Spatiotemporal dynamics for a diffusive HIV-1 infection model with distributed delays and CTL immune response

Abstract

<p style='text-indent:20px;'>In this study, we develop a diffusive HIV-1 infection model with intracellular invasion, production and latent infection distributed delays, nonlinear incidence rate and nonlinear CTL immune response. The well-posedness, local and global stability for the model proposed are carefully investigated in spite of its strong nonlinearity and high dimension. It is revealed that its threshold dynamics are fully determined by the viral infection reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \mathfrak{R}_0 $\end{document}</tex-math></inline-formula> and the reproduction number of CTL immune response <inline-formula><tex-math id="M2">\begin{document}$ \mathfrak{R}_1 $\end{document}</tex-math></inline-formula>. We also observe that the viral load at steady state (SS) fails to decrease even if <inline-formula><tex-math id="M3">\begin{document}$ \mathfrak{R}_1 $\end{document}</tex-math></inline-formula> increases through unit to lead to a stability switch from immune-inactivated infected SS to immune-activated infected SS. Finally, some simulations are performed to verify the analytical conclusions and we explore the significant impact of delays and CTL immune response on the spatiotemporal dynamics of HIV-1 infection.</p>