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Global Stability of a Secondary Dengue Viral Infection Model |
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PP: 635-643 |
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doi:10.18576/amis/140412
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Author(s) |
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A. A. Raezah,
A. M. Elaiw,
A. S. Alofi,
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Abstract |
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| This paper proposes and analyzes a secondary dengue viral infection model with two antibodies, namely heterologous antibody and homologous antibody. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We have shown that the model has four steady states, namely: infection-free steady state S0, infected steady state with inactive antibody immune response S1, infected steady state with only active heterologous antibody S2, and infected steady state with only active homologous antibody S3. We derive three bifurcation parameters: the basic infection reproduction number R0, the heterologous antibody immune response activation number R1, and the homologous antibody immune response activation number R2. These parameters define the existence and global stability of the steady states of the model. We prove the global asymptotic stability of all steady states utilizing Lyapunov function and LaSalle’s invariance principle. We illustrate the theoretical results via numerical simulations. |
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