Global dynamics of a compartmental system modeling ectoparasite-borne diseases
We analyse a four-dimensional compartmental system tha t describes the spread of ectoparasites and a disease carried by them in a population. We identify three threshold parameters tha t determine which of the four potential equilibria exist. These parameters completely characterize the stability pr...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2014
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| Sorozat: | Acta scientiarum mathematicarum
80 No. 3-4 |
| Kulcsszavak: | Matematika, Algebra |
| Tárgyszavak: | |
| mtmt: | http://dx.doi.org/10.14232/actasm-013-004-y |
| Online Access: | http://acta.bibl.u-szeged.hu/34846 |
| Tartalmi kivonat: | We analyse a four-dimensional compartmental system tha t describes the spread of ectoparasites and a disease carried by them in a population. We identify three threshold parameters tha t determine which of the four potential equilibria exist. These parameters completely characterize the stability properties of the equilibria and also the global behaviour of solutions. We provide a detailed description of the global attractor in each possible scenario. Th e key mathematical tools of the proofs are Lyapunov-LaSalle theory, persistence theory, Poincaré-Dulac criteria and unstable manifolds. In the most complicated case, the global attractor consists of four equilibria and various heteroclinic orbits connecting those equilibria, forming a two-dimensional manifold in the phase space. |
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| Terjedelem/Fizikai jellemzők: | 553-572 |
| ISSN: | 0001-6969 |