Dynamics of reaction–diffusion equations for modeling CD4+ T cells decline with general infection mechanism and distinct dispersal rates

Abstract In this paper, we are concerned with a diffusive viral infection dynamical model with general infection mechanism and distinct dispersal rates. In a general setting in which the model parameters are spatially heterogeneous, it is shown that if ℛ 0 ≤ 1 , the infection-free steady state is globally asymptotically stable; while if ℛ 0 > 1 , the model is uniformly persistent. The asymptotic profiles of the infection steady state are discussed as the dispersal rate of uninfected CD4 + T cells approaches zero by means of the persistence theory of semidynamical systems and the eigenvalue theory of elliptic equations.

[1]  Jindřich Nečas.  Les équations elliptiques non linéaires , 1969 .

[2]  Rui Peng,et al.  A reaction–diffusion SIS epidemic model in a time-periodic environment , 2012 .

[3]  Wei Wang,et al.  Block effect on HCV infection by HMGB1 released from virus-infected cells: An insight from mathematical modeling , 2018, Commun. Nonlinear Sci. Numer. Simul..

[4]  Robert F. Siliciano,et al.  HIV: Not-so-innocent bystanders , 2014, Nature.

[5]  Jianhong Wu.  Theory and Applications of Partial Functional Differential Equations , 1996 .

[6]  M. Martcheva,et al.  Analytical and numerical approaches to coexistence of strains in a two-strain SIS model with diffusion , 2012, Journal of biological dynamics.

[7]  Horst R. Thieme,et al.  Spectral Bound and Reproduction Number for Infinite-Dimensional Population Structure and Time Heterogeneity , 2009, SIAM J. Appl. Math..

[8]  Rui Peng,et al.  Global stability of the steady states of an SIS epidemic reaction–diffusion model☆ , 2009 .

[9]  Wei Wang,et al.  Repulsion Effect on Superinfecting Virions by Infected Cells , 2014, Bulletin of Mathematical Biology.

[10]  Yuan Lou,et al.  Dynamics and asymptotic profiles of steady states of an epidemic model in advective environments , 2017 .

[11]  Xiao-Qiang Zhao,et al.  Computation of the basic reproduction numbers for reaction-diffusion epidemic models , 2023, Mathematical biosciences and engineering : MBE.

[12]  A. Badley,et al.  Mechanisms of HIV-associated lymphocyte apoptosis: 2010 , 2010, Cell Death and Disease.

[13]  Xiao-Qiang Zhao,et al.  Threshold dynamics of a time periodic reaction–diffusion epidemic model with latent period , 2015 .

[14]  Xin Geng,et al.  Cell death by pyroptosis drives CD4 T-cell depletion in HIV-1 infection , 2013, Nature.

[15]  R. Nagel,et al.  One-parameter semigroups for linear evolution equations , 1999 .

[16]  Xingfu Zou,et al.  Dynamics and profiles of a diffusive host–pathogen system with distinct dispersal rates , 2018 .

[17]  Xiao-Qiang Zhao,et al.  A reaction–diffusion malaria model with incubation period in the vector population , 2011, Journal of mathematical biology.

[18]  P. Hosseini,et al.  Seasonality and the dynamics of infectious diseases. , 2006, Ecology letters.

[19]  Libin Rong,et al.  Modeling the Slow CD4+ T Cell Decline in HIV-Infected Individuals , 2015, PLoS Comput. Biol..

[20]  Rui Peng,et al.  Asymptotic profiles of the positive steady state for an SIS epidemic reaction-diffusion model. Part I , 2009 .

[21]  Xiao-Qiang Zhao,et al.  Dynamical systems in population biology , 2003 .

[22]  Horst R. Thieme,et al.  Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations , 1992 .

[23]  J. Hale.  Asymptotic Behavior of Dissipative Systems , 1988 .

[24]  O. Diekmann,et al.  On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations , 1990, Journal of mathematical biology.

[25]  A. Fauci,et al.  Analysis of apoptosis in lymph nodes of HIV-infected persons. Intensity of apoptosis correlates with the general state of activation of the lymphoid tissue and not with stage of disease or viral burden. , 1995, Journal of immunology.

[26]  K. Deimling.  Nonlinear functional analysis , 1985 .

[27]  T. Kuniya,et al.  Existence result for an age-structured SIS epidemic model with spatial diffusion , 2015 .

[28]  Hal L. Smith,et al.  Abstract functional-differential equations and reaction-diffusion systems , 1990 .

[29]  Yuan Lou,et al.  Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model , 2008 .

[30]  Toru Sasaki,et al.  Asymptotic behaviour of the solutions to a virus dynamics model with diffusion , 2017 .

[31]  Xiao-Qiang Zhao,et al.  Robust persistence for semidynamical systems , 2001 .

[32]  Wei Wang,et al.  Caspase-1-Mediated Pyroptosis of the Predominance for Driving CD4$$^{+}$$+ T Cells Death: A Nonlocal Spatial Mathematical Model , 2018, Bulletin of mathematical biology.