TheoreticalEconomicsLetters,2019,9,2354-2361
https://www.scirp.org/journal/tel
ISSNOnline:2162-2086
ISSNPrint:2162-2078
TaxEvasionDynamicsviaKineticModelsof
OpinionDynamics
F.W.S.Lima
DietrichStaufferComputationalPhysicsLab,DepartamentodeF´ısica,UniversidadeFederaldoPiau´ı,
Teresina,Brazil
Howtocitethispaper:Lima,F.W.S.
(2019)TaxEvasionDynamicsviaKinetic
ModelsofOpinionDynamics.TheoreticalE-
conomicsLetters,9, 2354-2361.
https://doi.org/10.4236/tel.2019.97149
Received:August20,2019
Accepted:September23,2019
Published:September26,2019
Copyright
c
2019byauthor(s)andScientific
Research PublishingInc.
This work is licensed under the Creative Com-
monsAttributionInternationalLicense(CC
BY4.0).
http://creativecommons.org/licenses/by/4.0/
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sociisnatoquepenatibusetmagnisdispar-
turientmontes,nasceturridiculusmus.Pel-
lentesquehabitantmorbitristiquesenectuset
netusetmalesuadafamesacturpisegestas.
Phasellusidmagna.Duismalesuadainter-
dumarcu.Integer metus.Morbipulvinarpel-
lentesquemi.Suspendissesedesteumagna
molestieegestas.Quisquemilorem,pulvinar
eget,egestasquis,luctusat,ante.Proinauc-
torvehiculapurus.Fusceac nislaliquamante
hendreritpellentesque.Classaptenttacitiso-
ciosquadlitoratorquentperconubianostra,
perinceptoshymenaeos.Morbiwisi.Etiam
arcumauris,facilisissed,eleifendnon,non-
ummyut,pede.Crasutlacustempormetus
mollisplacerat.Vivamuseutortorvelmetus
interdum malesuada.
Sedeleifend,erossitametfaucibuselemen-
tum,urnasapienconsectetuermauris,quis
egestasleojustononrisus.Morbinonfelisac
liberovulputatefringilla.Maurisliberoeros,
lacinianon,sodalesquis,dapibusporttitor,
pede.Classaptenttacitisociosquadlitora
torquentperconubianostra,perinceptoshy-
menaeos.Morbi dapibus mauris condimentum
nulla.Cum sociisnatoque penatibus etmagnis
disparturient montes,nasceturridiculusmus.
Etiamsitameterat.Nullavarius.Etiamt-
inciduntduivitaeturpis.Donecleo.Morbi
vulputateconvallisest.Integeraliquet.Pel-
lentesque aliquetsodalesurna.
Nullameleifendjustoinnisl.Inhachabitasse
plateadictumst.Morbinonummy.Aliquam
utfelis.Invelitleo,dictumvitae,posuereid,
vulputatenec,ante.Maecenasvitaepedenec
dui dignissim suscipit.Morbimagna.Vestibu-
lumidpurusegetvelitlaoreetlaoreet.Prae-
sentsedleovelnibhconvallisblandit.Ut
rutrum.Donecnibh.Donecinterdum.Fusce
sed pede sit amet elitrhoncus ultrices.Nullam
atenimvitaepedevehiculaiaculis.
Classaptenttacitisociosquadlitoratorquen-
tperconubianostra, perinceptoshymenaeos.
Aeneannonummyturpisidodio.Integereu-
ismodimperdietturpis.Utnecleonecdi-
amimperdietlacinia.Etiamegetlacuseget
miultriciesposuere.Inplacerattristiquetor-
tor.Sedportavestibulummetus.Nullaia-
culissollicitudinpede.Fusceluctustellusin
dolor.Curabiturauctorvelitasem.Mor-
bisapien.Classaptenttacitisociosquadl-
itoratorquentperconubianostra,perincep-
toshymenaeos.Donecadipiscingurnavehic-
ulanunc.Sedornareleoinleo.Inrhoncus
leoutdui.Aeneandolorquam,volutpatnec,
fringillaid,consectetuervel,pede.
Nullamalesuadarisusuturna.Aenean
pretiumvelitsitametmetus.Duisiaculis.In
hachabitasseplateadictumst.Nullammo-
lestieturpisegetnisl.Duisamassaidpede
dapibusultricies.Sedeuleo.Inatmaurissit
amettortorbibendumvarius.Phasellusjusto
risus,posuerein,sagittisac,variusvel,tor-
tor.Quisqueidenim.Phasellusconsequat,
liberopretium nonummy fringilla,tortor lacus
vestibulumnunc,utrhoncusligulanequeid
justo.Nullamaccumsaneuismodnunc.Proin
vitae ipsumac metusdictum tempus.Nam ut
wisi.Quisque tortor felis, interdum ac, sodales
a,sempera,sem.Curabiturinvelitsitamet
duitristiquesodales.Vivamusmaurispede,
laciniaeget,pellentesquequis,scelerisqueeu,
est.Aliquamrisus.Quisquebibendumpede
eudolor.
Donec tempusneque vitaeest.Aenean egestas
odio sed risus ullamcorper ullamcorper.Sed in
nullaatortortinciduntegestas.Namsapien
tortor,elementumsitamet,aliquamin,port-
titorfaucibus,enim.Nullamconguesuscipit
nibh.Quisqueconvallis.Praesentarcunibh,
vehicula eget,accumsaneu,tincidunta,nibh.
Suspendissevulputate,tortorquisadipiscing
viverra, lacus nibh dignissim tellus, eu suscipit
risusantefringilladiam.Quisquealiberov-
elpedeimperdietaliquet.Pellentesquenunc
nibh,eleifenda,consequatconsequat,hen-
dreritnec,diam.Sedurna.Maecenaslaoreet
eleifendneque.Vivamuspurusodio,eleifend
non,iaculisa,ultricessitamet,urna.Mau-
risfaucibusodiovitaerisus.Innisl.Praesent
purus.Integeriaculis,semeuegestaslacinia,
lacuspedescelerisqueaugue,inullamcorper
dolorerosaclacus.Nuncinlibero.
Fuscesuscipitcursussem.Vivamusrisusmi,
egestasac,imperdietvarius,faucibusquis,
leo.Aeneantincidunt.Donecsuscipit.Cras
idjustoquisnibhscelerisquedignissim.Ali-
quamsagittiselementumdolor.Aeneancon-
sectetuerjustoinpede.Curabiturullamcorper
ligula nec orci.Aliquam purus turpis, aliquam
id, ornarevitae, porttitornon, wisi.Maecenas
luctusportalorem.Donecvitae ligulaeuante
pretiumvarius.Prointortormetus,convallis
et,hendreritnon,scelerisquein,urna.Cras
quisliberoeuligulabibendumtempor.Viva-
mustellusquam,malesuadaeu,tempussed,
temporsed,velit.Doneclaciniaauctorlibero.
Praesentsednequeidpedemollisrutrum.
Vestibulumiaculisrisus.Pellentesquelacus.
Ut quisnunc sedodio malesuada egestas.Duis
amagnasitametligulatristiquepretium.Ut
pharetra.Vestibulumimperdietmagnanec
wisi.Maurisconvallis.Sedaccumsansollic-
itudinmassa.Sedidenim.Nuncpedeenim,
laciniaut,pulvinarquis,suscipitsemper,elit.
Crasaccumsaneratvitaeenim.Crassollici-
tudin.Vestibulumrutrumblanditmassa.
Sedgravidalectusutpurus.Morbilaoreet
magna.Pellentesque eu wisi.Proin turpis.In-
tegersollicitudinauguenecdui.Fuscelectus.
Vivamusfaucibusnullaneclacus.Integerdi-
am.Pellentesquesodales,enimfeugiatcursus
volutpat,semmaurisdignissimmauris,quis
consequatsemestfermentumligula.Nullam
justo lectus, condimentum sit amet, posuere a,
fringillamollis, felis.Morbi nulla nibh,pellen-
tesqueat,nonummyeu,sollicitudinnec,ip-
sum.Crasneque.Nuncaugue.Nullamvitae
quamidquampulvinar blandit.Nunc sitamet
orci.Aliquameratelit,pharetranec,aliquet
a,gravidain,mi.Quisqueurnaenim,viverra
quis,suscipitquis,tinciduntut,sapien.Cras
placeratconsequatsem.Curabituracdiam.
