Abstract
In this paper, we aim to analyze the effect of treatment and protection measures on the spread of infectious disease. Therefore, we formulate a delayed mathematical which contains a discrete delay which stands for the duration of protection and distributed delay that represents the repulsed individuals from treatment. The main result is to show that the model has threshold behavior governed by R-0. For R-0 < 1, it is shown that the disease-free equilibrium is globally stable. However, for R-0 > 1, it is proved that the semiflow is uniformly persistent, and the endemic equilibrium is globally stable. Another purpose is fixed in this paper, which consists of studying the effect of treatment and protection measures on the spread of the disease, and to distinguish the minimal protection and treatment measure for reducing the basic reproduction number below one. The results are supported numerically using numerical simulations.