Abstract
The paper presents a rigorous mathematical analysis of a deterministic model, which uses a standard incidence function, for the transmission dynamics of a communicable disease with an arbitrary number of distinct infectious stages. It is shown, using a linear Lyapunov function, that the model has a globally-asymptotically stable disease-free equilibrium whenever the associated reproduction threshold is less than unity. Further, the model has a unique endemic equilibrium when the threshold exceeds unity. The equilibrium is shown to be locally-asymptotically stable, for a special case, using a Krasnoselskii sub-linearity trick. Finally, a non-linear Lyapunov function is used to show the global asymptotic stability of the endemic equilibrium (for the special case). Numerical simulation results, using parameter values relevant to the transmission dynamics of influenza, are presented to illustrate some of the main theoretical results.
Original language | English (US) |
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Pages (from-to) | 202-217 |
Number of pages | 16 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 366 |
Issue number | 1 |
DOIs | |
State | Published - Jun 1 2010 |
Externally published | Yes |
Keywords
- Equilibria
- Infectious disease
- Lyapunov function
- Reproduction number
- Stability
ASJC Scopus subject areas
- Analysis
- Applied Mathematics