Global stability of the steady states of an epidemic model incorporating intervention strategies
In this paper, we investigate the global stability of the steady states of a general reaction-diffusion epidemiological model with infection force under intervention strategies in a spatially heterogeneous environment. We prove that the reproduction number $\mathcal{R}_0$ can be played an essentia...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017056 |
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| Summary: | In this paper, we investigate the global stability of the steady states of a general reaction-diffusion epidemiological model with infection force under intervention strategies in a spatially heterogeneous environment. We prove that the reproduction number $\mathcal{R}_0$ can be played an essential role in determining whether the disease will extinct or persist: if $\mathcal{R}_0 \lt 1$ , there is a unique disease-free equilibrium which is globally asymptotically stable; and if $\mathcal{R}_0 \gt 1$ , there exists a unique endemic equilibrium which is globally asymptotically stable. Furthermore, we study the relation between $\mathcal{R}_0$ with the diffusion and spatial heterogeneity and find that, it seems very necessary to create a low-risk habitat for the population to effectively control the spread of the epidemic disease. This may provide some potential applications in disease control. |
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| ISSN: | 1551-0018 |