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Math. Comput. Appl. 2017, 22(1), 7; doi:10.3390/mca22010007

Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth

School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China
Academic Editor: Fazal M. Mahomed
Received: 28 October 2016 / Revised: 21 December 2016 / Accepted: 21 December 2016 / Published: 14 January 2017
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Abstract

Viruses have important influences on human health: they not only cause some common diseases, but also cause serious illnesses. Moreover, the conventional medicines usually fail to prevent or treat them, and viral infections are hard to treat because viruses live inside the body’s cells. However, some mathematical models can help to understand the viral transmission mechanism and control viral diseases. In this paper, a delayed viral infection model with spatial diffusion and logistic growth is presented. The asymptotic stability of nonnegative uniform steady states is investigated by utilizing the linearized method and constructing the proper Lyapunov functional, respectively. The existence of Hopf bifurcation from the positive equilibrium point is established by analyzing the corresponding characteristic equation and the direction of bifurcation, and the properties of bifurcating periodic solutions are derived by the aid of the normal form theory for partial functional differential equations. Then, the cross-diffusion system is introduced. Furthermore, some numerical simulations are carried, out and discussions are given. View Full-Text
Keywords: reaction-diffusion system; viral infection model; Hopf bifurcation; time delay reaction-diffusion system; viral infection model; Hopf bifurcation; time delay
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Zhuang, K. Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth. Math. Comput. Appl. 2017, 22, 7.

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