While some health issues occur continent-wide in Africa, others are specific to certain countries. Continent-wide, access to healthcare is a big issue, as are malaria, AIDS, and access to prenatal care. The link below is about South Africa, where health care is an interesting topic; about 80% of the population is served by a national heath care system that is terribly underfunded, while the wealthiest (and whitest) 20% have access to good quality private health care.
The University of Pennsylvania's African Studies Center maintains an excellent database of articles about health issues on that continent; you can access the main page at this link.
The online journal Africa Health has lots of down loadable articles at this link. The World Health Organization publishes African Regional Health Reports; the current issue and back issues can be accessed here.