Based on Ayshe's comment, it's possible this is Wild in the World by John Donovan.
After an initial desolation that stretches belief, this becomes a natural and gently persuasive story of an inarticulate mountain boy and the animal that preoccupies his last days. At the book's opening there are three Gridleys left from a family of seven brothers and four sisters; the others have died of scarlet fever, rattlesnake bite, fire, childbirth, suicide, and mysterious illnesses attributed to leaving home. By page six Abraham has died of an infected fishhook cut, Amos is fatally kicked by a cow, and only John, the youngest, survives. This is told matter-of-factly and John accepts his multiple bereavement with fatalistic resignation. He never talked much to his brothers anyway; now his thoughts are of getting the chores done, selling apples, maybe buying a pipe. Then John by chance adopts a stray wolf (or maybe it's a dog) and his life changes. He names the animal Son, swims and eats and works with it, nurses it anxiously through a bout with rattlesnake poisoning when John and the reader are sure the dog will die, talks to it in torrents through his increasing delirium, then dies himself of pneumonia. Children who would cry if the animal died will accept the rightness of John's death; Son clearly enlarged the boy's life in a dimension other than time. Though the seemingly gratuitous deaths are a shock at first, their use to underline the value of the friendship results in a quietly convincing affirmation.
While most of the book is only following John and Son, it seems that there are at least two brothers who are alive at the start, one dies of an infection from a cut, and John dies of pneumonia. And it came out in 1971, which would fit your time frame.
