Global Stability Analysis of Dengue Transmission Model with Awareness, Vector Control and Time Delays

In this paper, a mathematical model for a single-strain dengue virus transmission, incorporating vector control, disease awareness of susceptible humans, and both the latent delays for human and mosquitoes, is proposed and studied. The global stability properties of disease-free equilibrium and ende...

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Bibliographic Details
Published in:Journal of physics. Conference series 2021-05, Vol.1899 (1), p.12104
Main Authors: De Lara-Tuprio, Elvira P., Teng, Timothy Robin Y., Macalalag, Jay Michael R.
Format: Article
Language:English
Subjects:
Asymptotic properties
Control stability
Dengue fever
Disease control
Equilibrium
Mathematical models
Physics
Stability analysis
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Summary:In this paper, a mathematical model for a single-strain dengue virus transmission, incorporating vector control, disease awareness of susceptible humans, and both the latent delays for human and mosquitoes, is proposed and studied. The global stability properties of disease-free equilibrium and endemic equilibrium are completely established through Lyapunov functionals and LaSalle’s invariance principle. The global dynamics of the equilibrium points are characterized by the value of basic reproductive number R 0 . If R 0 < 1, then the disease-free equilibrium is globally asymptotically stable. If R 0 > 1 , then the disease-free equilibrium is unstable, and the endemic equilibrium exists which is globally asymptotically stable. Lastly, this paper presents numerical simulations and possible recommendations for future works.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1899/1/012104