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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 147-162 |
| Number of pages | 16 |
| Journal | Mathematical Biosciences |
| Volume | 243 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jun 2013 |
| Externally published | Yes |
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Keywords
- Avian influenza
- Co-existence
- Competitive exclusion
- Highly-pathogenic
- Lowly-pathogenic
ASJC Scopus subject areas
- Medicine(all)
- Immunology and Microbiology(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Agricultural and Biological Sciences(all)
- Modeling and Simulation
- Statistics and Probability
- Applied Mathematics
Cite this
Qualitative dynamics of lowly- and highly-pathogenic avian influenza strains. / Agusto, F. B.; Gumel, Abba.
In: Mathematical Biosciences, Vol. 243, No. 2, 06.2013, p. 147-162.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Qualitative dynamics of lowly- and highly-pathogenic avian influenza strains
AU - Agusto, F. B.
AU - Gumel, Abba
PY - 2013/6
Y1 - 2013/6
N2 - 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.
AB - 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.
KW - Avian influenza
KW - Co-existence
KW - Competitive exclusion
KW - Highly-pathogenic
KW - Lowly-pathogenic
UR - http://www.scopus.com/inward/record.url?scp=84876839868&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84876839868&partnerID=8YFLogxK
U2 - 10.1016/j.mbs.2013.02.001
DO - 10.1016/j.mbs.2013.02.001
M3 - Article
C2 - 23485554
AN - SCOPUS:84876839868
VL - 243
SP - 147
EP - 162
JO - Mathematical Biosciences
JF - Mathematical Biosciences
SN - 0025-5564
IS - 2
ER -