In the early stages of a global outbreak, many ordinary citizens will disbelieve the reports of the walking dead and most nations will be caught unprepared. Furthermore, the state of the world after a zombie apocalypse will differ according to where the outbreak begins. For the purpose of this article it is assumed that the outbreak will begin in The Peoples Republic of China.
China will be one of the worst hit in the world due to it's huge population, however it has the largest military in the world and all citizens receive at least basic military training at some point in their lives meaning that many more will be conscripted to fight. Many millions will flee during initial stages, at first by legitimate transport, then illegally as the government attempts to cap the flood of refugees and finally when all out war arrives, en-masse into neighboring countries. Despite the best efforts of the Chinese government the virus will spread abroad (there will be simply to many infected even in the early stages to be stopped). After this any connected landmass is at threat. First world countries such as The United Kingdom and the United States will receive the brunt of the refugees that will soon be made up of millions of people from East Asia. Many of these will be infected. These countries will however have their own problems and will attempt to close borders. It is unlikely many will manage this, unless they are separated by sea and use military force to protect themselves. These nations may include Cuba and the UK. The rest of the world will have serious problems as large hordes will begin to form and surround any secured compounds.
If the United States is first hit, major cities will be the worst. The military forces will not be able to contain the massive population of large cities and the infection will rapidly spread through the low income areas. The infection will spread through the major cities and spiral outwards. It is likely that as the epidemic spreads through the U.S., military units will go AWOL, and most of America will be lost due to being undefended. Chances are, the American government will possible fall. Most likely all over the world has gathered in desperate prayer and planning. In Europe and Asia, most countries will close their borders and the people will begin to starve as trade and agriculture grind to a halt. They will panic, and the resulting riots will destroy what little infrastructure is left. In Russia, given its size and proximity to China, the military will be stretched thin.
Since a lot of countries have stricked laws related to firearm possession, these will quickly deteriorate, as the people living in those countries have no shooting experience prior to the outbreak. Only those with firearm knowledge, like military personnel and law enforcement officers, will stand a chance at surviving through a global catastrophe, like a zombie apocalypse, resources willing.