Skip to main content Accessibility help
Hostname: page-component-59b7f5684b-qn7h5 Total loading time: 0.359 Render date: 2022-10-05T03:41:01.659Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

Dynamic Epidemic Model for Influenza with Clinical Complications

Published online by Cambridge University Press:  02 January 2015

Sen-Te Wang
Department of Family Medicine, School of Medicine, College of Medicine, Taipei Medical University, Taipei, Taiwan Department of Family Medicine, Taipei Medical University Hospital, Taipei, Taiwan
Li-Sheng Chen
School of Oral Hygiene, College of Oral Medicine, Taipei Medical University, Taipei, Taiwan
Long-Teng Lee
Department of Family Medicine, National Taiwan University Hospital, Taipei, Taiwan
Hsiu-Hsi Chen*
Division of Biostatistics, Institute of Epidemiology/Center for Biostatistics, College of Public Health, National Taiwan University, Taipei, Taiwan
College of Public Health, National Taiwan University, Room 533, No. 17, Hsu-Chow Road, Taipei, Taiwan 100 (



To incorporate clinical complications in the susceptible-infectious-recovered model to estimate parameters needed in dynamic changes of infectious diseases and to further evaluate the impact of disease-controlling methods.


We developed a new extended epidemic model that incorporates of disease-related complications. This model was applied to empirical data on influenza during the epidemic season of 2001–2002 in Taipei County, Taiwan, to estimate the transmission parameters that were converted to the basic reproductive rate (R0). The proposed model, in conjunction with estimated parameters, was applied in quantifying the efficacy of different preventive strategies.


During the study period there were 5 outbreaks of influenza. The estimated transmission probability for outbreak 1 was 0.135, with corresponding estimate of R0, 2.7; for outbreak 2, 0.165, with estimated R0, 3.3; for outbreak 3, 0.15, with R0, 4.5; for outbreak 4, 0.165, with R0, 5; and for outbreak 5, 0.165, with R0 5. The efficacy of antiviral prophylaxis to reduce the total episodes was 18% (95% CI, 15%–21%) under the coverage rate of 30%, 31% (95% CI, 26%–36%) under the coverage rate of 50%, and 73% (95% CI, 59%–90%) under the coverage rate of 80%. The corresponding figures for the efficacy of vaccination were 17% (95% CI, 15%–20%), 41% (95% CI, 35%–48%), and 76% (95% CI, 61%–95%). Combination of both methods would yield efficacy of 32% (95% CI, 28%–38%), 59% (95% CI, 49%–71%), and 88% (95% CI, 66%–118%), respectively.


We demonstrate how to apply a novel extended model to empirical surveillance data of an influenza study for estimating parameters pertaining to dynamic changes in the infection process. These parameters were further used to evaluate the impact of antiviral prophylaxis alone, vaccination alone, or the use of both methods.

Original Articles
Copyright © The Society for Healthcare Epidemiology of America 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