Curabiturdiamtortor,molliset,viverraac,
tempusvel,metus.
Curabituraclorem.Vivamusnonjustoin
duimattisposuere.Etiamaccumsanligula
idpede.Maecenastinciduntdiamnecvelit.
Praesentconvallissapienacest.Aliquamul-
lamcorpereuismodnulla.Integermollisenim
veltortor.Nullasodalesplaceratnunc.Sed
tempusrutrumwisi.Duisaccumsangravi-
dapurus.Nuncnunc.Etiamfacilisisduieu
sem.Vestibulumsemper.Praesenteueros.
Vestibulumtellusnisl,dapibusid,vestibulum
sit amet,placerat ac, mauris.Maecenas et elit
uteratplaceratdictum.Namfeugiat,turpis
etsodalesvolutpat,wisi quamrhoncusneque,
vitaealiquamipsumsapienvelenim.Maece-
nassuscipitcursusmi.
Quisque consectetuer.In suscipit mauris a do-
lor pellentesque consectetuer.Mauris convallis
nequenonerat.Inlacinia.Pellentesqueleo
eros,sagittisquis,fermentumquis,tincidun-
tut,sapien.Maecenassem.Curabitureros
odio,interdumeu,feugiateu,portaac,nis-
l.Curabiturnunc.Etiam fermentum convallis
velit.Pellentesquelaoreetlacus.Quisquesed
elit.Namquistellus.Aliquamtellusarcu,
adipiscingnon,tincidunteleifend,adipiscing
quis,augue.Vivamuselementumplaceraten-
im.Suspendisseuttortor.Integerfaucibus
adipiscingfelis.Aeneanconsectetuermattis
lectus.Morbimalesuadafaucibusdolor.Nam
lacus.Etiamarcu libero,malesuada vitae,ali-
quamvitae,blandittristique,nisl.
Maecenasaccumsandapibussapien.Duis
pretiumiaculisarcu.Curabiturutlacus.Ali-
quamvulputate.Suspendisse utpurussed sem
tempor rhoncus.Utquam dui, fringillaat, dic-
tum eget,ultricies quis,quam.Etiam semest,
pharetra non, vulputate in, pretium at, ipsum.
Nunc semper sagittis orci.Sedscelerisque sus-
cipitdiam.Utvolutpat,doloratullamcorp-
ertristique,erospurusmollisquam,sitamet
ornareantenuncetenim.
Phasellusfringilla,metusidfeugiatcon-
sectetuer,lacuswisiultricestellus, quislobor-
tisnibhloremquistortor.Donecegestas
ornarenulla.Maurismitellus,portafau-
cibus,dictumvel,nonummyin,est.Ali-
quameratvolutpat.Intellusmagna,port-
titorlacinia,molestievitae,pellentesqueeu,
justo.Classaptenttacitisociosquadlitora
torquentperconubianostra,perinceptoshy-
menaeos.Sedorcinibh,scelerisquesitamet,
suscipitsed,placeratvel,diam.Vestibulum
nonummy vulputate orci.Donec et velit ac ar-
cuinterdumsemper.Morbipedeorci,cursus
ac,elementumnon,vehiculaut,lacus.Cras
volutpat.Namvelwisiquisliberovenenatis
placerat.Aeneansedodio.Quisqueposuere
purusacorci.Vivamusodio.Vivamusvar-
ius,nullasitametsemperviverra,odiomau-
risconsequatlacus,atvestibulumnequearcu
eutortor.Doneciaculistincidunttellus.Ali-
quameratvolutpat.Curabiturmagnalorem,
dignissimvolutpat,viverraet,adipiscingnec,
dolor.Praesentlacusmauris,dapibusvitae,
sollicitudinsitamet,nonummyeget,ligula.
Crasegestasipsumanisl.Vivamusvariusdo-
lorutdolor.Fuscevelenim.Pellentesque
accumsanligulaeteros.Crasidlacusnon
tortorfacilisisfacilisis.Etiamnislelit,cur-
sussed,fringillain,conguenec,urna.Cum
sociisnatoquepenatibusetmagnisdispar-
turientmontes,nasceturridiculusmus.In-
tegeratturpis.Cumsociisnatoquepenati-
busetmagnisdisparturientmontes, nascetur
ridiculusmus.Duisfringilla,ligulasedporta
fringilla,ligulawisicommodofelis,utadipisc-
ingfelisduiinenim.Suspendissemalesuada
ultricesante.Pellentesquescelerisqueaugue
sitameturna.Nullavolutpataliquettortor.
Crasaliquam,tellusataliquetpellentesque,
justosapiencommodoleo,idrhoncussapien
quamaterat.Nullacommodo,wisiegetsol-
licitudinpretium,orciorcialiquamorci,ut
cursusturpisjustoetlacus.Nullaveltor-
tor.Quisque eratelit, viverrasit amet, sagittis
eget,portasitamet,lacus.
In hac habitasse platea dictumst.Proin at est.
Curabitur tempusvulputate elit.Pellentesque
sem.Praesent eusapien.Duiselitmagna, ali-
quet at,tempus sed, vehicula non, enim.Mor-
biviverraarcunecpurus.Vivamusfringilla,
enimet commodomalesuada,tortor metusel-
ementumligula,necaliquetestsapienutlec-
tus.Aliquammi.Utnecelit.Fusceeuismod
luctustellus.Curabiturscelerisque.Nullam
purus.Namultricies accumsanmagna.Morbi
pulvinarloremsitametipsum.Donecutjus-
tovitaenibhmolliscongue.Fuscequisdiam.
Praesent tempuserosutquam.
Donecinnisl.Fuscevitaeest.Vivamusante
ante,mattislaoreet,posuereeget,conguevel,
nunc.Fuscesem.Namvelorcieuerosviver-
raluctus.Pellentesquesitametaugue.Nunc
sitametipsumetlacusvariusnonummy.In-
teger rutrum sem egetwisi.Aenean eu sapien.
Quisqueornaredignissimmi.Duisaurnavel
risus pharetraimperdiet.Suspendissepotenti.
Morbijusto.Aeneannecdolor.Inhac
habitasseplateadictumst.Proinnonummy
porttitorvelit.Sedsitametleonecmetus
rhoncusvarius.Crasante.Vestibulumcom-
modosemtinciduntmassa.Namjusto.Ae-
neanluctus,felisetcondimentumlacinia,lec-
tusenimpulvinarpurus,nonportavelitnisl
sed eros.Suspendisseconsequat.Mauris a dui
et tortormattis pretium.Sed nulla metus,vo-
lutpatid, aliquameget, ullamcorperut, ipsum.
Morbieununc.Praesentpretium.Duisali-
quampulvinarligula.Ut blanditegestasjusto.
Quisqueposueremetusviverrapede.
Vivamussodaleselementumneque.Viva-
musdignissimaccumsanneque.Sedatenim.
Vestibulumnonummyinterdumpurus.Mau-
ris ornarevelitid nibh pretiumultricies.Fusce
temporpellentesqueodio.Vivamusauguepu-
rus,laoreetin,scelerisquevel,commodoid,
wisi.Duisenim.Nullainterdum,nunceusem-
pereleifend,enimdolorpretiumelit,utcom-
modoligulanislaest.Vivamusante.Nulla
leomassa,posuerenec,volutpatvitae,rhon-
cuseu,magna.
Quisquefacilisisauctorsapien.Pellentesque
gravidahendreritlectus.Maurisrutrumso-
dalessapien.Fuscehendreritsemvellorem.
Integerpellentesquemassavelaugue.Integer
elit tortor, feugiat quis, sagittis et, ornare non,
lacus.Vestibulumposuerepellentesqueeros.
Quisquevenenatisipsumdictumnulla.Ali-
quam quis quam nonmetus eleifend interdum.
Nam eget sapien ac mauris malesuadaadipisc-
ing.Etiameleifendnequesedquam.Nulla
facilisi.Proinaligula.Sedidduieunibh
egestastincidunt.Suspendissearcu.
Maecenasdui.Aliquamvolutpatauctorlorem.
