GLOBAL DYNAMICS OF A REACTION AND DIFFUSION MODEL FOR AN HTLV-I INFECTION WITH MITOTIC DIVISION OF ACTIVELY INFECTED CELLS

Wei Wang; Wanbiao Ma

doi:10.11948/2017057

2017 Volume 7 Issue 3

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Wei Wang, Wanbiao Ma. GLOBAL DYNAMICS OF A REACTION AND DIFFUSION MODEL FOR AN HTLV-I INFECTION WITH MITOTIC DIVISION OF ACTIVELY INFECTED CELLS[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 899-930. doi: 10.11948/2017057

Citation:

Wei Wang, Wanbiao Ma. GLOBAL DYNAMICS OF A REACTION AND DIFFUSION MODEL FOR AN HTLV-I INFECTION WITH MITOTIC DIVISION OF ACTIVELY INFECTED CELLS[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 899-930. doi: 10.11948/2017057

GLOBAL DYNAMICS OF A REACTION AND DIFFUSION MODEL FOR AN HTLV-I INFECTION WITH MITOTIC DIVISION OF ACTIVELY INFECTED CELLS

Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

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Abstract

Abstract

This paper is concerned with the global dynamics of a reaction and diffusion model for an HTLV-I infection with mitotic division of actively infected cells and CTL immune response. The well posedness of the proposed model is investigated. In the case of a bounded spatial domain, we establish the threshold dynamics in terms of the basic reproduction number R₀ for the spatially heterogeneous model. Also, by means of different Lyapunov functions, the global asymptotic properties of the steady states for the spatially homogeneous model are studied. In the case of an unbounded spatial domain, there are no travelling wave solutions connecting the infection-free steady state with itself when R₀<1. Finally, numerical simulations and conclusions are given.
- HTLV-I infection model /
- CTL immune response /
- Threshold dynamics /
- Global stability /
- Travelling wave solutions
MSC: 34D23;34K20;92D30

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References

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