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.
Not the disease cause but the cause of their persistence. We got rid of the same diseases here like malaria and yellow fever, never mind measles, mumps and rubella which are ubiquitous there. The only thing different in Africa is some reservoirs, most of the vectors are the same. It's easy to blame "tropical" diseases when they are not in fact tropical. They are third world diseases. It's why, for example, Afghanistan has malaria and Costa Rica does not.