Crasplaceratestvitaelectus.Curabitur
massalectus,rutrumeuismod,dignissimut,
dapibus a, odio.Ut eros erat, vulputate ut, in-
terdumnon,portaeu,erat.Crasfermentum,
felis inporta congue,velit leo facilisis odio,vi-
taeconsectetuerloremquamvitaeorci.Sed
ultrices,pedeeuplaceratauctor,anteligula
rutrum tellus,vel posuerenibh lacus nec nibh.
Maecenaslaoreetdoloratenim.Donecmo-
lestie dolornec metus.Vestibulum libero.Sed
quiserat.Sedtristique.Duispedeleo,fer-
mentumquis,consectetuereget,vulputatesit
amet,erat.
Donecvitaevelit.Suspendisseportafermen-
tummauris.Utvelnuncnonmaurisphare-
travarius.Duisconsequatliberoquisurna.
Maecenasatante.Vivamusvarius,wisised
egestastristique,odiowisiluctusnulla,lobor-
tisdictumdolorligulainlacus.Vivamusali-
quam, urna sed interdum porttitor,metus orci
interdum odio,sit ameteuismod lectusfelis et
leo.Praesentacwisi.Namsuscipitvestibu-
lum sem.Praesent eu ipsumvitae pede cursus
venenatis.Duis sed odio.Vestibulum eleifend.
Nullautmassa.Proinrutrummattissapien.
Curabiturdictumgravidaante.
Phasellusplaceratvulputatequam.Maece-
nasattellus.Pellentesquenequediam,dig-
nissim ac, venenatisvitae, consequat ut, lacus.
Nam nibh.Vestibulum fringilla arcu mollis ar-
cu.Sedetturpis.Donecsemtellus,volut-
pat et,variuseu, commodo sed,lectus.Lorem
ipsumdolorsitamet,consectetueradipiscing
elit.Quisqueenimarcu,suscipitnec,tempus
at,imperdietvel,metus.Morbivolutpatpu-
rusaterat.Donecdignissim,semidsemper
tempus, nibh massa eleifendturpis,sedpellen-
tesquewisipurussedlibero.Nullamlobortis
tortorvelrisus.Pellentesqueconsequatnulla
eutellus.Donecvelit.Aliquamfermentum,
wisiacrhoncusiaculis,tellusnuncmalesuada
orci,quisvolutpat duimagnaidmi.Nuncvel
ante.Duisvitaelacus.Crasnecipsum.
Morbinunc.Aliquamconsectetuer varius nul-
la.Phaselluseros.Crasdapibusporttitorris-
us.Maecenasultricesmiseddiam.Praesent
gravida velit at elit vehicula porttitor.Phasel-
lusnislmi,sagittisac, pulvinarid,gravidasit
amet,erat.Vestibulumest.Loremipsumdo-
lorsit amet,consectetueradipiscingelit.Cur-
abitur idsem elementumleo rutrumhendrerit.
Utatmi.Donectinciduntfaucibusmassa.
Sed turpis quam, sollicitudin a, hendrerit eget,
pretiumut,nisl.Duishendreritligula.Nunc
pulvinarcongueurna.
Nuncvelit.Nullamelitsapien,eleifendeu,
commodo nec, semper sit amet, elit.Nulla lec-
tus risus,condimentum ut,laoreet eget,viver-
ra nec, odio.Proin lobortis.Curabitur dictum
arcuvelwisi.Crasidnullavenenatistortor
congueultrices.Pellentesqueegetpede.Sed
eleifendsagittiselit.Namsedtellussitamet
lectusullamcorper tristique.Maurisenim sem,
tristiqueeu,accumsanat,scelerisquevulpu-
tate, neque.Quisquelacus.Donec etipsum sit
amet elitnonummy aliquet.Sed viverranisl at
sem.Namdiam.Maurisutdolor.Curabitur
ornaretortorcursusvelit.
Morbitinciduntposuerearcu.Crasvenenatis
estvitaedolor.Vivamusscelerisquesemper
mi.Donecipsumarcu,consequatscelerisque,
viverraid,dictumat,metus.Loremipsum
dolor sit amet, consectetuer adipiscing elit.Ut
pede sem, tempus ut, porttitor bibendum, mo-
lestieeu,elit.Suspendissepotenti.Sedidlec-
tus sitamet purus faucibusvehicula.Praesen-
tsedsemnonduipharetrainterdum.Nam
viverra ultricesmagna.
Aeneanlaoreetaliquamorci.Nuncinterdum
elementumurna.Quisqueerat.Nullamtem-
porneque.Maecenasvelitnibh,scelerisquea,
consequatut,viverrain,enim.Duismagna.
Donecodioneque,tristiqueet,tincidunteu,
rhoncusac, nunc.Maurismalesuada malesua-
da elit.Etiam lacus mauris, pretium vel, blan-
ditin, ultriciesid,libero.Phasellus bibendum
eratutdiam.Incongueimperdietlectus.
Aeneanscelerisque.Fuscepretiumporttitor
lorem.Inhachabitasseplatea dictumst.Nulla
sitametnislatsapienegestaspretium.Nunc
nontellus.Vivamusaliquet.Namadipiscing
euismoddolor.Aliquameratvolutpat.Nul-
lautipsum.Quisquetinciduntauctorau-
gue.Nuncimperdietipsumegetelit.Ali-
quamquamleo,consectetuernon,ornaresit
amet,tristique quis,felis.Vestibulum ante ip-
sumprimisinfaucibusorciluctusetultrices
posuerecubiliaCurae;Pellentesqueinterdum
quamsitametmi.Pellentesquemaurisdui,
dictuma,adipiscingac,fermentumsitamet,
lorem.
Utquiswisi.Praesentquismassa.Vivamus
egestasrisusegetlacus.Nunctincidunt,risus
quisbibendumfacilisis,lorempurusrutrum
neque,necportatortorurnaquisorci.Ae-
neanaliquet,liberosempervolutpatluctus,
pedeeratlaciniaaugue,quisrutrumsemip-
sumsitametpede.Vestibulumaliquet,nibh
sediaculissagittis,odiodolorblanditaugue,
egetmollisurnatellusidtellus.Aeneanali-
quetaliquamnunc.Nullaultriciesjustoeget
orci.Phasellustristiquefermentumleo.Sed
massametus,sagittisut,semperut,pharetra
vel,erat.Aliquamquamturpis,egestasvel,
elementumin,egestassitamet,lorem.Duis
convallis,wisisitametmollismolestie,libero
mauris portadui, vitaealiquam arcuturpis ac
sem.Aliquamaliquetdapibusmetus.
Vivamuscommodoeroseleifenddui.Vestibu-
luminleoeuerattristiquemattis.Crasat
elit.Craspellentesque.Nullamidlacussit
ametliberoaliquethendrerit.Proinplacerat,
minonelementumlaoreet,eroselittincidun-
tmagna,arhoncussemarcuidodio.Nul-
laegetleoaleoegestasfacilisis.Curabitur
quisvelit.Phasellusaliquam,tortornecornare
rhoncus,purusurnaposuerevelit,etcommo-
dorisustellusquistellus.Vivamusleoturpis,
tempussitamet,tristiquevitae,laoreetquis,
odio.Proinscelerisquebibendumipsum.Eti-
amnisl.Praesentveldolor.Pellentesquevel
magna.Curabitururna.Vivamuscongueur-
na in velit.Etiam ullamcorper elementum dui.
Praesentnon urna.Sed placeratquam non mi.
Pellentesquediammagna,ultricieseget,ultri-
cesplacerat,adipiscingrutrum,sem.
Morbisem.Nullafacilisi.Vestibulumante
ipsumprimisinfaucibusorciluctusetultri-
cesposuerecubiliaCurae;Nullafacilisi.Mor-
bisagittisultriceslibero.Praesenteuligula
sedsapienauctorsagittis.Classaptenttaciti
sociosquadlitoratorquentperconubianos-
tra,perinceptoshymenaeos.Donecvelnunc.
Nuncfermentum,lacusidaliquamporta,dui
tortoreuismoderos,velmolestieipsumpurus
eulacus.Vivamuspede arcu,euismod ac,tem-
pusid,pretiumet,lacus.Curabitursodales
dapibusurna.Nunceusapien.Doneceget
nuncapededictumpretium.Proinmauris.
Vivamusluctusliberovelnibh.
