Advancing through relative dates using strtotime()
Working from previous calls to the same script isn't really a good idea for this type of thing.
What you want to do is always pass two values to your script, the date, and the movement. (the below example is simplified so that you only pass the date, and it will always add one day to it)
Example
http://www.site.com/addOneDay.php?date=1999-12-31
<?php
echo Date("Y-m-d",(strtoTime($_GET[date])+86400));
?>
Please note that you should check to make sure that isset($_GET[date]) before as well
If you really want to work from previous calls to the same script, you're going to have to do it with sessions, so please specify if that is the case.