Etymology
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infest (v.)
late 15c., "to attack, assail, hurt, distress, annoy," from Old French infester (14c.), from Latin infestare "to attack, disturb, trouble," from infestus "unsafe, hostile, threatening, dangerous," originally "inexorable, not able to be handled," from in- "not, opposite of" (see in- (1)) + -festus, perhaps "(able to be) seized" (see manifest (adj.)). Sense of "swarm over in large numbers, attack parasitically" first recorded c. 1600. Related: Infested; infesting.
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infestation (n.)
early 15c., "a being infested," from Old French infestacion, from Late Latin infestationem (nominative infestatio) "a troubling, a disturbing, a molesting," noun of action from past participle stem of Latin infestare "to attack, disturb" (see infest).
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manifest (adj.)
Origin and meaning of manifest

late 14c., "clearly revealed to the eye or the understanding, open to view or comprehension," from Old French manifest "evident, palpable," (12c.), or directly from Latin manifestus "plainly apprehensible, clear, apparent, evident;" of offenses, "proved by direct evidence;" of offenders, "caught in the act," probably from manus "hand" (from PIE root *man- (2) "hand") + -festus, which apparently is identical to the second element of infest.

De Vaan writes, "If manifestus may be interpreted as 'caught by hand', the meanings seem to point to 'grabbing' or 'attacking' for -festus." But he finds none of the proposed ulterior connections compelling, and concludes that, regarding infestus and manifestus, "maybe the two must be separated." If not, the sense development might be from "caught by hand" to "in hand, palpable." 

Manifest destiny, "that which clearly appears destined to come to pass; a future state, condition, or event which can be foreseen with certainty, or is regarded as inevitable" was much used in American politics from about the time of the Mexican War "by those who believed that the United States were destined in time to occupy the entire continent" [Century Dictionary].

Other nations have tried to check ... the fulfillment of our manifest destiny to overspread the Continent allotted by Providence for the free development of our yearly multiplying millions. [John O'Sullivan (1813-1895), "U.S. Magazine & Democratic Review," July 1845]

The phrase apparently is O'Sullivan's coinage; the notion is as old as the republic.

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parasitize (v.)

in zoology, "infest as a parasite," 1880, from parasite + -ize. Related: Parasitized; parasitizing.

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plague (v.)

late 15c. (Caxton), "infest with disease or other natural calamity," from Middle Dutch plaghen, from plaghe (n.) "plague" (see plague (n.)). The sense of "vex, harass, bother, annoy" is recorded from 1590s. Related: Plagued; plaguing.

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in- (2)
Origin and meaning of in-

element meaning "into, in, on, upon" (also im-, il-, ir- by assimilation of -n- with following consonant), from Latin in- "in," from PIE root *en "in."

In Old French (and hence in Middle English) this often became en-, which in English had a strong tendency to revert to Latin in-, but not always, which accounts for pairs such as enquire/inquire. There was a native form, which in West Saxon usually appeared as on- (as in Old English onliehtan "to enlighten"), and some of those verbs survived into Middle English (such as inwrite "to inscribe"), but all now seem to be extinct.

Not related to in- (1) "not," which also was a common prefix in Latin, causing confusion: to the Romans impressus could mean "pressed" or "unpressed;" inaudire meant "to hear," but inauditus meant "unheard of;" in Late Latin investigabilis could mean "that may be searched into" or "that cannot be searched into." Latin invocatus was "uncalled, uninvited," but invocare was "to call, appeal to."

The trouble has continued in English; the hesitation over what is meant by inflammable being a commonly cited example. Implume (1610s) meant "to feather," but implumed (c. 1600) meant "unfeathered." Impliable can mean "capable of being implied" (1865) or "inflexible" (1734). Impartible in 17c. could mean "incapable of being divided" or "capable of being imparted." Impassionate can be "free from passion" or it can mean "strongly stirred by passion." Inanimate (adj.) is "lifeless," but Donne uses inanimate (v.) to mean "infuse with life or vigor." Irruption is "a breaking in," but irruptible is "unbreakable."

In addition to improve "use to one's profit," Middle English also had a verb improve meaning "to disprove" (15c.). To inculpate is "to accuse," but inculpable means "not culpable, free from blame." Infestive has meant "troublesome, annoying" (1560s, from infest) and "not festive" (1620s). In Middle English inflexible could mean "incapable of being bent" or "capable of being swayed or moved." In 17c., informed could mean "current in information," formed, animated," or "unformed, formless" ("This was an awkward use" [OED]). Inhabited has meant "dwelt in" (1560s) and "uninhabited" (1610s); inhabitable likewise has been used on opposite senses, a confusion that goes back to Late Latin.

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