Fuscetristiquerisusidwisi.Integermolestie
massaidsem.Vestibulumveldolor.Pel-
lentesquevelurnavelrisusultricieselemen-
tum.Quisquesapien urna, blanditnec, iaculis
ac,viverrain,odio.Inhachabitasseplatea
dictumst.Morbinequelacus,convallisvitae,
commodoac,fermentumeu,velit.Sedinor-
ci.Infringillaturpisnonarcu.Donecinante.
Phasellustemporfeugiatvelit.Aeneanvar-
iusmassanonturpis.Vestibulumanteipsum
primisinfaucibusorciluctusetultricespo-
suerecubiliaCurae;
Aliquamtortor.Morbiipsum massa,imperdi-
etnon,consectetuervel,feugiatvel,lorem.
Quisqueeget loremnec elitmalesuadavestibu-
lum.Quisquesollicitudinipsum vel sem.Nul-
laenim.Proinnonummy felisvitaefelis.Nul-
lampellentesque.Duisrutrumfeugiatfe-
lis.Maurisvelpedesedliberotinciduntmol-
lis.Phasellussedurnarhoncusdiameuismod
bibendum.Phasellussednisl.Integercondi-
mentumjusto id orciiaculis varius.Quisque et
lacus.Phaselluselementum, justoat dignissim
auctor,wisi odiolobortisarcu, sedsollicitudin
felisfeliseuneque.Praesentatlacus.
Vivamussitametpede.Duisinterdum,nunc
egetrutrumdignissim,nisldiamluctusleo,
ettinciduntvelitnislidtellus.Inloremtel-
lus,aliquetvitae,portain,aliquetsed,lectus.
Phasellussodales.Utvariusscelerisqueerat.
Invelnibheuerosimperdietrutrum.Donec
ac odio nec neque vulputatesuscipit.Nam nec
magna.Pellentesquehabitantmorbitristique
senectus et netus et malesuada fames acturpis
egestas.Nullamporta,odioetsagittisiaculis,
wisi neque fringilla sapien, vel commodo lorem
loremidelit.Utsemlectus,scelerisqueeget,
placeratet,tinciduntscelerisque,ligula.Pel-
lentesque nonorci.
Etiamvelipsum.Morbifacilisisvestibulum
nisl.Praesentcursuslaoreetfelis.Integer
adipiscingpretiumorci.Nullafacilisi.Quisque
posuerebibendumpurus.Nullaquam mauris,
cursuseget,convallisac,molestienon,enim.
Aliquamcongue.Quisquesagittisnonummy
sapien.Proinmolestiesemvitaeurna.Mae-
cenas lorem.Vivamus viverra consequat enim.
Nuncsedpede.Praesentvitaelectus.Prae-
sentnequejusto,vehiculaeget,interdumid,
facilisiset,nibh.Phasellusatpurusetlibero
laciniadictum.Fuscealiquet.Nullaeuante
placeratleosemperdictum.Maurismetus.
Curabiturlobortis.Curabitur sollicitudinhen-
dreritnunc.Donecultriceslacusidipsum.
Donecanibhutelitvestibulumtristique.In-
tegeratpede.Crasvolutpatvariusmagna.
Phaselluseuwisi.Praesentrisusjusto,lobor-
tis eget, scelerisqueac, aliquet in, dolor.Proin
idleo.Nunciaculis,mivitaeaccumsancom-
modo, nequesemlacinianulla,quisvestibulum
justosemineros.Quisquesedmassa.Morbi
lectus ipsum, vulputate a, mollis ut,accumsan
placerat,tellus.Nullaminwisi.Vivamuseu
ligulaanuncaccumsancongue.Suspendisse
aclibero.Aliquameratvolutpat.Donecau-
gue.Nuncvenenatisfringillanibh.Fusceac-
cumsan pulvinar justo.Nullam semper,dui ut
dignissim auctor, orcilibero fringilla massa,b-
landitpulvinarpedetortoridmagna.Nunc
adipiscing justo sed velit tincidunt fermentum.
Integerplacerat.Pellentesquehabitantmorbi
tristique senectuset netus etmalesuada fames
acturpisegestas.Sedinmassa.Classaptent
tacitisociosquadlitoratorquentperconubi-
anostra,perinceptoshymenaeos.Phasellus
tempusaliquamrisus.Aliquamrutrumpurus
atmetus.Donecposuereodioaterat.Nam
nonnibh.Phasellusligula.Quisquevene-
natislectusinaugue.Sedvestibulumdapibus
neque.
Mauris tempus eros at nulla.Sed quisdui dig-
nissimmaurispretiumtincidunt.Maurisac
purus.Phasellusaclibero.Etiamdapibusia-
culisnunc.Inlectus wisi,elementumeu, sollic-
itudinnec,imperdietquis,dui.Nullaviverra
nequeaclibero.Maurisurnaleo,adipiscing
eu,ultricesnon,blanditeu,dui.Maecenas
duineque,suscipitsitamet, rutruma,laoreet
in,eros.Uteunibh.Fuscenecerattempus
urnafringillatempus.Curabituridenim.Sed
ante.Crassodalesenimsitametwisi.Nunc
fermentum consequatquam.
Utauctor,augueportadignissimvestibulum,
arcudiamlobortisvelit,velscelerisqueris-
usauguesagittisrisus.Maecenaseujusto.
Pellentesquehabitant morbitristique senectus
etnetusetmalesuadafamesacturpiseges-
tas.Mauriscongueligulaegettortor.Nul-
lam laoreeturnased enim.Donec egeteros ut
erosvolutpatconvallis.Praesentturpis.Inte-
germaurisdiam,elementumquis,egestasac,
rutrumvel,orci.Nullafacilisi.Quisqueadip-
iscing,nullavitaeelementum porta,semurna
volutpatleo,sedportaenimrisussedmassa.
Integeracenimquisdiamsodalesluctus.Ut
eget eros a ligula commodo ultricies.Donec eu
urnaviverradolorhendreritfeugiat.Aliquam
acorcivelerosconguepharetra.Quisque
rhoncus,justoeuvolutpatfaucibus,augueleo
posuerelacus,arhoncuspuruspedevelest.
Proinultricesenim.
Aenean tinciduntlaoreet dui.Vestibulumante
ipsumprimisinfaucibusorciluctusetultri-
cesposuerecubiliaCurae;Integeripsumlec-
tus,fermentumac,malesuadain,eleifendut,
lorem.Vivamusipsumturpis,elementumvel,
hendrerit ut,semper at,metus.Vivamus sapi-
entortor,eleifendid,dapibusin,egestaset,
pede.Pellentesquefaucibus.Praesentlorem
neque, dignissim in,facilisis nec, hendrerit vel,
odio.Namatdiamacnequealiquetviver-
ra.Morbidapibusligulasagittismagna.In
lobortis.Donecaliquetultricieslibero.Nunc
dictumvulputate purus.Morbi varius.Lorem
ipsumdolorsitamet,consectetueradipiscing
elit.Intempor.Phaselluscommodoporttitor
magna.Curabiturvehiculaodioveldolor.
Praesentfacilisis,augueaadipiscingvene-
natis,liberorisusmolestieodio,pulvinarcon-
sectetuerfeliseratacmauris.Namvestibu-
lumrhoncusquam.Sedveliturna,pharetra
eu,eleifendeu,viverraat,wisi.Maecenasul-
tricesnibhatturpis.Aeneanquam.Nulla
ipsum.Aliquamposuereluctuserat.Cur-
abiturmagnafelis,laciniaet,tristiqueid,ul-
tricesut,mauris.Suspendissefeugiat.Cras
eleifendwisivitaetortor.Phasellusleopurus,
mattissitamet,auctorin,rutrumin,magna.
Inhachabitasseplateadictumst.Phasellus
imperdietmetusinsem.Vestibulumacenim
nonsemultriciessagittis.Sedveldiam.
Integervelenimsedturpisadipiscingbiben-
dum.Vestibulumpededolor,laoreetnec,po-
suerein,nonummyin,sem.Donecimperdiet
sapienplaceraterat.Donecviverra.Aliquam
eros.Nunc consequat massaid leo.Sed ullam-
corper,loreminsodalesdapibus,risusmetus
sagittislorem,non porttitorpurusodioneco-
dio.Sedtinciduntposuereelit.Quisqueeu
enim.Donecliberorisus,feugiatac,dapibus
eget, posuere a,felis.Quisque vellectusutme-
tustincidunteleifend.Duis utpede.Duis velit
erat,venenatis vitae,vulputate a,pharetrasit
amet,est.Etiamfringillafaucibusaugue.
