What happens to Timothy in the end?

Mrs. Frisby is a poor, widowed field mouse, trying her best to raise her son Timothy, who's very sick. Timothy's suffering from pneumonia, and as well as medicine needs warmth and rest. Unfortunately, the peace of the Frisby family is about to be shattered. It's spring-time, and Mr. Fitzgibbons the farmer is going to plow the field. This is a disaster for Mrs. Frisby and her family, as it means their house will be destroyed. The owl tells Mrs. Frisby that she has no choice; she must move to safety. But Timothy's too sick; moving someplace else might kill him.
On the owl's advice, Mrs. Frisby seeks the assistance of a colony of rats—the rats of NIMH. These rats are very clever animals; they have an understanding of science which extends beyond their unwilling participation in human experiments. They've devised a novel solution to Mrs. Frisby's problem: instead of the Frisbys needing to move house, their house is going to be moved. This is to be achieved by a complex system of ropes and pulleys.
Thanks to the rats' remarkable ingenuity, the Frisbys' home is saved, and Timothy is able to get the rest and recuperation he needs before he and the rest of the family move to their summer home.