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Analysis of a Simple Vector-Host Epidemic Model with Direct Transmission

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  • Liming Cai
  • Xuezhi Li

Abstract

Vector-host epidemic models with direct transmission are proposed and analyzed. It is shown that the stability of the equilibria in the proposed models can be controlled by the basic reproduction number of the disease transmission. One model considers that the dynamics of human hosts and vectors are described by SIS and SI model, respectively, where the global asymptotical stability for the equilibria of the model is analyzed by constructing Lyapunov function, respectively. The other model considers that the dynamics of the human hosts and vectors are described by SIRS and SI model, respectively, where the global stability of the disease-free equilibrium and the persistence of the disease in the model are also analyzed, respectively.

Suggested Citation

  • Liming Cai & Xuezhi Li, 2010. "Analysis of a Simple Vector-Host Epidemic Model with Direct Transmission," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-12, May.
    • Handle: RePEc:hin:jnddns:679613
    DOI: 10.1155/2010/679613
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    Cited by:

    1. Cai, Li-Ming & Li, Xue-Zhi & Li, Zhaoqiang, 2013. "Dynamical behavior of an epidemic model for a vector-borne disease with direct transmission," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 54-64.

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