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Global dynamics of a two-strain avian influenza model. (English) Zbl 1154.92032
Summary: A deterministic model for the transmission dynamics of avian influenza in birds (wild and domestic) and humans is developed. The model, which allows for the transmission of an avian strain and its mutant (assumed to be transmissible between humans), as well as the isolation of individuals with symptoms of any of the two strains, has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the reproduction number, is less than unity. Further, the model has a unique endemic equilibrium whenever this threshold quantity exceeds unity. It is shown, using a nonlinear Lyapunov functions and the LaSalle invariance principle, that this endemic equilibrium is globally asymptotically stable for a special case of the avian-only system.
Numerical simulations show that, on average, the isolation of individuals with the avian strain is more beneficial than isolating those with the mutant strain. Furthermore, disease burden increases with increasing mutation rate of the avian strain.

MSC:
92C60 Medical epidemiology
34D23 Global stability of solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
92C50 Medical applications (general)
65C20 Probabilistic models, generic numerical methods in probability and statistics
34D20 Stability of solutions to ordinary differential equations
37N25 Dynamical systems in biology
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