Asthma is a chronic disease that involves inflammation of the airways. Pa¬tients with Asthma have a constriction of the airways in the lungs and con¬sequent difficulty in breathing out. This ailment can be alleviated by intro¬ducing the drug theophylline into the bloodstream. This is done by injecting another drug aminophvlline, which the body quickly converts to theophylline. Once present in the blood, however, the drug is steadily excreted from the body via the kidneys. In other words, 'the system leaks', and unless there is replenishment the quantity of the drug in the blood will fall. It is known from the experiments that thcophyllinc has hardly any therapeutic effect if its concentration in the blood stream is bellow 5mg/L and that the concen¬tration above 20mg/L are likely to be toxic. Medical researchers have long . recognized the need to administer Theophylline in such away that the con¬centration remains in the therapeutic range. Non of the existing models on asthma have considered this. This study presents a new mathematical model for drug therapy in asthmatics which includes external rate at which Theo- ➔ 7t phylline is being increased in the form X = AX + f(t) and whose solution was analyzed for equilibrium and stability to provide drug therapy in asth¬matics in such a way that the concentration remains in the therapeutic range. It was established that the final model is stable compared to the existing models, that is, the eigenvalues of the coefficient matrix real, negative, and distinct. Theophylline can be administered at lower doses to achieve plasma concentrations of 5 - 10mg/l, which can avoid the risk of side-effects. This is Rn important contribution to research in modeling and more particularly to research in the field of drug therapy in asthmatics. This model would help the medical practitioners to administered Theophylline in such in such a way that the concentration remains in the therapeutic range.