It does not talk long to find external conflicts when reading "Leiningen Versus the Ants" by Carl Stephenson. The most obvious conflict of the story, of course, is external, and it can be seen in man versus nature and, conversely, nature versus man.
The title of the story indicates the first conflict: while the ants are coming and will decimate everything in their way, Leiningen sets himself in direct opposition to them. The battle grows bloody and violent, and this is an example of man versus nature.
The ants are in conflict with everything that gets in their way. One Brazilian official describes the oncoming creatures this way:
"They're not creatures you can fight--they're an elemental--an 'act of God!' Ten miles long, two miles wide--ants, nothing but ants! And every single one of them a fiend from hell; before you can spit three times they'll eat a full-grown buffalo to the bones."
Clearly the ants versus everything is a second example of external conflict, nature versus man.
A third example is man versus man. The Brazilian official who characterized the plague of ants as an "act of God" does everything he can to get Leiningen to leave before the ants arrive. The official is a native and has seen the damage these creatures can do; Leiningen is overly confident that he will survive the coming onslaught because he has never experienced this massive army of ants.
These same three conflicts keep repeating themselves as the story progresses; as you keep looking, you will find more examples of the same three external conflicts. The ants take on anything in their way, Leiningen foolishly and unnecessarily pits himself against the marauders, and virtually everyone around Leiningen does his best to dissuade Leiningen from his stubborn position.
Leiningen wages war against the ants, just as the ants are on a course of destruction against Leiningen just because he is there.