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Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate

Author

Listed:
  • Salah Alsahafi

    (School of Mathematical and Physical Sciences, University of Technology Sydney, 15 Broadway, Ultimo, NSW 2007, Australia)

  • Stephen Woodcock

    (School of Mathematical and Physical Sciences, University of Technology Sydney, 15 Broadway, Ultimo, NSW 2007, Australia)

Abstract

In this article, we examine the dynamics of a Chikungunya virus (CHIKV) infection model with two routes of infection. The model uses four categories, namely, uninfected cells, infected cells, the CHIKV virus, and antibodies. The equilibrium points of the model, which consist of the free point for the CHIKV and CHIKV endemic point, are first analytically determined. Next, the local stability of the equilibrium points is studied, based on the basic reproduction number ( R 0 ) obtained by the next-generation matrix. From the analysis, it is found that the disease-free point is locally asymptotically stable if R 0 ≤ 1 , and the CHIKV endemic point is locally asymptotically stable if R 0 > 1 . Using the Lyapunov method, the global stability analysis of the steady-states confirms the local stability results. We then describe our design of an optimal recruitment strategy to minimize the number of infected cells, as well as a nonlinear optimal control problem. Some numerical simulations are provided to visualize the analytical results obtained.

Suggested Citation

  • Salah Alsahafi & Stephen Woodcock, 2021. "Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate," Mathematics, MDPI, vol. 9(18), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2186-:d:630698
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    References listed on IDEAS

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    1. Wang, Yan & Liu, Xianning, 2017. "Stability and Hopf bifurcation of a within-host chikungunya virus infection model with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 138(C), pages 31-48.
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    Cited by:

    1. Salah Alsahafi & Stephen Woodcock, 2022. "Exploring HIV Dynamics and an Optimal Control Strategy," Mathematics, MDPI, vol. 10(5), pages 1-26, February.

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