Aeneanvelitsem,viverraeu,tempusid,
rutrumid, mi.Nullam necnibh.Proinullam-
corper,dolorincursustristique,erosaugue
tempornibh,atgravidadiamwisiatpurus.
Donec mattis ullamcorper tellus.Phasellus vel
nulla.Praesentinterdum,erosinsodalessol-
licitudin,nunc nulla pulvinarjusto, aeuismod
erossemnecnibh.Nullamsagittisdapibus
lectus.Nullamegetipsumeutortorlobortis
sodales.Etiampurusleo,pretiumnec,feu-
giatnon,ullamcorpervel,nibh.Sedvelelit
etquamaccumsanfacilisis.Nuncleo.Sus-
pendissefaucibuslacus.
Pellentesqueinterdumsapiensednulla.Proin
tincidunt.Aliquamvolutpatestvelmassa.
Seddolorlacus,imperdietnon,ornarenon,
commodoeu,neque.Integerpretiumsem-
perjusto.Proinrisus.Nullamidquam.
Namneque.Duisvitaewisiullamcorperdi-
amcongueultricies.Quisqueligula.Mauris
vehicula.
Curabiturnuncmagna,posuereeget,vene-
natiseu,vehiculaac,velit.Aeneanornare,
massaaaccumsanpulvinar,quamlorem
laoreetpurus, eusodalesmagnarisus molestie
lorem.Nunceratvelit,hendreritquis,male-
suadaut,aliquamvitae,wisi.Sedposuere.
Suspendisseipsumarcu,scelerisquenec,ali-
quameu,molestietincidunt,justo.Phasellus
iaculis.Sedposuereloremnonipsum.Pel-
lentesquedapibus.Suspendissequamlibero,
laoreeta,tincidunteget,consequatat,est.
Nullamutlectusnonenimconsequatfacili-
sis.Maurisleo.Quisquepedeligula,auctor
vel,pellentesquevel,posuereid,turpis.Cras
ipsumsem,cursuset,facilisisut,tempuseu-
ismod,quam.Suspendissetristiquedoloreu
orci.Maurismattis.Aeneansemper.Viva-
mustortormagna,facilisisid,variusmattis,
hendreritin,justo.Integerpurus.
Vivamus adipiscing.Curabitur imperdiet tem-
pusturpis.Vivamussapiendolor,congueve-
nenatis,euismodeget,portarhoncus,magna.
Proincondimentumpretiumenim.Fusce
fringilla,liberoetvenenatisfacilisis,erosen-
imcursusarcu, vitaefacilisisodioauguevitae
orci.Aliquamvariusnibhutodio.Sedcondi-
mentumcondimentumnunc.Pellentesque
egetmassa.Pellentesquequismauris.Donec
utligulaacpedepulvinarlobortis.Pellen-
tesqueeuismod.Classaptenttacitisociosqu
adlitoratorquentperconubianostra,perin-
ceptoshymenaeos.Praesentelit.Utlaoreet
ornareest.Phasellusgravidavulputatenulla.
Donecsitametarcuutsemtempormalesua-
da.Praesenthendreritaugueinurna.Proin
enimante,ornarevel,consequatut,blandit
in,justo.Donecfeliselit,dignissim sed,sagit-
tisut,ullamcorpera,nulla.Aeneanpharetra
vulputateodio.
Quisqueenim.Proinvelitneque,tristiqueeu,
eleifendeget,vestibulumnec,lacus.Vivamus
odio.Duisodiourna,vehiculain,elementum
aliquam,aliquetlaoreet,tellus.Sedvelit.Sed
velmiacelitaliquetinterdum.Etiamsapi-
enneque,convalliset,aliquetvel,auctornon,
arcu.Aliquamsuscipitaliquamlectus.Proin
tinciduntmagnasedwisi.Integerblanditla-
cusutlorem.Sedluctusjustosedenim.
Morbimalesuadahendreritdui.Nuncmauris
leo, dapibus sitamet, vestibulum et, commodo
id,est.Pellentesquepurus.Pellentesquetris-
tique,nuncacpulvinaradipiscing,justoeros
consequatlectus, sitamet posuerelectusneque
velaugue.Cras consectetuerlibero aceros.Ut
egetmassa.Fuscesitametenimeleifendsem
dictum auctor.In eget risusluctus wisi conva-
llis pulvinar.Vivamus sapien risus,temporin,
viverra in, aliquetpellentesque, eros.Aliquam
euismodliberoasem.
Nunc velit augue,scelerisquedignissim, lobor-
tiset,aliquamin,risus.Ineueros.Vestibu-
lumanteipsumprimisinfaucibusorciluctus
etultricesposuerecubiliaCurae;Curabitur
vulputateelitviverraaugue.Maurisfringilla,
tortorsitametmalesuadamollis,sapienmi
dapibusodio,acimperdietligulaenimeget
nisl.Quisquevitaepedeapedealiquetsus-
cipit.Phasellustelluspede,viverravestibu-
lum,gravidaid,laoreetin,justo.Cumsoci-
isnatoquepenatibusetmagnisdisparturient
montes,nasceturridiculusmus.Integercom-
modoluctuslectus.Maurisjusto.Duisvar-
iuseros.Sedquam.Craslacuseros,rutrum
eget,variusquis,convallisiaculis,velit.Mau-
ris imperdiet, metus at tristique venenatis, pu-
rusnequepellentesquemauris,aultriceselit
lacusnectortor.Classaptenttacitisociosqu
adlitoratorquentperconubianostra,perin-
ceptoshymenaeos.Praesentmalesuada.Nam
lacuslectus,auctorsitamet,malesuadavel,
elementumeget,metus.Duisnequepede,fa-
cilisiseget,egestaselementum,nonummyid,
neque.
Proinnonsem.Donecnecerat.Proinlibero.
Aliquamviverraarcu.Donecvitaepurus.
Donecfelismi,semperid,scelerisqueporta,
sollicitudinsed,turpis.Nullainurna.Integer
variuswisinonelit.Etiamnecsem.Mau-
risconsequat,risusnecconguecondimentum,
ligulaligula suscipiturna,vitaeportaodioer-
at quissapien.Proinluctus leoid erat.Etiam
massametus,accumsanpellentesque,sagittis
sitamet,venenatisnec,mauris.Praesentur-
na eros, ornarenec, vulputate eget, cursussed,
justo.Phasellus nec lorem.Nullam ligula ligu-
la,mollissitamet,faucibusvel,eleifendac,
dui.Aliquameratvolutpat.
Fusce vehicula, tortor etgravida porttitor, me-
tusnibhconguelorem,uttempuspurusmau-
risapede.Integertinciduntorcisitamet
turpis.Aeneanametus.Aliquamvestibulum
lobortisfelis.Donecgravida.Sedsedurna.
Maurisetorci.Integerultricesfeugiatligu-
la.Seddignissimnibhamassa.Donecorci
dui,temporsed,tinciduntnonummy,viverra
sit amet, turpis.Quisque lobortis.Proin vene-
natistortornecwisi.Vestibulumplacerat.In
hachabitasseplateadictumst.Aliquampor-
tamiquisrisus.Donecsagittisluctusdiam.
Nam ipsumelit, imperdietvitae, faucibus nec,
fringillaeget,leo.Etiamquisdolorinsapien
porttitorimperdiet.
Craspretium.Nullamalesuadaipsumut
libero.Suspendissegravidahendrerittellus.
Maecenas quislacus.Morbifringilla.Vestibu-
lumodioturpis,temporvitae,scelerisquea,
dictumnon,massa.Praesenteratfelis,por-
tasitamet,condimentumsitamet,placer-
atet,turpis.Praesentplaceratlacusaen-
im.Vestibulumnoneros.Utcongue.Donec
tristiquevariustortor.Pellentesquehabitant
morbi tristique senectus et netus et malesuada
famesacturpisegestas.Namdictumdictum
urna.
