The best way to prevent a disease from turning into an epidemic is to closely monitor its development and put systems in place before it starts spreading rapidly through populations. This requires surveillance and monitoring of the disease and disease populations. This is fine for populations of livestock, or humans, but tends to be a neglected area when it comes to animals in the wild. There are plenty of examples of devastating diseases that have ranged through wild-animal populations relatively unchecked until the later stages as they were simply not caught early enough.
An example is the fungal skin infection of frogs (chytridiomycosis) which absolutely decimated amphibians, wiping out about 200 frog species world wide. Yet investigations into the disease didn't start until 15 years after its initial appearance.
One of the reasons for the delay was a general feeling that such a large decline in numbers couldn't be caused by a disease, but instead was more likely to be some form of chemical contamination or pollution. Most of the initial work exploring the idea of a pathogen cause was done by a PhD student and was not adequately resourced. For many frog species there was also a lack of proper 'baseline' data; information about the species and population prior to the disease outbreak.
The disease is caused by the fungus B. dendrobatidis which is able to swim through the water using flagella. As frogs take up water through their skin this may be how the disease spreads although there are likely to be other ways given that the fungi often doesn't swim particularly far. The mechanisms by which the fungi cause the disease are still uncertain - the fungi is always found where the disease is present, but the can also be found without the disease.
Efforts to save the frog populations are difficult as the fungi is hard to treat in the wild and can spread into nature reserves and protected areas. Some efforts have been made to preserve frog species including the Amphibian Ark which aims to manage and co-ordinate captive populations. Although life in captivity allows frogs to be kept safe from fungi and other diseases there are issues with breeding in captivity. Most frogs have a specific set of breeding requirements, often strongly tied to their living environment, for example the tropical frogs that only lay eggs in the water of tree-dwelling bromeliad flowers. These conditions are challenging to recreate in a lab!
Efforts to prevent further such devastating diseases in the wild would benefit from improved monitoring and systematic surveillance of wildlife populations. Strategies such as monitoring sentinel species and locations, ensuring spacial and taxonomic representation of monitored species, and focusing on the ecosystem as well as the species level allow diseases in the wild to be caught and studied before they spread. There's also the need for increased social and political will for setting up such monitoring systems, including supplying adequate funding towards them.
Reference 1: Grogan LF, Berger L, Rose K, Grillo V, Cashins SD, et al. (2014) Surveillance for Emerging Biodiversity Diseases of Wildlife. PLoS Pathog 10(5): e1004015. doi:10.1371/journal.ppat.1004015
Reference 2: Gewin V (2008) Riders of a Modern-Day Ark. PLoS Biol 6(1): e24. doi:10.1371/journal.pbio.0060024