Definition of "infest"

Sir, my liege,Do not infest your mind with beating onThe strangeness of this business; at pick’d leisureWhich shall be shortly, I’ll resolve you,Which to you shall seem probable, of everyThese happen’d accidents; till when, be cheerfulAnd think of each thing well.

1610–1611 (date written), William Shakespeare, “The Tempest”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, [Act V, scene i]

I come now to speak of the Pyrates infesting the West-Indies, where they are more numerous than in any other Parts of the World, on several Reasons […]

1724, Daniel Defoe (attributed), “Introduction”, in A General History of the Pirates‎, 2nd edition, London: T. Warner, page 24

It has often happened, that whole caravans have perished in crossing those deserts, either by the burning winds that infest them, or by the sands which are raised by the tempest, and overwhelm every creature in certain ruin.

1791, Oliver Goldsmith, “Of Mummies, Wax-Works, &c.”, in An History of the Earth, and Animated Nature. […], new edition, volume II, London: […] F[rancis] Wingrave, successor to Mr. [John] Nourse, […], page 252

Nor was the biscuit much better; nearly all of it was broken into hard, little gunflints, honeycombed through and through, as if the worms usually infesting this article in long tropical voyages had, in boring after nutriment, come out at the antipodes without finding anything.

1847 March 30, Herman Melville, chapter 3, in Omoo: A Narrative of Adventures in the South Seas; […], London: John Murray, […]

[…] The swarme of scaled snakesDid make an yrksome noyce to heare, as she her tresses shakes.About her shoulders some did craule, some trayling downe her brest,Did hisse, and spit out poison greene, and spirt with tongues infest.cited in Thomas Warton, The History of English Poetry, Volume 3, London: J. Dodsley et al., 1781, Section 40, p. 412,

1567, Ovid, “The Fourth Booke”, in Arthur Golding, transl., The XV. Bookes of P. Ouidius Naso, Entytuled Metamorphosis, […], London: […] Willyam Seres […], folio 51, recto

He stayed not t’advize, which way were bestHis foe t’assayle, or how himselfe to gard,But with fierce fury and with force infestUpon him ran […]

1596, Edmund Spenser, “Book VI, Canto IV”, in The Faerie Queene. […], London: […] [John Wolfe] for William Ponsonbie, page 5

Like as a fire, the which in hollow cave / Hath long bene underkept, and down supprest, / With murmurous disdayne doth inly rave, / And grudge, in so streight prison to be prest, / At last breakes forth with furious infest, / And strives to mount unto his native seat […]

1590, Edmund Spenser, The Faerie Queene, Book II, Canto Eleven, Stanza 32, Hackett, 2006, p. 191