Phasellusvestibulumorcivelmauris.Fusce
quamleo,adipiscingac,pulvinareget,mo-
lestiesitamet,erat.Seddiam.Suspendisse
erosleo,tempuseget,dapibussitamet,tem-
puseu,arcu.Vestibulumwisimetus,dapibus
vel,luctussitamet,condimentumquis,leo.
Suspendissemolestie.Duisinante.Utso-
dales sem sit amet mauris.Suspendisse ornare
pretiumorci.Fuscetristiqueenimegetmi.
Vestibulumeros elit,gravida ac,pharetrased,
lobortisin,massa.Proinatdolor.Duisac-
cumsanaccumsanpede.Nullamblanditelit
inmagnalaciniahendrerit.Utnonummyluc-
tuseros.Fusceegettortor.
Utsitametmagna.Crasaligulaeuurna
dignissimviverra.Nullamtemporleoporta
ipsum.Praesentpurus.Nullamconsequat.
Maurisdictumsagittisdui.Vestibulumsol-
licitudinconsectetuerwisi.Insitametdiam.
Nullammalesuadapharetrarisus.Proinlacus
arcu, eleifendsed, vehiculaat, conguesit amet,
sem.Sedsagittispedeanisl.Sedtincidunto-
dioapede.Seddui.Nameuenim.Aliquam
sagittislacusegetlibero.Pellentesquediam
sem,sagittismolestie,tristiqueet,fermentum
ornare,nibh.Nulla ettellusnon felisimperdi-
etmattis.Aliquameratvolutpat.
Vestibulumsodalesipsumidaugue.Integer
ipsumpede,convallissitamet,tristiquevi-
tae,temporut,nunc.Namnonligulanon
lorem convallis hendrerit.Maecenas hendrerit.
Sedmagnaodio,aliquamimperdiet,portaac,
aliqueteget,mi.Cumsociisnatoquepenati-
busetmagnisdisparturientmontes, nascetur
ridiculusmus.Vestibulumnislsem,dignissim
vel,euismodquis,egestasut,orci.Nuncvi-
taerisusvelmetuseuismodlaoreet.Crassit
ametnequeaturpislobortisauctor.Sedali-
quamsemacelit.Crasvelitlectus,facilisis
id,dictumsed,portarutrum,nisl.Namhen-
dreritipsumsedaugue.Nullamscelerisque
hendreritwisi.Vivamusegestasarcusedpu-
rus.Utornarelectussederos.Suspendisse
potenti.Maurissollicitudinpedevelvelit.In
hachabitasseplateadictumst.
Suspendisseeratmauris,nonummyeget,
pretiumeget,consequatvel,justo.Pellen-
tesqueconsectetuereratsedlacus.Nullam
egestasnullaacdui.Doneccursusrhoncus
ipsum.Nuncetsemeumagnaegestasmale-
suada.Vivamusdictummassaatdolor.Mor-
biestnulla,faucibusac,posuerein,interdum
ut,sapien.Proinconsectetuerpretiumurna.
Donecsit ametnibhnec purusdignissimmat-
tis.Phasellusvehiculaelitatlacus.Nullafa-
cilisi.Crasutarcu.Sedconsectetuer.Integer
tristiqueelitquisfelisconsectetuereleifend.
Crasetlectus.
Utcongue malesuadajusto.Curabiturcongue,
felisathendreritfaucibus,maurislacusport-
titor pede, nec aliquam turpisdiam feugiat ar-
cu.Nullamrhoncusipsumatrisus.Vestibu-
lumadolorseddolorfermentumvulputate.
Sednecipsumdapibusurnabibendumlobor-
tis.Vestibulumelit.Namligula arcu,volutpat
eget,laciniaeu,lobortisac,urna.Nammol-
lisultricesnulla.Crasvulputate.Suspendisse
atrisus atmetuspulvinarmalesuada.Nullam
lacus.Aliquamtempusmagna.Aliquamut
purus.Prointellus.
Vestibulumanteipsum primisinfaucibusorci
luctus et ultrices posuere cubilia Curae; Donec
scelerisquemetus.Maecenasnonmiutmetus
portahendrerit.Nuncsemper.Crasquiswisi
utloremposueretristique.Nuncvestibulum
scelerisquenulla.Suspendissepharetrasollic-
itudinante.Praesentatauguesitametante
interdum porta.Nunc bibendumaugue luctus
diam.Etiam nec sem.Sed eros turpis, facilisis
nec,vehiculavitae,aliquamsed,nulla.Cur-
abiturjustoleo,vestibulumeget,tristiqueut,
tempusat,nisl.
Nullavenenatisloremidarcu.Morbicur-
susurnaaipsum.Donecporttitor.Integer
eleifend,estnonmattismalesuada,minulla
convallismi,etauctorlectussapienutpu-
rus.Aliquamnullaaugue,pharetrasitamet,
faucibussemper,molestievel,nibh.Pellen-
tesquevestibulummagnaetmi.Sedfringilla
dolorveltellus.Nuncliberonunc,venenatis
eget,convallishendrerit,iaculiselementum,
mi.Nullamaliquam,felisetaccumsanvehic-
ula,magnajustovehiculadiam,eucondimen-
tumnislfelisetnunc.Quisquevolutpatmauris
avelit.Pellentesquemassa.Integeratlorem.
Nammetuserat,laciniaid,convallisut,pul-
vinarnon,wisi.Crasiaculismaurisutneque.
Crassodales,semvitaeimperdietconsequat,
pede purussollicitudin urna,ac aliquammetus
orciinleo.Utmolestieultricesmauris.Viva-
musvitaesem.Aliquameratvolutpat.Prae-
sentcommodo,nislacdapibusaliquet,tortor
orci sodales lorem, non ornare nulla lorem quis
nisl.
Sedatsemvitaepurusultricesvestibulum.
Vestibulumtinciduntlacusetligula.Pel-
lentesquevitaeelit.Vestibulumanteipsum
primisinfaucibusorciluctusetultricespo-
suerecubiliaCurae;Duisornare,erateget
laoreetvulputate,lacusipsumsuscipitturpis,
etbibendumnislorcinonlectus.Vestibu-
lumnecrisusnecliberofermentumfringilla.
Morbinonvelitinmagnagravidahendrerit.
Pellentesquequislectus.Vestibulumeleifend
lobortisleo.Vestibulumnonaugue.Vivamus
dictumtempordui.Maecenasatligulaidfe-
liscongueporttitor.Nullaleomagna,egestas
quis,vulputatesitamet,viverraid,velit.
Utlectuslectus,ultriciessitamet,semper
eget,laoreetnon,ante.Proinatmassaquis
nuncrhoncusmattis.Aliquamlorem.Cur-
abiturpharetraduiatneque.Aliquameutel-
lus.Aeneantempus,felisvitaevulputateia-
culis,estdolorfaucibusurna,inviverrawisi
nequenonrisus.Fusceveldolornecsapien
pretiumnonummy.Integerfaucibusmassaac
nulla ornarevenenatis.Nullaquis sapien.Sed
tortor.Phasellusegetmi.Crasnunc.Crasa
enim.
Quisque nisl.In dignissim dapibus massa.Ae-
neansemmagna,scelerisquenec,ullamcorper
quis,porttitorut,lectus.Fuscedignissimfa-
cilisistortor.Vivamusgravidafelissitamet
nunc.Nampulvinarodiovelenim.Pellen-
tesquesitametest.Vivamuspulvinar leonon
sapien.Aliquameratvolutpat.Utelementum
auctormetus.Maurisvestibulumnequevitae
eros.Pellentesquealiquamquam.Donecve-
nenatistristiquepurus.Innisl.Nullavelit
libero,fermentumat,portaa,feugiatvitae,
urna.Etiamaliquetornareipsum.Proinnon
dolor.Aeneannuncligula,venenatissuscipit,
porttitorsit amet, mattissuscipit, magna.Vi-
vamusegestasviverraest.Morbiatrisussed
sapiensodalespretium.
Morbicongueconguemetus.Aeneansedpu-
rus.Nampedemagna,tristiquenec,porta
id,sollicitudinquis,sapien.Vestibulumblan-
dit.Suspendisse ut augue ac nibhullamcorper
posuere.Integereuismod,nequeateleifend
fringilla,augueelitornaredolor,veltincidunt
purusest idlacus.Vivamusloremdui, commo-
doquis,scelerisqueeu,tinciduntnon,magna.
