As the world becomes more and more connected, there are hundred more reasons for world cooperation. A prosperous country cannot stay prosperous until it helps out its neighbors. A healthy country cannot stay healthy till countries around that country remain healthy as well.
The most important thing to understand is the fallout of this connected world is "United we rise, divided we fall". Why would you say that? Some of the reasons are:

1) Health: 
There are a number of new viruses which are coming out which have the ability to transcend the country boundaries with very much ease through air travellers, birds, animals, goods exchange, water flow etc. If we have a neighbouring country which is affected by a health emergency, it is wise to help them out because ultimately that disease will find its way to any country if not contained.
The biggest threat of the disease outbreak is it does not care if you are a rich country or poor country. It affects everyone equally.

2) Peace:
We may think that if our country is peaceful that should be enough. But as can be seen in many cases, if the neighbouring country is not peaceful, the threat of that violence reaching us becomes very very real. So, taking initiatives to make sure peace prevails in your neighbourhood as well is very important.
War can be devastating. It can destroy families. If a country's neighbour has war going on, the spill overs are going to reach you. You cannot escape. Making sure the wars do not escalate in your neighbourhood is very important.

3) Poverty:
Poverty is the driver of a number of crimes. Reason: empty stomach can think nothing else other than finding a way to get food. The way can be legal or illegal. This has implications for everyone. This leads to the poor not getting education, the one minimum requirement to find out whether something you are doing is right or wrong.

So, every country has now a shared responsibility to maintain happiness all around as we are connected to each other.