tetano
Editor, Senior Moderator
Math Biosci. 2013 Feb 25. pii: S0025-5564(13)00047-3. doi: 10.1016/j.mbs.2013.02.001. [Epub ahead of print]
Qualitative Dynamics of Lowly- and Highly-Pathogenic Avian Influenza Strains.
Agusto FB, Gumel AB.
Source
Department of Mathematics, Austin Peay State University, Clarksville, TN, 37040, USA.
Abstract
A new deterministic model for the transmission dynamics of the lowly- and highly-pathogenic avian influenza (LPAI and HPAI) strains is designed and rigorously analyzed. The model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium whenever the associated reproduction number is less than unity. It is shown that the re-infection of birds infected with the LPAI strain causes the backward bifurcation phenomenon. In the absence of such re-infection, the disease-free equilibrium of the model is globally-asymptotically stable when the associated reproduction number is less than unity. Using non-linear Lyapunov functions of Goh-Volterra type, the LPAI-only and HPAI-only boundary equilibria of the model are shown to be globally-asymptotically stable when they exist. A special case of the model is shown to have a continuum of co-existence equilibria whenever the associated reproduction numbers of the two strains are equal and exceed unity. Furthermore, numerical simulations of the model suggest that co-existence or competitive exclusion of the two strains can occur when the respective reproduction numbers of the two strains exceed unity.
Copyright ? 2013 Elsevier Inc. All rights reserved.
PMID:
23485554
[PubMed - as supplied by publisher]
http://www.ncbi.nlm.nih.gov/pubmed/23485554
Qualitative Dynamics of Lowly- and Highly-Pathogenic Avian Influenza Strains.
Agusto FB, Gumel AB.
Source
Department of Mathematics, Austin Peay State University, Clarksville, TN, 37040, USA.
Abstract
A new deterministic model for the transmission dynamics of the lowly- and highly-pathogenic avian influenza (LPAI and HPAI) strains is designed and rigorously analyzed. The model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium whenever the associated reproduction number is less than unity. It is shown that the re-infection of birds infected with the LPAI strain causes the backward bifurcation phenomenon. In the absence of such re-infection, the disease-free equilibrium of the model is globally-asymptotically stable when the associated reproduction number is less than unity. Using non-linear Lyapunov functions of Goh-Volterra type, the LPAI-only and HPAI-only boundary equilibria of the model are shown to be globally-asymptotically stable when they exist. A special case of the model is shown to have a continuum of co-existence equilibria whenever the associated reproduction numbers of the two strains are equal and exceed unity. Furthermore, numerical simulations of the model suggest that co-existence or competitive exclusion of the two strains can occur when the respective reproduction numbers of the two strains exceed unity.
Copyright ? 2013 Elsevier Inc. All rights reserved.
PMID:
23485554
[PubMed - as supplied by publisher]
http://www.ncbi.nlm.nih.gov/pubmed/23485554