Cras sodales.Quisquevestibulum pulvinar di-
am.Phasellustincidunt, leovitaetristique fa-
cilisis,ipsum wisiinterdum sem,dapibussem-
pernulla velit vel lectus.Cras dapibusmauris
etaugue.Quisquecursusnullainlibero.Sus-
pendisseetloremsitametmaurismalesuada
mollis.Nullamidjusto.Maecenasvenenatis.
Doneclacusarcu,egestasac,fermentumcon-
sectetuer,tempuseu,metus.Proinsodales,
seminpretiumfermentum,arcusapiencom-
modomauris,venenatisconsequataugueur-
nainwisi.Quisquesapiennunc,variuseget,
condimentumquis,laciniain,est.Fuscefacil-
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cipitvulputate.Sedinterdumlacusnonvelit.
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luctusetultricesposuerecubiliaCurae;
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gue.Morbimauriswisi,aliquetvitae,dignis-
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Vestibulumgravida.Morbimattisliberosed
est.
Abstract
Thesocioeconomicphenomenaastaxevasioninagent-basedcom-
munity can be studied numerically through theZaklan model (ZM).
TheZMhasbeenconfiguredasanexcellenttooltocontrolthetax
evasionfluctuationsin communitieswithagents orindividuals that
canbeconsideredtaxevadersorhonest.Thedynamicoftemporal
evolutionoftheZMwasstudiedinitiallyviatheequilibriumIsing
model(IM),non-equilibriumMajority-votemodel(MVM)andre-
centlyviaathree-statekineticagent-basedmodel.Here,through
MonteCarlosimulations,westudytheproblemofthetaxevasion
fluctuationsusingadiscreteversionofthekineticmodelofopinion
dynamics(BCS)inthedynamicofthetemporalevolutionofthe
ZM.UnlikepreviousmodelscitedhereintheBCSmodel,thein-
teractionsbetweenagentsoccurinpairs.Then,wefoundthatthe
BCS model is asefficient as the IMand MVM in controlling the tax
evasion fluctuations.Thiscontrol is even better when we use strong
punishmentvalueskevenforlowauditprobabilitiesp
a
.
Keywords
OpinionDynamics,Sociophysics,MajorityVote,Non-Equilibrium
1.Introduction
Theanalysisofthesocialandeconomicbehaviorofacommunity
ofpeoplefulfilledbyBloomquist(2006),Andreoni(1998),Lederman
(2003),Slemrodetal.[1–6](2003to2007),indicatesthatthetax
evasioninacommunityisamajorcauseofconcernforgovernments.
ThroughempiricalevidenceG¨achter[7](2006),FreyandTorgler[8]
(2006)haveprovided thatthegroupmembersorneighborhoodoftax
evadersareimportantindecidingwhetherornottopaytaxes.
Zaklanetal.[9,10](2008)developedaneconomicsmodeltostudy
the problem of tax evasion dynamics on a people community using the
equilibriumIMonasquarelattice(SL)andMonte-Carlosimulations
DOI: 10.4236/tel.2019.97149Sep.26,20192354TheoreticalEconomicsLetters
F.W.S.Lima
withtheGlauberalgorithms.Insomecomplexnetworkslikedirected
Barab´asi-Albert andApollonian networks itisnotpossible tosimulate
theZMviaIMbecausethishasnosocialnoiseonthesecomplex
networks,i.e.,doesnotpresentaphasetransition.
Tosolvethisproblem,Lima[11,12](1992,2008)proposedtheuse
ofthe non-equilibriumMVMtostudythetax evasion inany complex
network[13](2010).Hepointsoutthatpeopledonotliveinasocial
equilibrium, andany socialnoise can drive to agovernment or market
chaos.Then,itisreasonabletoexpectthatanon-equilibriummodel
(MVM)explainsbettereventsofnon-equilibrium.Inordertoshow
thattheproblemoftaxevasionfluctuationsisbetterdescribedbya
non-equilibriummodelthanbyanequilibriummodel,Lima[14–17]
(2010to2016)studiedtheZMonApollonian,Opinion-Dependent,
Solomon, andSmall-WorldNetworks.Inallthesecases thetax evasion
problem was analyzedusing thetwo-stateversion of MVM,wherethe
honestagentwasrated+1andtheevadedvalue1.
Crokidakis[18](2014)hasstudiedtheproblemoftaxevasionvia
ZMonafully-connectedpopulation.Inhiswork,theagentsmaybe
inthreedifferentstates,namelyhonesttaxpayers,taxevadersand
undecided.Theundecidesagentsareindividualsinanintermediate
class among honestsand evaders.Each agent canchange his statefol-
lowing a kinetic exchange opinion dynamics, where the agents interact
bypairswithnegative (probabilityp)andpositive(1p)affinity pa-
rametersµ
ij
,representingagreement/disagreementbetweenpairsof
agents.
Biswasetal.[19](2012)proposedakineticmodelofcontinuous
opiniondynamics(BCS).TheBCSmodelhasmutualinteractions
thatcanbebothpositiveandnegativeandasingleparameterprep-
resentingthefractionofnegativeinteractions.Numericalsimulations
of thecontinuous version of thismodel indicatethe existenceof a uni-
versal,continuousphasetransitionatp=p
c
withexponentsofmean
field(νd=2.00(1),β=0.50(1)andγ=1.00(1)).Mukherjeeand
Chatterjee[20]studiedtheBCSmodelonsquareandcubiclattices
(2Dand3D).Theirnumerical resultsindicatethatthe criticalbehav-
ioroftheBCSmodelontheselatticesisthesameasthatoftheIsing
modelinthecorrespondingdimensions.
Here, we study thebehavior ofthe taxevasion on anagentscommu-
nityofhonestcitizensand taxevaders, wheretheagentsarepositioned
onsitesofSL,butnowusingadiscreteversionofBCSmodelforthe
temporalevolutionofZM.
Thearticleisorganizedasfollows:wepresent,inthenextsection,
the modeland someof theMonte Carlo simulation details.InSection
3theresultsarepresentedand,inthefinalsection,someconcluding
remarksarediscussed.
2.ZMviaNon-EquilibriumDynamicsof
BCSModel
WeusetheZMviaBCSmodeltostudythetaxevasionfluctuations
on a community ofhomogeneous agents located on a SL.In every time
period, eachSLsite isinhabited byanagent(individuals)withopinion
O
i
,whocaneitherbeanhonesttaxpayerO
i
= +1oracheaterO
i
=
1.Itisassumedthatinitially,everybodyishonest.Each periodthe
agents can rethink their behavior and have the opportunity to become
theoppositetypeofagenttheywereinthepreviousperiod.Each
DOI: 10.4236/tel.2019.971492355TheoreticalEconomicsLetters
F.W.S.Lima
agent’ssocialSLmay eitherprefertaxevasion orrejectit.Individual
decisionmakingdependsonfourrules:
1)Each nodeintheSLisassignedadiscreteopinionvariableO
i
=
±1;
2)Ateachtimestepisrandomlychooseanetworknodeorsiteto
update;
3) Then oneof your links is randomlyselected, anda µ
ij
parameter
calledbindingaffinityisset.Theaffinityparameterassumesvalues
1withprobabilitypand+1withprobability1p;
4)Bothnodesiandjsharingtheselectedlinkwillbeupdated
accordingtothefollowingexpressions:
O
i
(t+1)=O
i
(t)+µ
ij
O
j
(t)(1)
O
j
(t+1)=O
j
(t)+µ
ij
0
i
(t),(2)
whereO
i
(t)andO
j
(t)aretheoldeststatesofopinion,andO
i
(t+1)
andO
j
(t+1)aretheupdatedstatesofopinion.
TheZMpresentsanenforcementmechanismthatconsistsoftwo
components:aprobabilityofanefficientauditp
a
;andanumberk
ofperiods.Thenoncethetaxevasionisdetectedthetaxevaders,
O
i
=1,canbecomehonestindividualsO
i
=+1,inthepresenceof
anauditprobabilityp
a
,foranumberkofperiods.Onetimeunit isone
sweepthroughtheentiresystem.Therefore,accordingtotheabove
rulesandunlikeothermodelssuchastheIMorMVM,forexample,
agents’opinionsareupdatedbypairsthatwererandomlyconnected
byµ
ij
affinitylinks.Theorderinginthesystemismeasuredbythe
quantitynamelyaverageopiniondefinedby
O=
*
1
N
N
X
i=1
O
i
+
,(3)
where<...>denotesconfigurationalaveragetakenatsteady
states.
