Information-related changes in contact patterns may trigger oscillations in the endemic prevalence of infectious diseases. (English) Zbl 1400.92570
Summary: It is well known that behavioral changes in contact patterns may significantly affect the spread of an epidemic outbreak. Here we focus on simple endemic models for recurrent epidemics, by modelling the social contact rate as a function of the available information on the present and the past disease prevalence. We show that social behavior change alone may trigger sustained oscillations. This indicates that human behavior might be a critical explaining factor of oscillations in time-series of endemic diseases. Finally, we briefly show how the inclusion of seasonal variations in contacts may imply chaos.
References:
| [1] | Alexander, M.E.; Moghadas, S.M., Periodicity in an epidemic model with a generalized nonlinear incidence, Math. biosci., 189, 75-96, (2004) · Zbl 1073.92040 |
| [2] | Anderson, D.; Watson, R., On the spread of a disease with gamma distributed latent and infectious periods, Biometrika, 67, 191-198, (1980) · Zbl 0421.92023 |
| [3] | Aron, J.; Schwartz, I.B., Seasonality and period-doubling bifurcations in an epidemic model, J. theor. biol., 110, 665-679, (1984) |
| [4] | Bacaer, N.; Abdurahman, X., Resonance of the epidemic threshold in a periodic environment, J. math. biol., 57, 649-673, (2008) · Zbl 1161.92044 |
| [5] | Bauch, C.T.; Galvani, A.P.; Earn, D.J.D., Group interest versus self-interest in smallpox vaccination policy, Proc. natl. acad. sci. USA, 100, 10564-10567, (2003) · Zbl 1065.92038 |
| [6] | Breban, R.; Vardavas, R.; Blower, S., Mean-field analysis of an inductive reasoning game: application to influenza vaccination, Phys. rev. E, 76, (2007), Art. no. 03112 |
| [7] | Buonomo, B.; d’Onofrio, A.; Lacitignola, D., Global stability of an SIR epidemic model with information dependent vaccination, Math. biosci., 216, 1, 9-16, (2008) · Zbl 1152.92019 |
| [8] | Capasso, V., The mathematical structure of epidemic systems, (2008), Springer Heidelberg, New York · Zbl 1141.92035 |
| [9] | Capasso, V.; Serio, G., A generalization of the kermack – mckendrick deterministic epidemic model, Math. biosci., 42, 43-61, (1978) · Zbl 0398.92026 |
| [10] | Chowell, G., Model parameters and outbreak control for SARS, Emerg. infect. dis., 10, 1258-1263, (2004) |
| [11] | Del Valle, S., Effects of behavioral changes in a smallpox attack model, Math. biosci., 195, 228-251, (2005) · Zbl 1065.92039 |
| [12] | d’Onofrio, A., Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times, Appl math. comput., 151, 181-187, (2004) · Zbl 1043.92033 |
| [13] | d’Onofrio, A.; Manfredi, P.; Salinelli, E., Vaccinating behaviour, information, and the dynamics of SIR vaccine preventable diseases, Theor. popul. biol., 71, 301-320, (2007) · Zbl 1124.92029 |
| [14] | d’Onofrio, A., Manfredi, P., Salinelli, E., 2008. Fatal SIR diseases and rational exemption to vaccination. Math. Med. Biol., in press, doi:10.1093/imammb/dqn019.; d’Onofrio, A., Manfredi, P., Salinelli, E., 2008. Fatal SIR diseases and rational exemption to vaccination. Math. Med. Biol., in press, doi:10.1093/imammb/dqn019. · Zbl 1154.92031 |
| [15] | Earn, D.J.D., A simple model for complex dynamical transitions in epidemics, Science, 287, 667-670, (2000) |
| [16] | Epstein, J.M., et al., 2007. Coupled contagion dynamics of fear and disease: mathematical and computational explorations. Center of Social and Economic Dynamics Working Paper no. \(50. \langle;\) http://ssrn.com/\(abstract=1024270 \rangle;\).; Epstein, J.M., et al., 2007. Coupled contagion dynamics of fear and disease: mathematical and computational explorations. Center of Social and Economic Dynamics Working Paper no. \(50. \langle;\) http://ssrn.com/\(abstract=1024270 \rangle;\). |
| [17] | Farkas, M., Periodic motions, (1994), Springer Heidelberg, New York · Zbl 0805.34037 |
| [18] | Fassin, D., La bonne mere. pratiques rurales et urbaines de la rougeole chez LES femmes haalpulaaren du senegal, Soc. sci. med., 23, 1121-1129, (1986) |
| [19] | Ferguson, N.M., Capturing human behaviour, Nature, 446, 733, (2007) |
| [20] | Ferguson, N.M., Planning for smallpox outbreaks, Nature, 425, 681-685, (2003) |
