Pharmaceutical companies in a capitalistic democracy have no legal obligation whatsoever to develop any vaccine or medication. That means this issue is strictly one of ethics and social responsibility and the pros and cons involved are mostly the same as they would be for any company that we would like to provide a free service or product to those in need.
A few arguments for researching and developing vaccines for diseases prevalent in third world countries are, first, that this would improve the reputation that pharmaceuticals have right now, which is that they are grasping, greedy, and gouging entities that use people's miseries to make money, second, that all profitable entities have a "debt" to society, since it is society that provides the infrastructure they capitalize upon and society that supports them, third, that such a program would be useful as a form of marketing, much as a yogurt maker supporting breast cancer research hopes to gain more customers through such donation campaigns, fourth, that such efforts will provide them with enormous tax write offs, and fifth, that it is to their advantage to provide such assistance, since, if they do not, first world nations of the world must address this problem, usually in the form of direct aid to third world countries or through the United Nations, and this could result in higher taxes for even pharmaceuticals.
There is one primary reason that pharmaceuticals should not enter into such a project, and that is that each has a duty to its shareholders to make a profit. To the degree that anything is given away, the shareholders' dividends are reduced or eliminated, their share value may decrease, and this really is a breach of that duty. For other businesses, the argument usually goes that businesses should not involve themselves in socially responsible projects because they are hardly experts at this, but in the case of the pharmaceuticals, for them to research and develop such vaccines, that would hardly be the case. That is, after all, their business.
I am aware that some pharmaceutical companies provide drugs to people at reduced cost on some occasions, but for them to provide such an extensive and expensive service to third world countries is not legally required, at least in the United States, and their willingness to do so is likely to be to the degree there is something in it for them.