Final answer:
The payment method that provides lump sums for healthcare services for a specific illness is the episode of care model.
Step-by-step explanation:
The payment method that reimburses healthcare providers in the form of lump sums for all healthcare services delivered to a patient for a specific illness is known as an episode of care. Unlike a fee-for-service model, where providers are paid for each service rendered, an episode of care model covers all care within a certain period for a particular condition. Capitation is similar but pays a set amount per patient regardless of the number of services provided, while a point of service plan combines features of HMOs and PPOs, with payment structures varying accordingly.