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A general treatment function with an epidemic model that involves the delay in the treatment period has been proposed and studied in this work. This model contains two compartments, namely susceptible denoted by S(t) and infected denoted by I(t). The existence of all the fixed points has been determined. The system has two equilibrium points, namely the uninfected equilibrium point (UIEP) and the endemic equilibrium point (EEP). The conditions for local stability and Hopf bifurcation have been discussed. The stability of the periodic solutions and the direction of the Hopf bifurcation properties have been studied analytically and numerically. [ABSTRACT FROM AUTHOR]