An SEIR epidemic model with constant latency time and infectious period
We present a two delays SEIR epidemic model with a saturation incidencerate. One delay is the time taken by the infected individuals to becomeinfectious (i.e. capable to infect a susceptible individual), the seconddelay is the time taken by an infectious individual to be removed from theinfection. B...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2011-07-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.931 |
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| Summary: | We present a two delays SEIR epidemic model with a saturation incidencerate. One delay is the time taken by the infected individuals to becomeinfectious (i.e. capable to infect a susceptible individual), the seconddelay is the time taken by an infectious individual to be removed from theinfection. By iterative schemes and the comparison principle, we provideglobal attractivity results for both the equilibria, i.e. the disease-freeequilibrium $\mathbf{E}_{0}$ and the positive equilibrium $\mathbf{E}_{+}$,which exists iff the basic reproduction number $\mathcal{R}_{0}$ is largerthan one. If $\mathcal{R}_{0}>1$ we also provide a permanence result for themodel solutions. Finally we prove that the two delays are harmless in thesense that, by the analysis of the characteristic equations, which result tobe polynomial trascendental equations with polynomial coefficients dependentupon both delays, we confirm all the standard properties of an epidemicmodel: $\mathbf{E}_{0}$ is locally asymptotically stable for $\mathcal{R}%_{0}1$, while if $\mathcal{R}_{0}>1$then $\mathbf{E}_{+}$ is always asymptotically stable. |
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| ISSN: | 1551-0018 |