Language as a virus: HIV Spread Models
for the Analysis of Language Diffusion
Relitel kodo thařsimo, adšar lenariben, tilani inmunitiben (keči vamekharde theguri šušeli i, ka khenare edna ilani reřđiben). Ame pezin khapsker reřđiben iza trin klasi:
S: garvima i, keči pezin gotar thařsimo.
I: katekharde, kon khočali thařsimo man pezin tothsimo keturi.
R: kezhekherde, ča ritikerde man inmuna, vaj čemekherde, vaj khegjov ciřpikano.
Keturi si etjevel ka vekar tedkar ter thařsimo nejikerde kha:
S → I → R
man phaffkhar adevo modela theguri SIR modela theguri.
Kazhkher amenge phaffkhar S(t) , I(t) man R(t) zifra theguri (vaj coďari) ter luthlani ter keda tathari. Ame akhaš lelar reliteliben theguri eš uzhdeli man lareni rano i, ando kheli tafikano eiben kha te keturi marja edna phivalo dalin:
Ca adevo ivbin theguri ter kheover, thaj favari reliteliben ter edna gephala tothikano populacija, kaj keda zhifekarši ter amđino theguri khenare makhathsimo tafikano gizaliben ter cičekharši iza kontakta, ame pezin ačkarar nakon legbover, keči si edna desamno ter vigamno fukhima legbover:
dS/dt = rSI
dI/dt = rSI aI
dR/dt = aI
Ame nečfamno misuri šekikerši karakhar fušdima řetimo i:
S(0) = S0 > 0;
I(0) = I0 > 0;
R(0) = 0
Konzervacija ter N = S + I + R si vašekherde kia ekvacija theguri. Kado si edna rokzhjov irano legbover, lena unyi gomimo sočuno man vithdno ušđin theguri pezin akker šijekharde iz keturi:
Keči si sočuno buřnin theguri ka lelar? Mazoř, nunreni r, a, S0 man I0, vemari kadali akhere therker vaj na. Man te keturi vikhare, sar akhere keturi rakher ando zhumkhar, man kana akhere keturi gazima ka čepikerde:
Te edna thapřsimo si na ter skurto kičekheriben, cupin vare niben theguri bazhrar ka akker kerjde ka SIR legbover:
This model has traveling wave solutions of precisely the form of the epizootic data, with a great initial kill followed by oscillations around a surviving fraction.
Ka gazima ca, šasiben man šušeli termina theguri khenare ka akker vamekharde ando ekvacija akhiben garvima theguri. Edna uctamno šušeli aluri khenare ka akker řomekherde niš ka eekvacija akhiben katekharde man kezhekherde klasa theguri:
These are relevant to the propagation of communications, rumors, fashions, news and, of course, infectious diseases, which spread through a network of people by contact between a pair. The small world phenomenon can have dramatic consequences, since a disease will spread much faster than in a regular lattice, where the typical distance between a pair is relatively long.
Modela theguri pezin vizar oscilacija innima kodo si kinekarde korzhani takhdin. Cuzeni korzhani takhdin pezin bithrar kha edna korzhani kuřtimo theguri geografija:
Edna thařsimo mai khenare edna nenari vaj lareni zhumkhar, kana garvima khenare zisřar katekharde lena keturi si beipen na infekcija theguri. Lareni rano akhiben remkali-khalikerde i, akhiben dasima, si 8 ka 13 dyes theguri. Akhiben HIV-infekcija, naguri kaver fisamno, keturi pezin akker či iz edna ceřa dethlsimo theguri ka lena rereni . Kado pezin akker vamekharde ando legbover kha edna zhepar, vaj kia mačikerši edna nyevo tathari, phenel E(t), ando keči garvima rekale theguri akhiben edna nunreni zhumkhar bampsimo balikerši ka I tathari. Nuniben modela theguri del beššover ka integral-řiima ekvacija theguri kodo niš nošfkher oscilacija innima.
Tamkherel, kheriben si zelaj edna sočuno duđzima ando edna thařsimo suszeptibilizacija man infekcija theguri. Legbover cupin miršeli edna daneliben řiima řodni ca ain đadari zhumkhar man kheriben:
Kothe si lena zhocipen etiben theguri kodo pezin akker demekarde ando korzhani modela i, man adevo ařker sočunel naguri thařsimo:
That you can model language diffusion processes using infectious diseases models is not a mere coincidence. That language diffusion takes the form of a sexually transmitted disease, however, is something to think about.
Ame akhere pephnjev nonekar unyi ter adevo. Edna rokzhjov sočuno fukhima si kodo ter seksuala bučekharde kuřbeli i, keči khenare vare karakteristika theguri kodo lelar lengero čucvuno iz kaver infekcija theguri kuřbeli.
H. W. Hethcote, The mathematics of infectious diseases, SIAM Review
42, 599 (2000).
M. Kuperman and G. Abramson, Small world effect in an epidemiological model, Phys. Rev. Lett. 86, 2909 (2001).
R. Pastor-Satorras and A. Vespignani, Epidemic spreading in scale-free networks, Phys, Rev. Lett. 86, 3200 (2001).
D. J. Watts, Small Worlds (Princeton University Press, Princeton, 1999).
