28 Something Later

In 28 Days Later and 28 Weeks Later why do the people who are infected with the rage virus not attack each other? Why do they only attack people who are not infected? That doesn't make sense. It also isn't consistent with the description of the virus. Supposedly if infected you become consumed with rage and the need to kill/destroy anything. They even beat themselves up to an extent.
So why not kill each other? It isn't logical.