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4-5rhOctober 2010 Syioh Kuolo universlty - A.odemic Activity C€nt€r Dorussolom - Eondo Aceh lndoneiio rsBN 978-502-8892-17-9 illll|ililtilllilIilil]il [ [ 91 786028 892179 EDITOR: Dr, d.h. Mahdi Abrar, M.sc Dr. drh. Yudha Fahrimal, lvl.sc or. d.h. M. Hambal Prof. Dr. drh. Tongku Nizwan Siregar, MP Dr. drh. T. Reza F€rasvi, li.Sc Orh. Owinna Aliza, M.sc Orh. Amaiia Sutriana, M,Sc Drh. Henni Vanda, M,Si dfi. Nuzul Arnilia M.Si iilrl M'll,'' PERPUSTAKAAN NASlOtlAr: XATALOG DATAM TERBIAN Think clobally Act Locally: Entering the clobal Market of Animal Health end Livestock through Utilizing Loca, Resources Based on 6reen Vision Erttd': '- a.E krasyi, '-ste Dwlnna Aliza, Amalia Sitriana, Hennivanda, Fahrimal, M.HambaL Mahdi Abrar, dan Tongku Nizwan -3arda S. Aceh: Universitas Syiah Kuala,2010 6SN 978-602-8892-17-9 1. Pelernalan l. T. Reza Ferasyi 636 O Hak Cipta dilindungi berdasarkan Undang-Undang No. 19 Tahun 2002 tentang Hak Cipta Dilarang memperbanyat sebagian atau seluruh isi buku ini dengan cara apapun, termasuk dengan czra penggunaan mesin fotocopy tanpa izin dari p€nerbit Cetakan pertama, Ollober 20 I 0 T. Reza Ferasyi, dkk THINK GLOBALLY ACT LOCALLY: ENTERING TI{E GLOBAL MARKET OF ANIMAL HEALTH AND LIVESTOCK THROUGH UTILIZING LOCAT RESOIIRCES BASED ON GREEN VISTON Hak penerbitan pada Falultas Kedokteran Hewan Universitas Syiah Kuala. Editor dan Penerbit tidak bertanggung jawab atas substansi tulisan. Desain cover: T. Reza Ferasyi dan Dwinna Aliza CONTENTS Keynote Sp€aker I - Natuml Methods for lncreasing Reproductive Eflici€noy in Small Ruminants the'Clean, Green, and Ethical'Concept in Actio Craeme B Manin and l euku R. Ferasyi 2. Development ofoptical Freshness. ,. .., .,.--.... - 1-8 Sensor Algorilhms to Detect Agricultural Product 9-16 Faisal Abdullah, Mohammad Zubir Mat Jafri, Mohammad Suhaimi bin Jaafar List ofPaper 1. Modeling the Dynamics ofMalaria.......... Rinidar, Hermao Mawengkang and M- Isa 2. 3. ..............: \. Study on Prevalence ofAnisakiasis and lts Causes in Banda Aceh Major Fishpors..... ..... .. . .. .. Muhammad Hanafiah, Mufti Kamaruddin, and Madzani Ulfah Daulay 17-25 26-30 Study ofl,arvacidal Activity olMunaya Paniculata LeafExtract Againsl Aedes Aegipty Lat rae 31-34 Ilennivand4 Amalia Sutriana, and Hamny 4. Ascaridia galli Populations in Laying Hens Resulting from Varying l*vels Repeated Dosage with Embryonated Eggs........ of 35-39 Muhammad llambal, Ummu Balqis, and Darmawi 5. The Sensitivity Test of Bacterial Mastitis Pathogen, Stapylococctts aereus T 768 to Pliek U Oil and Ethanol Extract of Pliek U..................., 4045 Nurliana 6. 7. Aniimalaria Activity Of Aza<lirachtd Indica A. IussTo PL7\modium Berghei t Mus \"lu:rulus........... Sofi4 Hanifah, and Maryatun 46-51 Determination ofArsenic Accumulation in Livers and Feces ofKacang Goats Grazing in Tsunami Affected Cut Dahlia Iskandar and Triva Murtina Lubis 52-60 tfid Deer.. 8. Moryhometry ofThe Reproductive Tracts ofThe Female Lesser- Mouse Hamny, Idawati Nasution. and Triva MurtinaLub;s 9 Idcntification of Slaugltte.ed Death Chicken Meat Using Seveml Pammeter of BiologicalValues......- Razali and Teuku Re7-a Fcrasyi 6l-63 64-69 MODELING THE DYNAMICS OF MALARIA Keamey, sentative p. s8. Rinidarl, Il€rman Mawengkangz, atrd M.Isar ming and | 'VerennaD Medh in( I.r.utrJ. Syiai Krala I.nrrc^:,, ,Vdrh(mric taut1, Lni!Fh r ot Sumlrcra r Lrn ud shea }ial and i) during listracl evaluate Malaria is one of the leading causes of death i 4ctious.disease caured b)) plasmodium , pp. 20, 0nsumer ietables. the developing workl today_ Malnria is an parasitcs. tn thts pap.r ie iadress a-iinenaticat noaet ':rh tuo latent petiodi in the non-con.etun host and wctor jopulations, in tri, io-in"oriticary assx :ae palenlial impact oJ peftonal protection, Iredtment, ,-i p^"itt" ,occination strateg) on the irtlsmi.rsion dynamic of naloria. Tha thtes]tolds and equilib;ia the nodel arc ctetermined. The fot aDdel is then andly:ed to determine criteriafor control ifa aiiis usea n conpute ^olaiia the lhreshold faccination and treatment rate necessary "pidenic comnmity_t ide control oJ dtaria. The for u.e oftJe model is the main prioriry in devetoping the'hialrh systen_biscd tnt"*"rtion". I.he anat),si, ihoilj that raccination and peftondl prctection can et'fectiyety decrease the (levelopment oJ nalatid in c communiry, whereas treat e t m(r/ increose the development of the epidenic uniess some c(,nditiow Ket-teotds: malaria, model ing, dyanic Iotroduction .Plasnodium :falciparum malaria is still a major cause of morlality and morbidity in the areas of the globe, *here around 200 mittion persoris are at constant risk of r n rect ron {Ma rsh. l oo8). A lthough there is optimism about developing a mala a vaccine since they are being produced and tested (Baflou er ar., 1999; Brown, rre;, ..r;", t"u"iry -ir"t"" "."t "i on personal pmtection and chemothempy. "ui"niry The.efforts ofreducing the sprcad of malaria through chemotherapy are now becoming mildll Ph modiun.fatcipoun k becoming ;sistanr to cheap anrJ avaitabre drugs such :::Tr.,!l :.i"":jh", zrs chloroqutne (trah et al.. 2001). Resistance to newer second and thidJine drugs continues tJ grow. Unfortunately many ofthese new drugs are not only expensive and have seriousiide effects, but most lvill eventuallY be rendered ineffectiv€ hv the malaria organism,s complex epidemiology and fircility for rapid mutation- Mass administration ofantimalarial diugs reduces p.""ut"'n"e oi.ar-r" inr""tion. Such inlerventions may not sustaioably reduce transmissi-on .t"at"gi"" 1G;."s ;; Sahzar, 1990: Garfield and Vermund, 1983). Although chemotherapy may have little eff€ct on the transmission of i\ intense {comes ana sahzar, iSOO; Collett and Lye, r9azl stuaies have T-^]1:.i1..,".:"i..i"iry cemonstrated thar e\,en a sub_optimal theEpeutic regimen reduces the duration of infectiousness sufficiently to teminate s€asonal malaria transmission during a large outbreak in an isolated Yanomami population (Frceman et al., t999). Although the use ofmalaria prophylaxis as w€ll as treatment contributes in reducir€ mortality, . a better control strates/ will be the use ofeffective malaria vaccines. Until immonity dcvelops though several years of endemic exposurc people living in malarious regions of the workt are at prolonged risk of death or severc malaria and an effeotivc vaccine could make an enormous contribution to reducing the impact ofthis devastating disease (Bush et al., 2001). Since a number ofvaccines have . glpical and-subtropic,3l Seminar lniernasionat datam Rangka Lustrum X Fakunas Kedokleran Hewan Unrversitas Syiah Kuata, Darussatam - Banda Aceh.4 dan 5 Oktober2Oi0 t1 been undergoing clinical trials, th€re is tbus an urgent need to qualitatively analyse their poteori impact using tools ofmathematical modelling. Mathematical models have been used to assess the impact of vaccination on malri epidemiolory (Chikaya et al., 2007) and a few anal,,tic studies of stage-specific malaria vaccines hr. been documented (Halloran and Struchiner, 1992). Economic impact of malaria vaccines borb r individual and population levels have been conoborated by clinical studies (Smith, 2006)- There hzrt also been seveml published mathematical models of malaria treatment, but these have mainly analysed the spread ofresistance (Bacae ret a1.,2005; Aneke,2002; Koella and Antia,2003). The aim of this study is to use mathematical modeling to gain some insiShts into th. bansmission dynamics of malaria in the population and to explore the impact of the aforemention€d intervention stoategies. Methodolos/ In our model based on monitoring the dynamics in human and mosquito population with rbe total population size at till1e t given is by r'r'h(r) and N.(t), respectively. The human population (Nh) i,s divided into four g.oups, susceptible human (Sh), infected human (lh), tseated humans (fJ. €xposd humans (Er), and vaccinated humans (lrJ. The mosquito popolation (Nm) is divided into tree grouPs, susceptible mosquito (Sm), infected mosquito ( ,I. ), and exposed mosquitoe (E ). Here, Nh(o = S(ri +fh(r)+th(l)+(r+yh0)+4,(/)isthetotalhumanpopulationand-|y'.