More than 2,500 health care providers that serve Vermonters could be working together to help control costs by focusing on keeping people healthy rather than being paid to treat patients when they are sick, Gov. Peter Shumlin and other top officials said Wednesday. The two new ''shared savings programs'' offered through health insurance plans offered by Vermont Health Connect and the state's Medicaid program are designed to move away from the traditional fee-for-service model of health care to encourage providers to work together, keep people healthier and as a result reduce the growth of health care costs. Shumlin said the three-year-program getting underway in Vermont is the first such statewide program in the country.