Inefficient healthcare is a major concern among many African nations and can be mitigated by building world-class infrastructure connecting different medical facilities for collaboration and resource sharing. Such infrastructure should support collection and exchange of medical data for the purpose of accessing expertise not available locally. It should be equipped with modern technologies of the fourth industrial revolution, providing decision support to doctors thereby enabling African nations leapfrog from poorly equipped to medically prepared. Sadly, world-class healthcare infrastructure are a missing piece in the African public health ecosystem. Medical facilities are either non-existent or prohibitively expensive when they exist. Federated cloud computing can provide a solution to this challenge. Being a model that allows collaboration between multiple Cloud service providers through resources pooling; it allows for the execution of tasks on computing resources flexibly and cost efficiently. This paper aims to connect unconnected medical facilities in Africa by proposing a Cloud federation for healthcare using cooperative and competitive collaboration models. Simulations were carried out to test the efficacy of these models using five different workload allocation schemes: First-Fit-Descending (FFD), Best-Fit-Descending (BFD), Binary-Search-Best-Fit (BSBF); Genetic Algorithm meta-heuristic and Stable Roommate Allocation economic model for both light and heavy workloads. Results of simulations revealed that the cooperative model resulted in lower delays but higher resource utilisation; while the competitive provided faster service delivery and better quality of service. BSBF and BFD resulted in the best resources utilisation and energy conservation. Finally, deployment considerations and potential business models for federated Cloud for African healthcare were presented.