1. Kermack, WO, McKendrick, AG. A contribution to the mathematical theory of epidemics. Proc R Soc Lond A 1927;115:700721.CrossRefGoogle Scholar
2. Anderson, RM, May, RM. Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press, 1992.Google Scholar
3. Diekmann, O, Heesterbeek, JAP. Mathematical epidemiology of infectious diseases: model building analysis and interpretation. Wiley Series in Mathematical and Computational Biology. New York: Wiley; 2000.Google Scholar
4. Gomes, MGM, White, LJ, Medley, GF. Infection, reinfection and vaccination under suboptimal immune protection: epidemiological perspectives. J Theoret Biol 2004;228:539549.CrossRefGoogle ScholarPubMed
5. Grenfell, BT, Bjornstad, ON, Kappey, J. Traveling waves and spatial hierarchies in measles epidemics. Nature 2001;414:716723.CrossRefGoogle Scholar
6. Becker, NG, Rouderfer, V. Simultaneous control of measles and rubella by multidose vaccination schedules. Math Biosci 1996; 131:81102.CrossRefGoogle ScholarPubMed
7. Andreasen, V, Lin, J, Levin, SA. The dynamics of cocirculating influenza strains conferring partial cross-immunity. J Math Biol 1997;35:825842.CrossRefGoogle ScholarPubMed
8. Ackerman, E, Longini, IM Jr, Seaholm, SK, Hedin, AS. Simulation of mechanisms of viral interference in influenza. Int J Epidemiol 1990;19:444454.CrossRefGoogle ScholarPubMed
9. Deguen, S, Flahault, A. Impact on immunization of seasonal cycle of chickenpox. Eur J Epidemiol 2000;16:11771181.CrossRefGoogle ScholarPubMed
10. Osborne, K, Gay, NJ, Hesketh, L, Morgan-Capner, P, Miller, E. Ten years of serological surveillance in England and Wales: methods, results, implications and action. Int J Epidemiol 2000;29:362368.CrossRefGoogle ScholarPubMed
11. Hethcote, HW. Simulations of pertussis epidemiology in the United States: effects of adult booster vaccinations. Math Biosci 1999;158:4773.CrossRefGoogle ScholarPubMed
12. van Boven, M, de Melker, HE, Schellekens, JFP, Kretzschmar, M. Waning immunity and sub-clinical infection in an epidemic model: implications for pertussis in the Netherlands. Math Biosci 2000;164:161182.CrossRefGoogle Scholar
13. Vynnycky, E, Fine, PEM. The natural history of tuberculosis: the implications of age-dependent risks of disease and the role of reinfection. Epidemiol Infect 1997;119:183201.CrossRefGoogle ScholarPubMed
14. Feng, Z, Castillo-Chavez, C, Capurro, AF. A model for tuberculosis with exogenous reinfection. Theoret Popul Biol 2000;57:235247.CrossRefGoogle ScholarPubMed
15. White, LJ, Waris, M, Cane, PA, Nokes, DJ, Medley, GF. The transmission dynamics of groups A and B human respiratory syncytial virus (hRSV) in England and Wales and Finland: seasonality and cross-protection. Epidemiol Infect 2005;133:279289.CrossRefGoogle Scholar
16. Cane, PA. Molecular epidemiology of respiratory syncytial virus. Rev Med Virol 2001;11:103116.CrossRefGoogle ScholarPubMed
17. Weber, A, Weber, M, Milligan, P. Modeling epidemics caused by respiratory syncytial virus (RSV). Math Biosci 2001;172:95113.CrossRefGoogle Scholar
18. Hay, AJ, Gregory, V, Douglas, AR, Lin, YP. The evolution of human influenza viruses. Philos Trans R Soc Lond B 2001;356:18611870.Google ScholarPubMed
19. Earn, DJD, Dushoff, J, Levin, SA. Ecology and evolution of the flu. Trends Ecol Evol 2002;17:334340.CrossRefGoogle Scholar
20. Rothman, KJ, Greenland, A. Modern Epidemiology. Philadelphia: Lippincott-Raven, 1998:chap 27.Google Scholar
21. Shih, SR, Chen, GW, Yang, CC, et al. Laboratory-based surveillance and molecular epidemiology of influenza virus in Taiwan. J Clin Microbiol 2005;43:16511661.CrossRefGoogle ScholarPubMed
22. Anderson, R, May, R. Population biology of infectious diseases: part I. Nature 1979;280:361.CrossRefGoogle ScholarPubMed
23. Longini, IM Jr, Halloran, EM, Nizam, A, and Yang, Y. Containing pandemic influenza with antiviral agents. Am J Epidemiol 2004; 159:623633.CrossRefGoogle ScholarPubMed
24. Hayden, FG, Aoki, FY. Amantadine, rimantadine, and related agents, antiviral agents. In: Yu, V, Meigan, T, Barriere, S, eds. Antimicrobial Therapy and Vaccines. Baltimore: Williams & Wilkins, 1999:13441365.Google Scholar
25. Hayden, FG, Gubareva, LV, Monto, AS, et al. Inhaled zanamivir for the prevention of influenza in families. N Engl J Med 2000; 343:12821289.CrossRefGoogle ScholarPubMed
26. Monto, AS, Robinson, DP, Herlocher, ML, et al. Zanamivir in the prevention of influenza among healthy adults: a randomized controlled trial. JAMA 1999;282:3135.CrossRefGoogle ScholarPubMed
27. Welliver, R, Monto, AS, Carewicz, O, et al. Effectiveness of oseltamivir in preventing influenza in household contacts: a randomized controlled trial. JAMA 2001;285:748754.CrossRefGoogle ScholarPubMed
28. Galbraith, AW, Oxford, JS, Schild, GC, et al. Study of 1-adaman-tanamine hydrochloride used prophylactically during the Hong Kong influenza epidemic in the family environment. Bull World Health Organ 1969;41:677682.Google Scholar
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the or variations. ‘’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Dynamic Epidemic Model for Influenza with Clinical Complications
Available formats

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Dynamic Epidemic Model for Influenza with Clinical Complications
Available formats

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Dynamic Epidemic Model for Influenza with Clinical Complications
Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *