Gómez-Acevedo and Li [16] investigated a mathematical model for human T-cell lymphotropic virus type I (HTLV-I) infection of CD4 + T cells that incorporates both horizontal transmission through cell-to-cell contact and vertical transmission through mitotic division of infected T cells. They assumed that a fraction σ of the infected cells survive the immune system attack after the error-prone viral replication. Under the biologically sound assumptions that the fraction σ should be very low and the rate of the mitotic division should be high, their model has a bifurcation that predicts persistent infection for an extended range of the basic reproduction R 0 > R 0 (σ 0 ), where R 0 (σ 0 ) < 1. This model undergoes a backward bifurcation as σ increases: multiple stable equilibria exist for an open set of parameter values, when the basic reproduction number is below one.