Dynamics of a diffusive HTLV and HIV coinfection model with macrophages, latent cells and two delays

Human T-lymphotropic virus (HTLV) and human immunodeficiency virus (HIV) are two retroviruses that pose a certain threat to human psychology and physiology. In this paper, we propose a diffusive HTLV and HIV coinfection model with macrophages, two delays, cell-to-cell transmission and three latently infected cells in which latent HIV infected CD4<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:math>T cells, latent HIV infected macrophages, and latent HTLV infected CD4<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:math>T cells are considered. Four reproduction number and four equilibria, namely, infection-free equilibrium, HIV infection equilibrium, HTLV infection equilibrium and HTLV and HIV coinfection equilibrium, are calculated and proved the global asymptotic stability of the coinfection model. Numerical simulations are executed to showcase the corresponding theoretical outcomes and uncover how macrophages and latently infected cells influence the dynamics of HTLV and HIV coinfection.