Actually the Peloponnesian war says otherwise.
Sparta's economy actually relied on trade, if i used Athens's superior navy to bring the spartan trade to a halt, it would affect their supply lines greatly, and if i used that in combo with launching disease ridden corpses into Sparta's camps, it would inflict many deaths, i would then attack the spartan camp after i was sure the navy and infection had taken affect in the spartan army. I would call back my navy as they had fulfilled their purpose.
I would send the weakest members of my army with the infection in first as cannon fodder, and keep sending in infected citizens & soldiers, saving those still healthy in reserve. Once my navy came back, presumably back to the area of attack before new supplies could reach the Spartans, i would send in my aforementioned reserves and navy in combination to launch a daring attack on the spartan encampment, focusing on a two pronged attack and focusing about 65% of my strength on the right flank, 35% on the left flank. Athens has major numerical superiority over Sparta, so the deaths of those infected citizens and soldiers would take my army's numbers down to where i have a few more men then the Spartans still. used in combo with a naval attack should ensure victory.