This article uses an in-universe perspective.
Alpha Teams were small, elite anti-zombie task forces comprised of United States Army Special Forces teams. Details are sketchy, as a large portion of the facts of who they were and how they operated are considered confidential information by the United States Government. Various high ranking sources have gone on the record to confirm their existence, and their purpose - to limit and contain the smaller initial outbreaks within the borders of the contiguous United States, to buy time for a more thorough mobilization of both troops, and a sort of wartime economy, governance, and societal restructuring that could adequately prepare for the zombie menace. While the Alpha Teams are unanimously considered successful at their goals, the overall failure to eradicate the zombies before they could take major cities, or large areas of the nation is considered the catalyst for The Great Panic, and the start of World War Z.
The Alpha Teams were United States Army Special Forces (whose teams are referred to as "Alpha Teams" both pre and post-war). Alpha Teams are comprised of 12 men in each team; there is no eyewitness testimony as to the size of these Alpha teams, but it is presumably the same. Equipment for Special Forces is varied and normally comprises the entire armory of the United States Army, in addition to whatever weapons may be predominant in the region of deployment, such as Kalashnikovs in Africa; however, most operatives were reliant on M4A1 SOPMOD carbines, M249 SAWs, and M21 sniper rifles during the time of their deployment, as well as the M67 hand fragmentation grenade.
Roles and Objectives
The Alpha Team's role was to gather intelligence on a situation that was reported as a possible outbreak. This intelligence was quickly supplied to, and quickly processed by US Military Intelligence departments. Upon receiving the go-ahead signal, they would terminate all Zombies in the area. It is also possible that the team would terminate any humans who did not immediately cooperate or who provided resistance or interference.
At the time when Alpha Teams were being employed, few Americans believed the rumored zombie menace was possible. To a certain extent, the government was desperate to avoid mass panic, and wanted to keep as low of a profile as possible. This meant using black ops tactics, such as the Alpha Teams, on domestic ground without any notification to the press or local law enforcement.
Another potential controversy was the brutal efficiency in which many of them acted. Frequently, zombies were defended by family and friends, who did not understand or weren't able to accept what was truly happening to their loved one. Likewise, in outbreak areas, refugees would beg and plead to be taken to receive medical attention, all the while showing obvious signs of infection. It is argued by some researchers of Alpha Team incidents that civilians that could not be safely spared (safe to themselves, and the community they would be escaping to) were summarily executed by order of the President. The primary objectives of the Alpha Teams, and the overall containment of the outbreak were more important than any law and any life. Years later, as the rebuilding continues, few Americans are clamoring against these tactics.
By the time of the Battle of Yonkers, Alpha Teams were overrun. That is not to say the concept failed: in fact, unknown to many, they had been extremely efficient. Nevertheless, they were only ever meant as a stopgap measure, and the full scale mobilization that was supposed to follow them never occurred.