USAID provided funding for a lot of stuff, but specifically with regards to infectious disease control, providing funding for infectious disease control in countries that don't have the resources or priorities to do it on their own addresses the risk that such diseases are not controlled and spread to the US and also the risk that such diseases spread and result in (negative) economic impact for the US.

The disease control interventions really are a mix of teaching and doing. In acute situations, experts are brought in to do (some of) the things. But mostly it's training and outreach and supplying equipment to do routine disease control and surveillance of issues that need help.