Citrus Tristeza Virus (CTV) causes a most destructive citrus disease in many parts of the world. The strategy for controlling the disease in Israel is based on the eradication of virus-infected trees, detected by an immunological method. A model for the spread and control of CTV is described. The disease spread depends on an infection rate parameter and on a detection coefficient. Both parameters vary with time. Simulation of the model under different conditions assists us to make decisions regarding the control of CTV disease.