Traveling waves for a diffusive SIR-B epidemic model with multiple transmission pathways
In this work, we consider a diffusive SIR-B epidemic model with multiple transmission pathways and saturating incidence rates. We first present the explicit formula of the basic reproduction number R0. Then we show that if R0 > 1, there exists a constant c ∗ > 0 such that the system admits tra...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Reakció-diffúziós egyenlet |
| doi: | 10.14232/ejqtde.2019.1.86 |
| Online Access: | http://acta.bibl.u-szeged.hu/64730 |
| Tartalmi kivonat: | In this work, we consider a diffusive SIR-B epidemic model with multiple transmission pathways and saturating incidence rates. We first present the explicit formula of the basic reproduction number R0. Then we show that if R0 > 1, there exists a constant c ∗ > 0 such that the system admits traveling wave solutions connecting the disease-free equilibrium and endemic equilibrium with speed c if and only if c ≥ c Since the system does not admit the comparison principle, we appeal to the standard Schauder’s fixed point theorem to prove the existence of traveling waves. Moreover, a suitable Lyapunov function is constructed to prove the upward convergence of traveling waves. |
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| Terjedelem/Fizikai jellemzők: | 1-19 |
| ISSN: | 1417-3875 |