The dynamics of thalassemia management in the United Arab Emirates

We consider a genetic disease called Thalassemia. Thalassemia is a genetic blood disorder caused by abnormal hemoglobin. Hemoglobin is a composite of proteins in red blood cells that carries oxygen and is made of two proteins from four alpha-globin genes and two beta-globin genes. Individuals with thalassemia have defects in one or more of such genes. The treatment of thalassemia requires a life-long blood transfusion and removal of excessive iron in the blood stream from the frequent blood transfusion. These life-long treatments demand a strong personal commitment and a constant supply of blood stock that leads to a high medical cost, which can be a burden on a health care system in some countries like the United Arab Emirates. 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. We develop a mathematical model including three age groups and thalassemia control measures, and analyze the stability of two types of equilibrium points that reflect the eventual status of thalassemia prevention. Through the stability analysis of the two types of equilibrium points, we reveal that control measures are positively effective only in the short term to reduce the prevalence of the disease but not enough to eradicate thalassemia in the long term. We illustrate our stability results via computer simulations by using the demographic data of the United Arab Emirates.