That's mostly an effect, not a cause. Unlike here, there is a primate reservoir for some of those diseases there. But the main cause of infectious disease is poverty and corrupt government.
Poverty and corruption are not causes, but reasons they cannot get rid of disease. It's a big feedback loop. Childhood development is stunted because of disease and malnutrition, and those intellectually stunted children grow up to be the trouble makers who perpetuate the poverty and corruption. Progress is being made in this area, but it will be a while before the effects of disease on development are eradicated.
I know this is not a complete answer as to why Africa is so backwards, but I think disease is a major contributor. As others have pointed out, the climate and abundance of food probably also contribute a lot to the lack of development in Africa.