(I)=3.(D+E(1)+1.(t)is the total mosquito population. Our model has the following variables and parameters defined in Table 1. Tible I .Model variable and ParameteN Variable and parameter Meaning t sho The number of susceptible human at time (1) The number of ;nfected human at time t s.(, The number ofsusceptible mosquiro a! tirne /,,(r) The numb€r ryr) rh(t Ih(r 4(.t\ vh@ of The number of The number of The ntrmber 6f The number of The nrmber of infected mosquito at time seated humans at time t t t expos€d humans at aime t infectioirs vaccinated humans at time exposed mosquitoes at time vaccinated homans attime t t t The rate ofmosquitoes susceptible The rare ofhuman susceptible '1n The rale human population via birth or immigrat'onThe natuml deatb mte ofthc homan. The natural death rate ofthe mosquito. The number death rate ofhuman from the infection. The number death rate ofmosquito iom the infection. Ihe Drobabiliry thal a bile fiom an infectrcus mo.quilo lead. Semjnar lnternasional dalam Rangka Lustrum X Fakultas KedoKeran Hewan Unjversitas Syiah Kuala, Darussalam - Banda Aceh. 4 dan 5 Oktober 2010 t8 C 'Ihe probabiliry that a bile from a susceptible mosquilo to a human with infeclious eametoc\'tes leads to infcction ofthe mosouito The bitins rate offemale mosquiroet. z Efficacy of pe.sonal prolection tial ria The fraction ofthe community employing ii (compliancc) at The rat€ in €d he ed fie r, class are lrealed "l The cfficac) orthe pre-eryhJoclak vaccine e1 The lndividuals rale recovery in the infectious vaccioated hurnans (vh) treated e, The lndividuals death rate in the inf€ctious vaccinated humans ()i,) treated The effectiveness ofth€ d.ue in inc.easing the recovery rate The elTectiveness ofthe druc The climate change due to the global wanning t/ is The efTectiv€ness ofthe drug as a factor reducing individual deaths due to n The €fficacy ofthe transmission blockins vaccinc subunii r) Th€ effeci ofrbe mal&iadmg in rcducing the infectiousness oftreated humans to is ! €R' Contained in real number Result and Discussiotr lndividu move from one class to the other as thei. slatus with respect to the diseas€ evolves. It is assumed that at any timc new recruits enter the human population at a rate,'1h via birth o. immigration. As it is assumed that there is no vertical transmission or irnmigration of infectious humans, this inflow does not enter the infcctious classes. Allhuman individuals are subject to a natural death, which occurs at a ratc 14. A proportion p € [0,1) of these individuals are successfully vaccinated;pll, enters the ,1, class and (l- p).lh enters th€ Shclass. Susceptible humans are infected by the malaria parasite at a ratej,(l) and move into the exposed class. This infection rate is assumed to depend on average number of mosquito bites and on the fiansmission probability normalizcd by total human population. Therefore the infection mte suscept;ble humansJ4(l) is given as of (l) 1.!1 1,.1t tzl]!]: ^^() It is assumed that personal protection is adopted in the community. The efJect of personal protection is modelled by the factor (l- ,z), whcre 0 < z < I is the efficacy of personal protection slrategr' adopled, and 0<6:l is the fraction of th€ communiql employing it, where i= I means I00% compliance and ,=0 represents no compliance at all- fiose who are successlirlly vaccinated may only be partially protected and hcnce will acquire inlection at a mt€ t(l-y) where l is the efficacy ofthe prc e$,throcltic vaccine \r'ith 1 6 [0,1]. lfy = 0, then the pre€rr,throcfic vaccine is useless, \rhile lor y = l, it is completely effective. lf 0 < y < 1, the vaccine is leaky. It is asslmed that the exposed human (susccptible and vaccinated human) take thc sam€ time zi,, to becomc infcctious. The susc€ptible and vaccinated hunans who are infected and have survived Seminar lnlernasional dalam Rangka Lustrum X Fakullas Kedoheran Hewan Universitas Syiah Kuala, Darussalam Banda Aceh,4 dan 5 Oktober20l0 t9 the latent period enter