“The all-rounder will not be at England’s training session at SuperSport Park this afternoon so that he can be at his father’s bedside,” the ECB statement said.
Stokes, this month named BBC Sports Personality of the Year after his heroics in helping England lift the Cricket World Cup, is a vital member of the team, providing balance to the line-up as both a front-line batsman and bowler.
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His potential absence for the Test would be a major blow for an England side that has battled with illness in the camp in the build-up to the series, with bowlers Jofra Archer and Stuart Broad missing both warm-up fixtures with flu.
They are in a race to be fit for the first Test, but have come through net sessions on Sunday and Monday.