Mudassar Imran, Mohammad T. Malik, Salisu M. Garba
Abstract:
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 | |
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Mohammad Tufail Malik Department of Mathematics, University of Manitoba Winnipeg, Manitoba, R3T 2N2, Canada email: malik@cc.umanitoba.ca http://home.cc.umanitoba.ca/~malik |
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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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