In many "poorer non-first world countries" it's going to be very challenging. People often need to work every day in order to "eat" the next day, which prohibits social distancing measures. They have a problem with the availability of sanitation - for hand cleaning. The density of the population in some of these countries is also very significant, which can provide an additional risk factor for a greater spread of the virus.
From past epidemics for example in sub-Saharan Africa, they needed a lot of mostly international humanitarian help. Medical systems in poor countries usually have little capacity to deal with a huge number of cases. They also don't have a way for effective testing for the virus, laboratories... The question is to what extent can humanitarian help be made available.
"Rich countries" and international organizations providing governance, medicine, and other resources are currently in the core of epidemics themselves. This crisis is also economically challenging, which adds prohibitive cost to invest in humanitarian help for poorer countries. IMF is currently planning to lend around $1trn to developing countries, and hopefully, G20 will also provide at least some humanitarian capacity to help them. From a political point of perspective, China can use this as an opportunity to extend its influence over developing economies requiring help with fighting Covid virus.
Prohibitive measures could also be used by some of the political regimes to tighten their grip on power which could lead to destabilization.
On the other hand for example in India, you have a huge pharmaceutical sector which makes medicine, which can help in providing antibiotics or other types of medicine which could be beneficial for sick people.
The virus could also be weakened by a warm climate, which is not yet scientifically proven. Population structure in poor countries is usually much younger, which is another benefit, although people can be malnourished and have different medical problems which could make things worse if they were to become infected by Coronavirus.
Sources, to read more: The coronavirus could devastate poor countries economist-coronavirus-in-india