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Global dynamics of a diffusive SEICR HCV model with nonlinear incidences

Author

Listed:
  • Qi, Ke
  • Liu, Zhijun
  • Wang, Lianwen
  • Chen, Yuming

Abstract

To capture the transmission dynamics of hepatitis C virus, we propose and study a reaction–diffusion nonlinear SEICR model, which includes latent, acute, and chronic infection stages. We first establish the well-posedness and boundedness of the model. It is shown the disease-free steady state is globally asymptotically stable if the basic reproduction number R0<1 while the model is uniformly persistent if R0>1. For the special case where the model parameters are spatially homogeneous, we not only derive the explicit expression of R0 but also show that the positive steady state is globally asymptotically stable if R0>1 through the approach of Lyapunov functionals. The feasibility of the theoretical results is demonstrated by numerical simulations. Moreover, we carry out the sensitivity analysis of R0 with respect to the parameters and thus the important parameters significantly influencing the dynamic behaviors are identified.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:181-197
    DOI: 10.1016/j.matcom.2022.11.017
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    References listed on IDEAS

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    1. Zhang, Chao & Gao, Jianguo & Sun, Hongquan & Wang, Jinliang, 2019. "Dynamics of a reaction–diffusion SVIR model in a spatial heterogeneous environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    2. Zhang, Chao & Gao, Jianguo & Sun, Hongquan & Wang, Jinliang, 2019. "Dynamics of a reaction–diffusion SVIR model in a spatial heterogeneous environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C), pages 1-1.
    3. Mingwang Shen & Yanni Xiao & Weike Zhou & Zhen Li, 2015. "Global Dynamics and Applications of an Epidemiological Model for Hepatitis C Virus Transmission in China," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-13, January.
    4. Sun, Chengjun & Lin, Yiping & Tang, Shoupeng, 2007. "Global stability for an special SEIR epidemic model with nonlinear incidence rates," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 290-297.
    5. 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).
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