What is the state's duty to provide medical care to an ill inmate?

(I)dentification of the specific dictates of due process generally requires consideration of . . . the private interest that will be affected . . . , the risk of an erroneous deprivation of such interest . . . and the probable value, if any, of additional . . . procedural safeguards, and, finally, the government interest, including the function involved and the fiscal and administrative burdens that the additional procedural requirement would entail.

Mathews v. Eldridge, 424 U.S. 319, 335, 96 S.Ct. 893, 903, 47 L.Ed.2d 18 (1976).

Another constraint on state actions affecting the health of prisoners is the prohibition against cruel and unusual punishments. Because an ill inmate must rely on his warder's aid, the state has a duty to supply him with medical care. Estelle v. Gamble, 429 U.S. 97, 103, 97 S.Ct. 285, 50 L.Ed.2d 251 (1976). Deliberate indifference to a prisoner's serious medical needs violates

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