Global dynamics of a two-strain avian influenza model

Abstract

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 non-linear Lyapunov function and 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.

In memory of my wonderful father, Alhaji Babandi (‘Zaki’) Gumel (1915–2008)

Keywords:

• avian influenza
• equilibria
• stability
• reproduction number
• Lyapunov function

2000 AMS Subject Classification :

• 92B05
• 92C60

Acknowledgements

The author acknowledges, with thanks, the support in part of the Natural Science and Engineering Research Council (NSERC) and Mathematics of Information Technology and Complex Systems (MITACS) of Canada. The author is grateful H. Guo, C.C. McCluskey, C.N. Podder and J. Watmough for useful suggestions. The author is grateful to the anonymous reviewers for their constructive comments.

Notes

In memory of my wonderful father, Alhaji Babandi (‘Zaki’) Gumel (1915–2008)