| [21] | Freedman, I.H.; Ruan, S.; Tang, M., Uniform persistence and flows near a closed positively invariant set, J. dyn. diff. eq., 6, 583-600, (1994) · Zbl 0811.34033 |
| [22] | Grassly, N.C.; Fraser, C., Seasonal infectious disease epidemiology, Proc. R. soc. London B, 273, 2541-2550, (2006) |
| [23] | Green, E.C., Uganda’s HIV prevention success: the role of sexual behavior change and the national response, AIDS behav., 10, 335-345, (2006) |
| [24] | Gregson, S., HIV decline associated with behavior change in eastern zimbabwe, Science, 311, 664-666, (2006) |
| [25] | Grossman, Z., Ongoing HIV dissemination during HAART, Nat. med., 5, 1099-1104, (1999) |
| [26] | Halverson, M.S., 2007. Native American beliefs and medical treatments during the smallpox epidemics: an evolution. Native American Rev. Summer Fall \(2007 \langle;\) http://www.earlyamerica.com/review/2007_summer_fall/native-americans-smallpox.html \(\rangle;\).; Halverson, M.S., 2007. Native American beliefs and medical treatments during the smallpox epidemics: an evolution. Native American Rev. Summer Fall \(2007 \langle;\) http://www.earlyamerica.com/review/2007_summer_fall/native-americans-smallpox.html \(\rangle;\). |
| [27] | Keeling, M.J.; Grenfell, B.T., Understanding the persistence of measles: reconciling theory, simulation and observation, Proc. R. soc. London B, 269, 335-343, (2002) |
| [28] | Kremer, M., Integrating behavioral choice into epidemiological models of the AIDS epidemic, Q. J. econ., 111, 549-573, (1996) · Zbl 0845.92022 |
| [29] | Liu, W.M.; Levin, S.A.; Iwasa, Y., Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models, J. math. biol., 23, 187-204, (1986) · Zbl 0582.92023 |
| [30] | Lloyd, A.L., Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods, Proc. R. soc. London B, 268, 985-993, (2001) |
| [31] | London, W.P.; Yorke, J.A., Recurrent outbreaks of measles, chickenpox and mumps: I. seasonal variation in contact rates, Am. J. epidemiol., 98, 453-468, (1973) |
| [32] | MacDonald, N., Biological delay systems: linear stability theory, (1989), Cambridge University Press Cambridge · Zbl 0669.92001 |
| [33] | McKusick, L., Longitudinal predictors of reductions in unprotected anal intercourse among gay men in San Francisco: the AIDS behavioral research project, Public health rep., 100, 622-629, (1985) |
| [34] | Mossong, J., Social contacts and mixing patterns relevant to the spread of infectious diseases, Plos med., 5, e74, (2008) |
| [35] | Reiss, J. 2001. The analysis of chaotic time series. Ph.D. Thesis \(\langle;\) http://www.elec.qmul.ac.uk/people/josh/documents/Reiss-PhDThesis.pdf \(\rangle;\).; Reiss, J. 2001. The analysis of chaotic time series. Ph.D. Thesis \(\langle;\) http://www.elec.qmul.ac.uk/people/josh/documents/Reiss-PhDThesis.pdf \(\rangle;\). |
| [36] | Reluga, T.; Bauch, C.; Galvani, A., Evolving public perceptions and stability in vaccine uptake, Math. biosci., 204, 185-198, (2006) · Zbl 1104.92042 |
| [37] | Ruan, S.; Wang, W., Dynamical behavior of an epidemic model with a nonlinear incidence rate, J. diff. eq., 188, 135-163, (2003) · Zbl 1028.34046 |
| [38] | van den Driessche, P.; Watmough, J., A simple SIS epidemic model with a backward bifurcation, J. math. biol., 40, 525-540, (2000) · Zbl 0961.92029 |
| [39] | Vardavas, R.; Breban, R.; Blower, S., Can influenza epidemics be prevented by voluntary vaccination ?, PLOS comput. biol., 3, e85, (2006) |
| [40] | Velasco-Hernandez, J.X.; Brauer, F.; Castillo-Chavez, C., Effects of treatment and prevalence-dependent recruitment on the dynamics of a fatal disease, IMA J. math. appl. biol. med., 13, 175-196, (1996) · Zbl 0857.92015 |
| [41] | Wang, W., Epidemic model with nonlinear forces of infection, Math. biosci. eng., 3, 267-279, (2006) · Zbl 1089.92052 |
| [42] | Wang, W.; Zhao, X.Q., Threshold dynamics for compartmental epidemic models in periodic environments, J. dyn. diff. eq., 20, 699-717, (2008) · Zbl 1157.34041 |
| [43] | Wolf, A., Determining Lyapunov exponents from a time series, Physica D, 16, 285-317, (1985) · Zbl 0585.58037 |
| [44] | Zhou, Y.; Xiao, D.; Li, Y., Bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action, Chaos solitons fractals, 32, 1903-1915, (2007) · Zbl 1195.92058 |
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