This is specific to the field of public health software:
Step 1: Figure out what group might want to pay money for this.
In this case, options might be orgs like the UN in Geneva, CDC in Atlanta, NGOs in Washington DC, people give give money to NGOs on the US West Coast, or specific NGOs supporting the region most affected by the disease in question.
Research, funding and staff organization tends to follow specific diseases. So you need to learn about the world of the disease you are targeting. You need to find out who cares about eradicating that disease and talk to them directly.
2. Figure out if any of those groups actually have money to give you for this work
NGOs are involved in thousands of these kinds of projects, from tiny one-off research projects to larger co-ordinated efforts. You need to meet some of the actual people working in this area, see what the state of the art is, see who is funding research, etc. Some diseases get tons of funding (Polio, HIV, etc) and some get almost none.
3. Convince one of these groups that you have the expertise to solve the problem. Your public health background could help here.
This can be done best by first building contacts and convincing someone let you do a proof-of-concept. But this is going to be hard if you have few contacts or in the field already.
Conferences about the specific disease you want to target can be a good way to network. Talk to the people who pay the research bills. They go to tons of these conferences.
4. Failing that, join or work with a small consulting group that already has existing contracts with NGOs/Government and is looking to expand into a new area
This is a great option and probably your best bet. Many of these consulting companies are really small and work on personal trust. But it still requires finding out who does work in the field and making some contacts.
5. After all this, see if any of these groups are even able to budget for this work
You'll quickly learn some hard truths of public health software:
* Most of the problems are organizational (not technical) and not easy to solve
* People are really busy and change jobs frequently. Turnover (due to unstable funding, etc) is a big problem.
* The world is overflowing with prototype solutions that half work and no one remembers they exist or how to use them.
* Solutions that work great on your computer might fail completely in the field running on a 486 with a radio internet connection.
You might find out that a solution like you imagine already exists and just needs someone to come in and help run it or improve it. Maybe that's a quicker way to help.