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Analysis of a diffusive virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence

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  • Luo, Yantao
  • Zhang, Long
  • Zheng, Tingting
  • Teng, Zhidong

Abstract

In this paper, we investigate a reaction–diffusion virus infection model with humoral immunity and nonlinear incidence in heterogeneous and homogenous environments. The model includes simultaneously the virus-to-cell and cell-to-cell transmissions of the infection. The well-posedness of solutions, including the existence of global solutions and the ultimate boundedness, is established. The virus infection reproduction number R0 is calculated. When R0≤1, it is proved that the infection-free steady state is globally asymptotically stable. Otherwise, when R0>1 then the infection with antibody-free response is uniformly persistent. Furthermore, the antibody-free infection equilibrium is also globally asymptotically stable in spatially homogeneous case. In order to investigate the effect of humoral immunity, the virus infection with antibody response model in the spatially homogeneous environment is considered. The antibody response reproduction number R1 is calculated. The threshold criteria on the uniform persistence of total model and the global asymptotic stability of the antibody-response infection equilibrium are established. Finally, the numerical examples are presented to illustrate the theoretical results and verify the conjectures.

Suggested Citation

  • Luo, Yantao & Zhang, Long & Zheng, Tingting & Teng, Zhidong, 2019. "Analysis of a diffusive virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    • Handle: RePEc:eee:phsmap:v:535:y:2019:i:c:s0378437119313913
    DOI: 10.1016/j.physa.2019.122415
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    References listed on IDEAS

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    1. Zhang, Baoxiang & Cai, Yongli & Wang, Bingxian & Wang, Weiming, 2019. "Pattern formation in a reaction–diffusion parasite–host model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 732-740.
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    Cited by:

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    2. Noura H. AlShamrani & Ahmed Elaiw & Aeshah A. Raezah & Khalid Hattaf, 2023. "Global Dynamics of a Diffusive Within-Host HTLV/HIV Co-Infection Model with Latency," Mathematics, MDPI, vol. 11(6), pages 1-47, March.
    3. Qi, Ke & Liu, Zhijun & Wang, Lianwen & Chen, Yuming, 2023. "Global dynamics of a diffusive SEICR HCV model with nonlinear incidences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 181-197.
    4. Chen, Wei & Teng, Zhidong & Zhang, Long, 2021. "Global dynamics for a drug-sensitive and drug-resistant mixed strains of HIV infection model with saturated incidence and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 406(C).

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