What killed Edmund in King Lear? Was there a sickiness in his family? Was it biological?

In the last scene of Act 5 of King Lear, Edmund is exposed as a traitor for plotting against the Duke of Albany with Albany's wife Regan with their mutual intention of murdering him and marrying each other. Albany then calls for Edmund to sound his trumpet summoning any challenger to appear and verify his charge of treason. Edgar appears in armor, having abandoned his disguise as a mad vagrant, and the following exchange ensues between the two half-brothers.

EDGAR

Draw thy sword,
That, if my speech offend a noble heart,
Thy arm may do thee justice: here is mine.
Behold, it is the privilege of mine honours,
My oath, and my profession: I protest,
Maugre thy strength, youth, place, and eminence,
Despite thy victor sword and fire-new fortune,
Thy valour and thy heart, thou art a traitor;
False to thy gods, thy brother, and thy father;
Conspirant 'gainst this high-illustrious prince;
And, from the extremest upward of thy head
To the descent and dust below thy foot,
A most toad-spotted traitor. Say thou 'No,'
This sword, this arm, and my best spirits, are bent
To prove upon thy heart, whereto I speak,
Thou liest.

EDMUND

In wisdom I should ask thy name;
But, since thy outside looks so fair and warlike,
And that thy tongue some say of breeding breathes,
What safe and nicely I might well delay
By rule of knighthood, I disdain and spurn:
Back do I toss these treasons to thy head;
With the hell-hated lie o'erwhelm thy heart;
Which, for they yet glance by and scarcely bruise,
This sword of mine shall give them instant way,
Where they shall rest for ever. Trumpets, speak!

Trumpets, speak! Alarums. They fight. Edmund falls.

Edmund is badly wounded but not killed instantly. While dying he confesses that he is guilty of the crimes charged against him by Albany and Edgar. He goes on to warn them that he has ordered one of his officers to murder King Lear and Cordelia, who are being held captive after the defeat of the invading French army. The officer arrives too late. Cordelia is slain offstage. Moments later Lear appears carrying her body.

There are many deaths in the last scene of the play. Regan is poisoned by her jealous sister Goneril in order to prevent her from marrying Edmund. Then it is discovered that Goneril has committed suicide with a dagger. Edmund is fatally wounded in the duel with Edgar and dies after confessing his sins. Cordelia is slain in prison. After winning the duel, Edgar tells Albany that his father the Duke of Gloucester had died of something like a heart attack only a short time before Edgar appeared in answer to Edmund's trumpet challenge. Edgar was able to identify himself to his father before he expired. Then, finally, King Lear himself dies of old age, exposure, and heartbreak over the death of his beloved daughter Cordelia, the only one of his daughters who truly loved him and was loyal to him.

There is no disease in Gloucester or in either of his sons. Edmund is especially handsome and virile, as shown by the fact that both Regan and Goneril fall madly in love with him. Edgar proves himself to be comparably strong and hardy, surviving in the outdoors, killing Oswald with a wooden staff while protecting his father, and finally killing Edmund in their duel.