A　Susceptible　Infective　Recovered　(SIR)　model　is　usually　unable　to　mimic　the　actual　epidemiological　system　exactly.　The　reasons　for　this　inaccuracy　include　observation　errors　and　model　discrepancies　due　to　assumptions　and　simplifications　made　by　the　SIR　model.　Hence,　this　work　proposes　calibration　and　prediction　methods　for　the　SIR　model　with　a　one-time　reported　number　of　infected　cases.　Given　that　the　observation　errors　of　the　reported　data　are　assumed　to　be　heteroscedastic,　we　propose　two　predictors　to　predict　the　actual　epidemiological　system　by　modeling　the　model　discrepancy　through　a　Gaussian　Process　model.　One　is　the　calibrated　SIR　model,　and　the　other　one　is　the　discrepancy-corrected　predictor,　which　integrates　the　calibrated　SIR　model　with　the　Gaussian　Process　predictor　to　solve　the　model　discrepancy.　A　wild　bootstrap　method　quantifies　the　two　predictors＇　uncertainty,　while　two　numerical　studies　assess　the　performance　of　the　proposed　method.　The　numerical　results　show　that,　the　proposed　predictors　outperform　the　existing　ones　and　the　prediction　accuracy　of　the　discrepancy-corrected　predictor　is　improved　by　at　least　49.95%.