Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 155, pp. 1-21.

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

Authors: Mudassar Imran (Lahore Univ. of Management Sciences, Pakistan) 
         Mohammad T. Malik (Univ. of Manitoba, Winnipeg, Canada)
	 Salisu M. Garba   (Univ. of Pretoria, South Africa)

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.