Thefractionoftaxevadersis
tax evasion =
NN
honest
N
,(4)
where Nis the totalnumber and N
honest
the honest number of agents.
The taxevasioniscalculated atevery timestep tof systemevolution.
HereN= 10
4
agents.
Similarto IMand MVMmodelsin BCSmodel forp>p
c
, halfofthe
peoplearehonest,O
i
= +1,andtheotherhalfcheatO
i
= 1,while
for p<p
c
either oneopinionor theother opiniondominates.Because
ofthisbehavior,we setafixednoise(p)tosomevalues slightlybelow
p
c
, where the case that agents distribute in equal proportions onto the
twoalternativesisexcluded.Wesetp=0.95p
c
withp
c
=0.1340 ±
0.0001 onSL.Thenwe vary thedegrees ofpunishment (k= 10, 50and
100) andauditprobability rate(p
a
= 0.5%, 10%and 90%).Therefore,
if tax evasion is detected, the enforcement mechanism p
a
and the time
of punishment karetriggered in order to control the tax evasion level.
Thepunishedindividualsremainhonestforacertainnumberkof
periods,asexplainedbefore.
DOI: 10.4236/tel.2019.971492356TheoreticalEconomicsLetters
F.W.S.Lima
3.ResultsandDiscussion
FollowingtheZM,westartwithapopulationofN= 10
4
individuals
whereinitiallyeveryoneisconsideredhonestO
i
(t=0)=+1.Then
we applytherulesof theZMasthe punishment period kand the audit
probabilitiesp
a
.
In Figure 1, we show thetax evasion as afunction of timevia a BCS
model fortwodifferent values ofp>p
c
= 0.1340(1) ,namelyp= 0.35
Figure1(a)andFigure1(b)andp=0.25((c)and(d)).Inthiscase,
forp>p
c
,wewillhavethebaselinecase(k=0andp
a
=0),i.e.,
thekineticexchangedynamicsdefinedbyEquation(1)andEquation
(2)leadsthesystemtoadisorderedstatewithanequalfraction1/2
(50%)for±1states.Thus, fromFigure1thatiftheauditsareefficient
(p
a
= 90%)thetaxevasioncanbeconsiderablyreducedto20%for
k=10andto7.5%fork=50.Thisbehavioroffluctuationsof
thetaxevasionisidenticaltothatreportedinZMonregularlattices
andnetworks[9,10,12,13].Forthecaseswherep
a
=5%,considered
more realisticby the literature,thepunishment ismoreefficient when
thepenaltydurationishighask=50.Inthiscase,thetaxevasion
canbereducedforvaluesaround30%.Noticethatwhenthevalue
ofpdecreasethefractionoftaxevadersalsodecreases,thatis,for
high pthefractionof opinions1is greaterthaninthe casesoflower
valuesofp.Thisbehaviorisduetothefactthattherearemany
negative affinity parametersµ
ij
in thepopulation,which allows many
transitionsO
i
= +1O
i
= 1forp>p
c
.
Figure1.(Coloronline)TimeevolutionoftaxevasionviaBCSmodelfordifferentvaluesof
degreesofpunishmentk=10and50andtwodistinctauditprobabilitiesp
a
=0.9((a)and(c))
andp
a
= 0.05((b)and(d)).Theresultsareforp= 0.35((a)and(b))andp= 0.25((c)and(d)).
Forrealizationofeachcurve,weuseapopulationofsizeN= 10
4
individualsatp= 0.95p
c
.
DOI: 10.4236/tel.2019.971492357TheoreticalEconomicsLetters
F.W.S.Lima
InFigure2(a) andFigure2(b),we present resultsforp= 0.15,this
is,anothervalueofp>p
c
whichisveryclosetothecriticalpoint
p
c
.Seethatforahighauditprobabilityp
a
=90%thetaxevasion
canbedramaticallyreducedforbothpunishmentperiodsk=10
andk=50.Seealsothatevenforp
a
=5%consideredhereasthe
realisticvalueinacommunityof taxevaders theapplicationofsevere
punishments ask= 50can leadtheevasiontolow levels like 20%,see
Figure2(b).Still,inFigure2,weshow resultsforp<p
c
,Figure2(c)
andFigure2(d).Thenforp=0.05thetimedynamicsoftheBCS
modeldrivethesystemtoasteady-statewithalargenumber ofhonest
individuals(O
i
=+1).Forp
a
=90%(Figure2(c))thetaxevasion
isreducedto6%ask=10andto5%ask=50andasp
a
=5%
(Figure2(d))thetaxevasionisnowreducedto6%regardlessofthe
valuesofthepunishmentperiodsk= 10and50.
InFigure3,weexhibittheaveragetaxevasioninthestationary
states as afunction ofthe auditprobability p
a
.Figure 3(a)-(c) display
theresultsforp= 0.05, 0.15and0.35,respectively,andforpunishment
periodvaluesofk=10,50,and100.Forp=0.05,i.e.,p<p
c
the
averagetaxevasionissmallenoughanddecreaseswiththegrowth
ofp
a
.Thisdecreasesto4.5%forhighpunishmentperiodvalueslike
k= 100.Otherwise,thetaxevasionfork= 100andvaluesofp>p
c
as 0.15and 0.35decrease for6%and 5%,respectively.In Figure3(d),
weshowthebehaviorofthetaxevasionfork=10andforp= 0.05,
0.15,and0.35.Onecanseethatforp<p
c
thetaxevasionremains
constantforallvaluesofp
a
.Forvaluesofp>p
c
thetaxevasionis
reducedto15%and25%for0.15and0.35,respectively.
Figure2.ThesameofFigure1,butnowtop= 0.15((a)and(b)),andp= 0.05((c)and(d)).
DOI: 10.4236/tel.2019.971492358TheoreticalEconomicsLetters
F.W.S.Lima
Figure3.(Color online) Average stationary tax evasion as a function of the audit probability
p
a
.Inthe(a)-(c),weshowtheresultsforp=0.05,0.15and0.35,respectively,andvalues
ofdegreesofpunishmentk=10,50,100.Inthelast(d)itisshowntheresultsfork=10
and different fractions ofnegative interactions p.Each point is averaged over 100 independent
simulationsforpopulationsizeN= 10
4
.
4.Conclusions
Thefirstnumericalattempttomodelthefluctuationstaxevasion
problemwasperformedbyZaklanetal.[9].TheyusedMonteCarlo
SimulationandtheIsingmodel(equilibriummodel)asatoolforthe
dynamicevolutionofZaklan.InsomegeometriessuchasApollonius
andBarabasiannetworkstheIsingmodelcannotbeusedduetothe
lackofphasetransition.Lima[12]overcamethis obstaclebyproposing
to use the majority vote model (non-equilibrium model) as a temporal
evolution of the Zaklan model.Both proposals weresuccessful in their
particulartopologies.
Here,westudiedthebehaviorofthetaxevasionviathenon-
equilibriumBCSmodel.AswesawabovetheBCSmodelisamodel
ofopinionformationinasocialcommunity.Thebehaviorof theBCS
modelinrelationtocontrolthetaxevasionfluctuationisverysimi-
lartothosefoundbytheIsingandmajorityvotemodels.Then,the
sociophysicsBCSmodelisanotherusefultoolforstudyingthetax
evasionprobleminacommunity.Therefore,wefoundtheplausible
resultthattaxevasionisdiminishedbystrongerpunishmentkand
auditprobabilityp
a
.
Acknowledgements
F.W.S.LimathanksDietrichStaufferformanysuggestionsand
fruitfuldiscussionsduringthedevelopmentofthiswork.We
DOI: 10.4236/tel.2019.971492359TheoreticalEconomicsLetters
F.W.S.Lima
thankCNPqandFUNCAPforfinancialsupport.Thisworkalso
wassupportedthesystemSGIAltix1350thecomputationalpark
CENAPAD.UNICAMP-USP,SP-BRAZIL.
ConflictsofInterest
Theauthordeclaresnoconflictsofinterestregardingthepublication
ofthispaper.
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