Thalassemia is a genetic disease that causes abnormal hemoglobin. Hemoglobin is a protein in red blood cells that carries oxygen and is made of two proteins from four alpha-globin genes and two beta-globin genes. A defect in one or more such genes causes thalassemia. The treatment of thalassemia includes a life-long blood transfusion and removal of excessive iron in the blood stream. To reduce thalassemia major population, various forms of thalassemia control measures have been used and hence, the substantial reduction of thalassemia major population has been achieved. However, the prevalence of thalassemia carrier population still remains high, which leads to a potential growth of thalassemia major population through carrier-carrier marriages. Thus, in this paper, we investigate a long term effectiveness of thalassemia control measures via a mathematical model at a population level. We develop a compartment model including three age groups and thalassemia control measures. Through the stability analysis of the disease free equilibrium point, namely, thalassemia and carrier free equilibrium point, our study reveals that control measures are positively effective only in a short term to reduce the prevalence of the disease.