I'd rather think it's like saying "with a total case of [integer] of whooping cough reported in last year", where 'total' is sorta redundant.
去年 or 昨年 themselves don't necessarily refer to a whole calendar year, especially for describing whooping cough, a seasonal epidemic. For example the usage seen in "患者数は昨年末1週で44.6万人" in this news is similar to something like "summer last year", "last year Christmas". Again, you could think it as an extra, and a tradeoff between precision and succinct that exists in many languages.