How is the manner in which Colonel Gaddafi covers up his treachery similar to that of Macbeth in Shakespeare's play?
In particuluar by comparing Gaddafi and Macbeth, we see some stark similarities. There is no question that both men are reprehensible, tryannical leaders.
One way these two figures are similar is found in the secretive way that they arrange for and support the annihiliation of those who stand in their way. In the case of the Libyan leader Gaddafi, his intent has been to disrupt regions in West Africa, trying to start an uprising. For some "disgruntled West Africans," as well as...
...[t]he men who led the war on Sierra Leone — former Liberian leader and warlord, Charles Taylor and Sierra Leone’s rebel leader, Foday Sankoh, and The Gambian Fugitive, Kukoi Samba Sanyang...
Gaddafi has quietly arranged for their training in guerilla warfare. Additionally, enormous amounts of financial support were supplied to the factions trying to overthrow the government of Sierra Leone, with funds also secretly provided by Gaddafi. The monstrous reality of who Gaddafi truly is, has been hidden behind a front concealed by "his so-called positive gestures, such as his abandoning of WMD [Weapons of Mass Destruction] programs." (This was a step that he never actually took.)
In looking at the character of Shakespeare's Macbeth, this tyrant is also secretive about what he does. (Of course, first he murders Duncan and places the blames on the King's guards, who Macbeth kills in a "remorseful distress" because he was so overcome by Duncan's murder.)
However, more closely aligned to Gaddafi's reign of terror, Macbeth also sets about destroying those loyal to Duncan (specifically Banquo) by arranging to have people murdered. In arranging Banquo's death, Macbeth makes excuses to the murderers that he cannot be involved because of the political ties Banquo has a court, which is only a part of the lie he feeds this unfortunate men. Macbeth also blames the poverty-stricken circumstances his hirelings must face each day to survive on Banquo, when the truth is that Macbeth is truly to blame.
Well then, now
Have you consider'd of my speeches? Know
That it was [Banquo], in the times past, which held you
So under fortune, which you thought had been
Our innocent self? (III.i.80-84)
In these ways, Macbeth arranges for the murder of the one man who knows about the witches predictions, who is also noble and completely loyal to Duncan. Secretly, Macbeth carries out the murder of Banquo (though the murderers cannot catch his son, Fleance).
However, as is the case with Gaddafi, it does not take long for those around each man to realize that "fair is foul and foul is fair" (I.i.11). In other words, that which (or he who) seems good outwardly, can actually represent evil beneath the surface. In Act Three, scene four, Lennox begins by recounting how decent men, finding themselves too close to Macbeth, have ended up dead. And while others may agree with Lennox, they must be careful for what they say, while Macbeth has tried to hide his treachery by blaming others for misdeeds carried out—he blames Duncan's death on the guards who "must" have been working for Malcolm and Donalbain. (Lennox knows in his heart that if Macbeth was ever to get ahold of the King's sons, even for a short time, some calamity would befall them.) Macbeth even blames Fleance for killing Banquo. Macbeth's people know that this tyrant's heart is black, as do those in Serria Leone and around the world with regard to Muammar Gaddafi.