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Global Stability of a Delay Virus Dynamics Model with Mitotic Transmission and Cure Rate

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Mathematical Modelling and Analysis of Infectious Diseases

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 302))

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Abstract

In this paper, we study the global properties of a basic model for viral infection with mitotic transmission, “cure” of infected cells, saturated infection rate, and a discrete intracellular delay. For our model, we derive some threshold parameters and establish a set of conditions which are sufficient to determine the global dynamics of the models. By using suitable Lyapunov functionals and the Lyapunov–Lasalle type theorem for delay systems, we prove the global asymptotic stability of all equilibria of our model. We also establish the occurrence of a Hopf bifurcation, determine conditions for the permanence of model, and the length of delay to preserve stability. Furthermore, we present some numerical simulations to illustrate the analytical results.

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Acknowledgements

This work was supported by Universidad Autónoma de Yucatán and Mexican CONACYT under SNI grant numbers 15284 and 33365.

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Authors and Affiliations

  1. Facultad de Matemáticas, Universidad Autónoma de Yucatán, Anillo Periférico Norte, Tablaje 13615, 97119, Mérida, Yucatán, Mexico

    Eric Avila-Vales, Abraham Canul-Pech, Gerardo E. García-Almeida & Ángel G. C. Pérez

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  1. Eric Avila-Vales
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  2. Abraham Canul-Pech
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  3. Gerardo E. García-Almeida
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  4. Ángel G. C. Pérez
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Correspondence to Eric Avila-Vales .

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Editors and Affiliations

  1. Centre Régional des Métiers de l’Education et de la Formation (CRMEF), Casablanca, Morocco

    Khalid Hattaf

  2. Department of Mathematics, Gauhati University, Guwahati, India

    Hemen Dutta

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Avila-Vales, E., Canul-Pech, A., García-Almeida, G.E., Pérez, Á.G.C. (2020). Global Stability of a Delay Virus Dynamics Model with Mitotic Transmission and Cure Rate. In: Hattaf, K., Dutta, H. (eds) Mathematical Modelling and Analysis of Infectious Diseases. Studies in Systems, Decision and Control, vol 302. Springer, Cham. https://doi.org/10.1007/978-3-030-49896-2_4

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  • DOI: https://doi.org/10.1007/978-3-030-49896-2_4

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  • Online ISBN: 978-3-030-49896-2

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