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<p>In this paper, the dynamical behavior of a within-host HIV-1 infection model with nonlocal diffusion operator, nonlinear incidence rate, intracellular delays and CTL-immune response, in a spatially heterogeneous environment is investigated. The model includes the proliferation rate of CTL from natural resources. The global existence, dissipativity and compactness of the semiflow generated by the system are established. By using the perturbation technique, we define the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal R_0\)</EquationSource> </InlineEquation> as the spectral radius of the next generation operator and this threshold number determines the global behavior of the model. That is, we show that the spatially heterogeneous infection-free equilibrium is globally asymptotically stable whenever <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal R_0\)</EquationSource> </InlineEquation> is less than unity. Furthermore, we establish the uniform persistence and the existence of at least one chronic infection equilibrium which is globally attractive whenever <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal R_0\)</EquationSource> </InlineEquation> is greater than unity. Finally, we perform numerical simulations to illustrate our theoretical results and investigate the impact of the proliferation rate of CTL from natural resources, intracellular delays and nonlocal dispersal coefficient on infection dynamics.</p>

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CTL Inclusive HIV-1 Infection Model with Nonlocal Diffusion Process, Intracellular Delays and Spatial Heterogeneity

  • 期刊论文

  • 发表日期：

    2025年12月23日

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  • Yannick -L. Djeunankam,
  • Martin L. Mann-Manyombe,
  • Denis F. Nkoa-Onana,
  • Joseph Mbang

摘要

In this paper, the dynamical behavior of a within-host HIV-1 infection model with nonlocal diffusion operator, nonlinear incidence rate, intracellular delays and CTL-immune response, in a spatially heterogeneous environment is investigated. The model includes the proliferation rate of CTL from natural resources. The global existence, dissipativity and compactness of the semiflow generated by the system are established. By using the perturbation technique, we define the basic reproduction number \(\mathcal R_0\) as the spectral radius of the next generation operator and this threshold number determines the global behavior of the model. That is, we show that the spatially heterogeneous infection-free equilibrium is globally asymptotically stable whenever \(\mathcal R_0\) is less than unity. Furthermore, we establish the uniform persistence and the existence of at least one chronic infection equilibrium which is globally attractive whenever \(\mathcal R_0\) is greater than unity. Finally, we perform numerical simulations to illustrate our theoretical results and investigate the impact of the proliferation rate of CTL from natural resources, intracellular delays and nonlocal dispersal coefficient on infection dynamics.