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Lyapunov functions for a dengue disease transmission model

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  • Tewa, Jean Jules
  • Dimi, Jean Luc
  • Bowong, Samuel

Abstract

In this paper, we study a model for the dynamics of dengue fever when only one type of virus is present. For this model, Lyapunov functions are used to show that when the basic reproduction ratio is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is also globally asymptotically stable.

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  • Tewa, Jean Jules & Dimi, Jean Luc & Bowong, Samuel, 2009. "Lyapunov functions for a dengue disease transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 936-941.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:2:p:936-941
    DOI: 10.1016/j.chaos.2007.01.069
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    References listed on IDEAS

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    1. Zeng, Guang Zhao & Chen, Lan Sun & Sun, Li Hua, 2005. "Complexity of an SIR epidemic dynamics model with impulsive vaccination control," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 495-505.
    2. Li, Guihua & Zhen, Jin, 2005. "Global stability of an SEI epidemic model with general contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 997-1004.
    3. Li, Guihua & Wang, Wendi & Jin, Zhen, 2006. "Global stability of an SEIR epidemic model with constant immigration," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 1012-1019.
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    1. Zhu, Min & Xu, Yong & Cao, Jinde, 2019. "The asymptotic profile of a dengue fever model on a periodically evolving domain," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    2. Cai, Liming & Guo, Shumin & Li, XueZhi & Ghosh, Mini, 2009. "Global dynamics of a dengue epidemic mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2297-2304.
    3. Kolebaje, Olusola & Popoola, Oyebola & Khan, Muhammad Altaf & Oyewande, Oluwole, 2020. "An epidemiological approach to insurgent population modeling with the Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Abidemi, A. & Abd Aziz, M.I. & Ahmad, R., 2020. "Vaccination and vector control effect on dengue virus transmission dynamics: Modelling and simulation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    5. Anusit Chamnan & Puntani Pongsumpun & I-Ming Tang & Napasool Wongvanich, 2022. "Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis," Mathematics, MDPI, vol. 10(6), pages 1-25, March.
    6. Zhu, Min & Xu, Yong, 2019. "A time-periodic dengue fever model in a heterogeneous environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 115-129.
    7. Liao, Shu & Wang, Jin, 2012. "Global stability analysis of epidemiological models based on Volterra–Lyapunov stable matrices," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 966-977.
    8. Helena Sofia Rodrigues & M. Teresa T. Monteiro & Delfim F. M. Torres, 2013. "Dengue in Cape Verde: Vector Control and Vaccination," Mathematical Population Studies, Taylor & Francis Journals, vol. 20(4), pages 208-223, October.
    9. Malik, Hafiz Abid Mahmood & Abid, Faiza & Wahiddin, Mohamed Ridza & Waqas, Ahmad, 2021. "Modeling of internal and external factors affecting a complex dengue network," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    10. Saha, Pritam & Sikdar, Gopal Chandra & Ghosh, Jayanta Kumar & Ghosh, Uttam, 2023. "Disease dynamics and optimal control strategies of a two serotypes dengue model with co-infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 16-43.
    11. Srivastav, Akhil Kumar & Ghosh, Mini, 2019. "Assessing the impact of treatment on the dynamics of dengue fever: A case study of India," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    12. Dany Pascal Moualeu-Ngangue & Susanna Röblitz & Rainald Ehrig & Peter Deuflhard, 2015. "Parameter Identification in a Tuberculosis Model for Cameroon," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-20, April.
    13. Xue, Ling & Zhang, Hongyu & Sun, Wei & Scoglio, Caterina, 2021. "Transmission dynamics of multi-strain dengue virus with cross-immunity," Applied Mathematics and Computation, Elsevier, vol. 392(C).

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