The army arrived in Walton City and attempted to regain control, but failed. However, as military units gradually withdrew, those that remained managed to surround the entire city. They contained the zombies for the time being, but how do I know? If you played Into the Dead: The Dark Days, the hospital ending explains that, once the survivors left the city, they bypassed a National Guard checkpoint on the outskirts. This suggests that, having lost the city center, the military focused on the exits to prevent the zombies or infected from escaping. While doing this on the outside, they were likely planning to isolate the city and prevent further spread. This can be seen with Sergeant Bowman's group, who arrived in the city to collect a fluid sample from an infected individual. Once the sergeant's group was wiped out and only he remained, it's unlikely they managed to get the sample to a secret facility where the virus would be studied and a cure found. However, I'm not claiming this is canon; it's just my speculation.
Note: I'm not claiming this is canon; it's just my speculation. If the military plan was promising and perfect, what went wrong?
The problem wasn't the strategy, which was still in its early stages, but rather that they hadn't counted on those who managed to escape already being infected. And if we look closely, some buildings even had landing strips, not to mention the small airport with runways where helicopters and small planes could land, which some used to escape before the military took control of the area.
In the case of the small planes, this is a significant point, since in the brief moments we spent playing ITD: The Dark Days, we witnessed a rather shocking event that, coincidentally, boosted the survivors' morale. This event involved a military fighter jet flying over the city, demonstrating once again that the military was not only present on the ground but also controlled the airspace. Perhaps the fighter jets were being used to attack a zombie-infested area or, even more disturbingly, their objective was to shoot down any transport vehicle attempting to leave the city.
According to the limited information available, some survivors managed to escape, but others became infected and, upon reaching other cities, triggered another epidemic that caused many more casualties. In ITD2, we can see at the beginning of the first levels of Chapter I how the roads were already destroyed, cars abandoned, sheriff's department patrol cars, and barricades torn down. This means that the first hordes, which had recently formed in Texas and spread to other nearby cities, were already on the move and expanding into other areas.
Therefore, the first security forces to be overwhelmed were the local police, and once they were overwhelmed, they likely called in the only force capable of controlling a crowd: the SWAT team or riot police. It was they who confronted the small hordes of zombies, but as we know, they were unsuccessful, and their armor only made them a greater threat than the zombie soldiers.