First of all, I have not seen the show, only read the comics.
In that scenario, there are four very important things to know about the zombie apocalypse.
No matter where it originated, the virus travels by air, and faster than people. It will infect the entire landmass, maybe the entire world, within a very short delay.
Being infected makes no difference whatsoever before you die, but when you die no matter the cause you will turn into a zombie within 24 hours, sometimes much faster.
Any zombie bite will kill you within hours.
There is no known cure to either being alive and infected, or full blown zombie.
Let's assume that the people responsible for the original outbreak were both prepared and responsible. They reacted fast enough, either by alerting or being the autorities, so that everyone got the information quickly enough to avoid a complete disaster like in TWD.
They couldn't prevent the infection, but zombies didn't take control of the country or world, not even a city.
After that, since everyone turns into zombies on death, but it won't take you by surprise, I guess zombies will become a notable risk in society.
How would society adapt to this new zombie element added to regular deaths?
I assume funerals would be very different, considering that even by killing the zombie, you'd still have a much more disgusting corpse, therefore open caskets would probably disapear.
I am asking specifically what measures could a country take, whether it is by law or by religion, to avoid mass murders every time someone dies? What habits would people adopt to react to this important change from a safety point of view? Is it even possible to avoid complete anihilation, assuming we know what we're dealing with from the start?