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Mathematical Biosciences and Engineering

2017, Volume 14, Issue 5&6: 1159-1186. doi: 10.3934/mbe.2017060
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Global dynamics of a vector-host epidemic model with age of infection

  • 1.
    Department of Public Education, Zhumadian Vocational and Technical College, Zhumadian 463000, China
  • 2.
    School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
  • 3.
    Department of Mathematics and Physics, Anyang Institute of Technology, Anyang 455000, China
  • 4.
    Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL 32611-8105, USA
  • Received: 01 July 2016 Accepted: 01 December 2016 Published: 01 October 2017

  • MSC : Primary: 92D30

  • In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. The model includes both incubation age of the exposed hosts and infection age of the infectious hosts which describe incubation-age dependent removal rates in the latent period and the variable infectiousness in the infectious period, respectively. The reproductive number $\mathcal R_0$ is derived. By using the method of Lyapunov function, the global dynamics of the PDE model is further established, and the results show that the basic reproduction number $\mathcal R_0$ determines the transmission dynamics of vector-borne diseases: the disease-free equilibrium is globally asymptotically stable if $\mathcal R_0≤ 1$ , and the endemic equilibrium is globally asymptotically stable if $\mathcal{R}_0 \gt 1$ . The results suggest that an effective strategy to contain vector-borne diseases is decreasing the basic reproduction number $\mathcal{R}_0$ below one.

    Citation: Yan-Xia Dang, Zhi-Peng Qiu, Xue-Zhi Li, Maia Martcheva. Global dynamics of a vector-host epidemic model with age of infection[J]. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1159-1186. doi: 10.3934/mbe.2017060

    Related Papers:

  • In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. The model includes both incubation age of the exposed hosts and infection age of the infectious hosts which describe incubation-age dependent removal rates in the latent period and the variable infectiousness in the infectious period, respectively. The reproductive number $\mathcal R_0$ is derived. By using the method of Lyapunov function, the global dynamics of the PDE model is further established, and the results show that the basic reproduction number $\mathcal R_0$ determines the transmission dynamics of vector-borne diseases: the disease-free equilibrium is globally asymptotically stable if $\mathcal R_0≤ 1$ , and the endemic equilibrium is globally asymptotically stable if $\mathcal{R}_0 \gt 1$ . The results suggest that an effective strategy to contain vector-borne diseases is decreasing the basic reproduction number $\mathcal{R}_0$ below one.


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