How can a citizen contribute to get his country out of the poverty trap? I am from Madagascar. We are in what is called a "povery trap".
Building a business is very difficult because the population is agglomerating in the capital and the competition is very high. Moreover, there is a lack of public infrastructure that freezes the economy.

What do you suggest me to do as a citizen without any governmental control to have a good impact in the economy?
I think the best way for an individual citizen to improve their country's economic development is to raise their productivity, while also following ethical standards. "Raising productivity" is a very traditional economic viewpoint, and it basically requires one to move away from rural or subsistence living and towards activities that contribute to society, as measured by the income that you generate. But, I think there also needs to be a focus on long-term developmental outcomes, which may not necessarily be tied to economic profit because of negative externalities.

I haven't done a lot of research into the lives of poor people, but after reading some chapters from Banerjee and Duflo's Poor Economics, I would say that the economy loses out when people are not persistent, motivated, or when they make economically irrational decisions. For example, poor people in India do not use the most cost-effective treatment for diarrhea (rehydration liquid with salt and sugar) because they do not trust and are not accustomed to Western medicine. Another example is that poor people in Morocco who can't afford food buy televisions, but I understand the reason for this. The reason is that poor people cannot be expected to cut out all luxuries in their lives, because they also need things that make their life bearable and pleasurable. If poor people didn't buy expensive food and other luxury items, the generations below them might rise out of poverty sooner, but such a process takes a long time. Income-earners would not want to forego a better life for themselves just so that their children's children will not live in poverty.

All in all, I advise you to become a change agent in your community. Strive to motivate others to do work. Technology will help, so you will need to try to find out what the most technologically advanced way of doing your work is. That knowledge comes with education, which may be difficult to access in your situation, but nevertheless try to find it. Lastly, public participation in governance is important for economic development, so try to actively participate in your country's governance.