Electron. J. Diff. Equ., Vol. 2011 (2011), No. 155, pp. 1-21.

Deterministic model for the role of antivirals in controlling the spread of the H1N1 influenza pandemic

Mudassar Imran, Mohammad T. Malik, Salisu M. Garba

A deterministic model is designed and used to theoretically assess the impact of antiviral drugs in controlling the spread of the 2009 swine influenza pandemic. In particular, the model considers the administration of the antivirals both as a preventive as well as a therapeutic agent. Rigorous analysis of the model reveals that its disease-free equilibrium is globally-asymptotically stable under certain conditions involving having the associated reproduction number less than unity. Furthermore, the model has a unique endemic equilibrium if the reproduction threshold exceeds unity. The model provides a reasonable fit to the observed H1N1 pandemic data for the Canadian province of Manitoba. Numerical simulations of the model suggest that the singular use of antivirals as preventive agents only makes a limited population-level impact in reducing the burden of the disease in the population (except if the effectiveness level of this "prevention-only" strategy is high). On the other hand, the combined use of the antivirals (both as preventive and therapeutic agents) resulted in a dramatic reduction in disease burden. Based on the parameter values used in these simulations, even a moderately-effective combined treatment-prevention antiviral strategy will be sufficient to eliminate the H1N1 pandemic from the province.

Submitted July 6, 2011. Published November 18, 2011.
Math Subject Classifications: 92D30.
Key Words: H1N1 influenza; deterministic model; antiviral; Lyapunov function.

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  Mudassar Imran
Department of Mathematics
Lahore University of Management Sciences
Lahore, Pakistan
email: mudassar.imran@gmail.com
Mohammad Tufail Malik
Department of Mathematics, University of Manitoba
Winnipeg, Manitoba, R3T 2N2, Canada
email: malik@cc.umanitoba.ca
Salisu M. Garba
Department of Mathematics and Applied Mathematics
University of Pretoria
Pretoria 0002, South Africa
email: Salisu.Garba@up.ac.za

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