Image source Burrard-Lucas Photography
Before 1992, as well as the Lions and Cheetah, there were huge packs of African Wild Dog (also called African Hunting Dogs) that would follow the herds as well. This was one of the largest populations of African Wild Dog population so it was devastating to have the population wiped out so quickly. However, the land given to the nomadic people of the Serengeti
at the formation of the park suddenly started having attacks on their livestock, and it was found that these wild dog were actually surviving members of the Serengeti population. Due to the problems they were causing on the Maasi conservancy they were translocated into the Serengeti forming 5-6 packs. African Geographic describes this more.
This is the advantage in Tanzania, that even outside national parks there is so much wild land that there is the space for species to survive illnesses that would eradicate them from smaller parks. Wild Dogs, as with Cheetahs, are often considered as hunters of livestock, and while both will do so, mitigation is easier than with Lions or Hyenas.
Wild Dog had an unfortunate reputation of being vermin, and as late as the 1960s Serengeti rangers would shoot them on sight. Thankfully, these days Wild Dog, far from being thought of as vermin, are regarded as a highly valuable species to have. Increasing number of tourists are coming to Africa, with the Eco-tourism big 7 in mind to tick off rather than the big 5 (big 7 adds Cheetah and Wild Dog, to Lion, Leopard, Rhino, Elephant and Buffalo). The smaller predators are seen as a better indication of the health of an ecosystem, as while you can have a popuation of Lions and Leopards within a relatively small national park, Wild Dog only occur in breeding numbers in the larger areas.