Optimal Timing of Disease Transmission in an Age-Structured Population
It is a common medical folk-practice for parents to encourage their children to contract certain infectious diseases while they are young. This folk-practice is controversial, in part, because it contradicts the long-term public health goal of minimizing disease incidence. We study an epidemiological model of infectious disease in an age-structured population where virulence is age-dependent and show that, in some cases, the optimal behavior will increase disease transmission. This provides a rigorous justification of the concept of “endemic stability,” and demonstrates that folk-practices may have been historically justified.
KeywordsAge-dependent virulence Population games Optimal behavior
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- Anderson, R.M., May, R.M., 1991. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, New York. Google Scholar
- Arrow, K.J., Kurz, M., 1970. Public Investment, the Rate of Return, and Optimal Fiscal Policy. Hopkins Press, Baltimore. Google Scholar
- Leavitt, J.W., 1997. Typhoid Mary: Captive to the Public’s Health. Beacon Press, Boston. Google Scholar
- Mandell, G.L., Bennett, J.E., Dolin, R. (Eds.), 2005. Principles and Practice of Infectious Disease. Elsevier, Philadelphia. Google Scholar
- Morisse, J.P., Le Gall, G., Boilletot, E., 1991. Hepatitis of viral origin in Leporidae: Introduction and aetiological hypotheses. Rev. Sci. Tech. 10, 269–310. Google Scholar
- Nathanson, N., Martin, J., 1979. The epidemiology of poliomyelitis: enigmas surrounding its appearance and disappearance. Am. J. Epidemiol. 110, 672. Google Scholar
- Pado, F., 2005. Where the play dates are fun, but itchy. New York Times, August 21. Google Scholar
- Panagiotopoulos, T., Antoniadou, I., Valassi-Adam, E., 1999. Increase in congenital rubella occurrence after immunisation in Greece: retrospective survey and systematic review. Br. Med. J. 319, 1462–1466. Google Scholar
- Parashar, U.D., Hummelman, E.G., Bresee, J.S., Miller, M.A., Glass, R.I., 2003. Global illness and deaths caused by rotavirus disease in children. Emerg. Infect. Dis. 9, 565–572. Google Scholar
- Paul, J.R., 1971. A History of Poliomyelitis. Yale University Press, New Haven. Google Scholar
- Preblud, S.R., 1986. Varicella: complications and costs. Pediatrics 79, 728–735. Google Scholar
- World Health Organization, 2000. Rubella vaccines. Weekly Epidemiol. Rec. 75, 161–172. Google Scholar