[saspinski (OP)]

There are several species of mosquitoes. What is so special in the Aedes aegypti that yellow fever, dengue, zika and other viruses don't die but apparently thrive inside  them?  And not in the Culex type for example?

[evan_au]

The question asks about the affinity between the mosquito and the human pathogen.

However, another important aspect as a human disease vector is the affinity between the mosquito and humans.

Humans have carried this mosquito to tropical areas around the world. They can breed in very small quantities of water in and around our homes - in potplants, tyres and in general household rubbish. Proximity and affinity for humans make them a more dangerous vector.

http://en.wikipedia.org/wiki/Aedes_aegypti#Spread_of_disease_and_prevention_methods

[exothermic]

What is so special in the Aedes Aegyptis that yelow fever, dengue, zika and other virus don't die but apparently thrives inside  them?  And not in the Culex type for example?

I'm fairly certain this has more to do with the population density of Aedes aegyptis. Take a look at the Zika virus as an example: while A. aegyptis is the primary culprit, A. albopictus, A. Apicoargenteus, A. africanus, A. furcifer, A. hensilli, A. luteocephalus, and A. vitattus are also documented Zika vectors as well.

For clarification, the Culex genus are definitely arbovirus vectors.

[chris]

Aedes mosquitoes, such as A. aegypti, are vectors for viruses such as yellow fever, dengue and zika because - through their behaviour and preferred habitats - these mosquitoes favour the transmission of these viruses. As such, the viruses have evolved to more optimally exploit these mosquitoes.

Originally (about half a century ago) dengue was a sylvian (forest) infection of primates transmitted between then chiefly by A. albopictus (tiger) mosquitoes. Humans were occasional hosts. But when rising population provoked dramatic urbanisation in the tropics post World War II, this created ideal habitats for Aedes aegypti mosquitoes, which thrive in stagnant water collecting in rubbish dumps. These mosquitoes also prefer to feed from large mammalian hosts that are day-active - like humans.

As a result, the dengue agent was placed under selective pressure to adapt to exploit A. aegypti, which was achieved through the acquisition of a handful of mutations. Through this adaptation, dengue entered "urban cycle" with humans as the optimal host and A. aegypti as the dominant vector.

In summary, because viruses are biological entities capable of evolution and adaptation driven by selective pressure from their environments, it is unsurprising that human-favouring mosquitoes, like A. aegypti, should end up being the ideal host.

[saspinski (OP)]

But when rising population provoked dramatic urbanisation in the tropics post World War II, this created ideal habitats for Aedes aegypti mosquitoes,

What amazes me is that Aedes existed already in tropical areas (Panama channel construction in the first years of the XX century or Rio de Janeiro at the same period for example). When Dengue made its debut, the same mosquito species was selected by the virus. 
And other types of mosquitos, the annoying night singers, are much more common but (luckily) don't carry the virus.
Maybe the virus kills those other mosquitos when they are infected or it doesn't survive inside them.