On the Role of Asymptomatic Infection in Transmission Dynamics of Infectious Diseases
- 210 Downloads
We propose a compartmental disease transmission model with an asymptomatic (or subclinical) infective class to study the role of asymptomatic infection in the transmission dynamics of infectious diseases with asymptomatic infectives, e.g., influenza. Analytical results are obtained using the respective ratios of susceptible, exposed (incubating), and asymptomatic classes to the clinical symptomatic infective class. Conditions are given for bistability of equilibria to occur, where trajectories with distinct initial values could result in either a major outbreak where the disease spreads to the whole population or a lesser outbreak where some members of the population remain uninfected. This dynamic behavior did not arise in a SARS model without asymptomatic infective class studied by Hsu and Hsieh (SIAM J. Appl. Math. 66(2), 627–647, 2006). Hence, this illustrates that depending on the initial states, control of a disease outbreak with asymptomatic infections may involve more than simply reducing the reproduction number. Moreover, the presence of asymptomatic infections could result in either a positive or negative impact on the outbreak, depending on different sets of conditions on the parameters, as illustrated with numerical simulations. Biological interpretations of the analytical and numerical results are also given.
KeywordsInfluenza Asymptomatic infection Basic reproduction number Bistability Threshold asymptomatic fraction
Unable to display preview. Download preview PDF.
- Bell, D.M., World Health Organization Writing Group, 2006. Nonpharmaceutical interventions for pandemic influenza, international measures. Emerg. Infect. Dis. 12(1), 81–87. Google Scholar
- Coppell, W.A., 1965. Stability and Asymptotic Behavior of Solutions of Differential Equations. Heath, Boston. Google Scholar
- Diekmann, O., Heesterbeek, J.A.P., 2000. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Wiley Series in Mathematical and Computational Biology. Wiley, New York. Google Scholar
- Graat, J.M., Schouten, E.G., Heijnen, M.L., Kok, F.J., Pallast, E.G., de Greeff, S.C., Dorigo-Zetsma, J.W., 2003. A prospective, community-based study on virologic assessment among elderly people with and without symptoms of acute respiratory infection. J. Clin. Epidemiol. 56(12), 1218–1223. CrossRefGoogle Scholar
- Nafta, I., Turcanu, A.G., Braun, I., Companetz, W., Simionescu, A., Birt, E., Florea, V., 1970. Administration of amantadine for the prevention of Hong Kong influenza. Bull. World Health. Organ. 42, 423–427. Google Scholar
- Pettersson, R.F., Hellstrom, P.E., Penttinen, K., Pyhala, R., Tokola, O., Vartio, T., Visakorpi, R., 1980. Evaluation of amantadine in the prophylaxis of influenza A (H1N1) virus infection: a controlled field trial among young adults and high-risk patients. J. Infect. Dis. 142, 377–383. Google Scholar
- Stilianakis, N.I., Perelson, A.S., Hayden, F.G., 1998. Emergence of drug resistance during an influenza epidemic: insights from a mathematical model. J. Infect. Dis. 177(4), 863–873. Google Scholar