Search

A deterministicmodel for the transmission dynamics of a communicable disease is developed and rigorously analysed. Themodel, consisting of five mutually exclusive compartments representing the human dynamics, has a globally asymptotically stable diseasefree equilibrium (DFE) whenever a certain epidemiological threshold, known as the basic reproduction number (R0), is less than unity; in such a case the endemic equilibrium does not exist. On the other hand, when the reproduction number is greater than unity, it is shown, using nonlinear Lyapunov function of Goh-Volterra type, in conjunction with the LaSalle's invariance principle, that the unique endemic equilibrium of the model is globally asymptotically stable under certain conditions. Furthermore, the disease is shown to be uniformly persistent whenever R0 > 1. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]