rate on the behaviour of infectious diseases: a simulation study, Computers in biology and medicine, 37, 1582-1590, (2007)
[25] Nowak, M.A.; Sigmund, K., Evolutionary dynamics of biological games, Science, 303, 793, (2004)
[26] O’Malley, R.E., Singular perturbation methods for ordinary differential equations, (1991), Springer Berlin · Zbl 0743.34059
[27] Risau-Gusman, S., Zanette, D., 2008. Contact switching as a control strategy for epidemic outbreaks. arXiv[q-bio.PE]:0806.1872.; Risau-Gusman, S., Zanette, D., 2008. Contact switching as a control strategy for epidemic outbreaks. arXiv[q-bio.PE]:0806.1872.
[28] Shaw, L.B.; Schwartz, I.B., Fluctuating epidemics on adaptive networks, Physical review E, 77, 6, 066101, (2008)
[29] Tikhonov, A., Systems of differential equations containing a small parameter multiplying the derivative, Matematicheskii sbornik (N.S.), 73, 31, 576-585, (1952), (in Russian)
[30] von Neumann, J.; Morgenstern, O., The theory of games and economic behavior, (1947), Princeton University Press Princeton · Zbl 1241.91002
[31] Wallinga, J.; Teunis, P., Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures, American journal of epidemiology, 160, 509-516, (2004)
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