$date = date("Y-m-d");// current date

$date = strtotime(date("Y-m-d", strtotime($date)) . " +1 day");
$date = strtotime(date("Y-m-d", strtotime($date)) . " +1 week");
$date = strtotime(date("Y-m-d", strtotime($date)) . " +2 week");
$date = strtotime(date("Y-m-d", strtotime($date)) . " +1 month");
$date = strtotime(date("Y-m-d", strtotime($date)) . " +30 days");

or

$newDate = strtotime('+15 days',$dateInt);

Adding Days To Dates In MySQL

DATE_ADD(date_starts,INTERVAL 14 DAY)

eg.
UPDATE events SET date_starts = DATE_ADD(date_starts,INTERVAL 14 DAY) 
WHERE event_id = 3;
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