Department of Health and Human Services
Centers for Disease Control and Prevention

Emerging Infectious Diseases

ISSN: 1080-6059

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Article Contents

Deterministic Model
Model Calibration and Attributable Risk
References
Suggested Citation

Volume 13, Number 6–June 2007

Research

Strategies to Reduce Person-to-Person Transmission during Widespread Escherichia coli O157:H7 Outbreak

Edmund Y.W. Seto,* Jeffrey A. Soller,† and John M. Colford Jr*
*University of California at Berkeley School of Public Health, Berkeley, California, USA; and †Soller Environmental/Eisenberg, Olivieri, & Associates, Berkeley, California, USA

Appendix

Deterministic Model

The equations used for the Escherichia coli transmission model are as follows:

where at day t, state S is the number of persons susceptible to infection, E is the number of latent infections, C is the number of infected but asymptomatic, D is the number of infected with symptoms, and P is the number recovered from infection with partial and short-term resistance to subsequent infection. The model accounts for transmission of infection through the environment-to-person (), person-to-person (), and spinach-consumption routes of exposure (), and allows for a reduction in secondary transmission, , due to an assumed intervention.

Model Calibration and Attributable Risk

The model was first calibrated to the annual incidence in the United States by setting and and then solving for values of andsuch that

where 73,80 is the Centers for Disease Control and Prevention's estimate of annual cases in the United States (1), 1/δ is the average duration of symptoms, 1/365 converts the annual cases to an average number of daily cases, and time, t, is large (i.e.,is at equilibrium). was constrained so that it produced the correct proportion of cases caused by secondary transmission (2,3), .

The model was subsequently calibrated to the reported outbreak conditions of 131 new illnesses between August 1 and September 19 and 93% of the illnesses (122 persons infected) between August 19 and September 5 (4). This calibration was done by allowingto be greater than zero starting on August 19 (approximately when cases attributable to the outbreak were first identified) for a varied number of days. We solved for both the value of and the number of days of transmission, such that they best-fit the outbreak conditions.

To compute the number of cases attributable to the outbreak, we subtracted the number of cases for the endemic disease model () from the number of cases for the outbreak model () during the outbreak period, August 1–September 19. The effect of proposed interventions on secondary transmission was evaluated by using the time-varying function, . was set equal to 1 until the time of intervention and then changed to represent a reduction in secondary transmission.

References

Mead PS, Slutsker L, Dietz V, McCaig LF, Bresee JS, Shapiro C, et al. Food-related illness and death in the United States. Emerg Infect Dis. 1999;5:607–25.
Parry SM, Salmon RL. Sporadic STEC O157 infection: secondary household transmission in Wales. Emerg Infect Dis. 1998;4:657–61.
Katz DE, Heisey-Grove D, Beach M, Dicker RC, Matyas BT. Prolonged outbreak of giardiasis with two modes of transmission. Epidemiol Infect. 2006;134:935–41.
Centers for Disease Control and Prevention. Update on multi-state outbreak of E. coli O157:H7 infections from fresh spinach, September 19, 2006. 2006. [cited 2006 Oct 17]. Available from http://www.cdc.gov/foodborne/ecolispinach/091906.htm