the infectious classes th and yb, respectively. Members ofthe /h class are eith€r treated at a rate K and €nter a class of treated infectives fh, or they can recover at a mte /h 10 the susceptible class (with no immunity), or they can die from the infection at a rate h. Individuals in the fh chss are also treated at a mte K, recover at a rate 4/h or die from the disease at a rate ( I h. 4) Theparameters4Zland4(where0<4S1)modeltheeffectoftheerlthrocyticvaccinein increasing recovery and reducing death from the infection. It is assumed that there is no recovery to the fh class. Members ofthe fh chss are assumed to recover at a rate 4 where >l is tbe param€ter that models the effectiv€ness ofthe drug in increasing the recovery rate, or they may die at a rate (l b wher€ 0 < r S I determines the effectiveness ofthe drug as a reduction factor in the diseas€ induced death ofthe infectious individual. For mosquito population, it is assumed that susceptible mosquitoes are re€ruited, at a rate l-(w). All mosquito€s are subject to a natural death (due to their finite life span), which occurs at a rate p,n. Mosquitoes in the &, class are infected by the malaria parasite at a ratel.(l), where v) (2) From thc expression off", the probability that a bite fiom a susceptible mosquito to a human with infectious gametoc],t€s leads to iufection ofthe mosquito. The pammeter smodels the efficacy of the transmission blocking vaccine subunit with r€l0,ll. It d€termines th€ effectiveness in reducing transmission from the vaccinated human to a susceptible mosquito. If F0, then transmission blocking vaccine is completely uscless, while for Fl the transmission blocking vaccine is completely eff€ctive in blocking the tmnsmission of pamsites from inGctious humans to mosquitoes- Th€ parameter g t, where 1e [0,1] rnodels the egrect of the malaria drug in reducing the infectiousness oftreated human to mosquitoes. If /f=0, then the drug does not reduce infectiousness ofthe treated human to mosquitoes, if /Fl, then the drug is completely effective in reducing the infectiousness of the aeated human. Susceptible mosquito€s which are infected move to the expos€d class. After a period t-, these expos€d mosquitoes become inf€ctious. It is assumed that the infectious mosquitoes experienc€ an excess death rat€ due to the presence ofpa.asite in their body at a rate - and that they do not rccover befo.c they die. The assumptions result in the following system of equations, sJ)=0 p)\ y;(r= pL" E"@ = t(l)s"()+/"\1,()+ejv,t)+ nr,Q))+ ot/,(t)- p,s\(t), l"(t{] /)y"(t\-(o + p")v,(tt, !-.,f,A:N.s,(")*(t ivt@rih@'d,, (3) L(l a\S,(t 'nF "'^ \k+\+q+hrtt\tj. f"(t r;Xt y\11(-rh)f- !,', -G+q\+t-€Daj r,O= k(.tto+v/) (n,+(t yV,+ !,)L(t). s;O=^.(,) ,O AE(r). r u\=I It,tst,Ea'',1, 1;(.t)= Y;(!t= t^(.t, = L(-r")5"(1 t.h et'") -(p Arv,(t), ^+d")I-(!). Differentialing the equations for th(/) and -c (1), in model system (l-),we got the following system of delay differential equations. Seminar lnternasional dalam Rangka Lustrum X Fakultas KedoKeran Hewan Unaversjbs Syiah Kuala, Darussalam - Banda Aceh,4 dan 5 Oktober2010 2.O . =n" it.ls,\t) +,"(t(o+^tt) + 0,\(t ) +,1,(tt) + o\(t) 4s,(t), ..: -p.\, ^Itlxl r)yttt) u,)yt(l). .. t, = J"\t )15t()+| " /)t/,(oJ r('-t,x,r,(, , '1)+0 llti( JE1t,qE\(t). ,: = f,lt..4)s,(t.rhtc !r. l*+\+a\+/,)rte, ..: =Llt-.,\t /)yN( tht:,'r lk+4\+| q)d^+ /^)yatt). :, he in to l- p) (4t +lt r:0."+ 4)\tt). r, r!=,\-(F) /_O /-s-(7), a- tt= LQ)s-tt) !_( -.-)s"( t-\F artt_E-. :- t= J"(-r-)s^Q tELt t lp-+a-)t^{t). :,.1= kltt()+r\(t)),(n, fte mtes ofchange ofthe total populations ofhumans and mosquitoes are N h() = a ^h - aruh(\+ (t -e;)y,(t) +(t i\c)\ hNb(). (5) d_rn(t) pnN_(!), ;O=^.(,) l. Reproductiv€ numbel3 ,f _g The reproductive number is defined as the number of secondary infections due to a single primary infection in a popubtion of susleptibles. Mathematically, ir is defiled as the dominant eigenvalue ofthe positive linear operator (van den Driessche and Watrnough, 2002). To determine the .eproductivc number ofmodel G-51, \ae first note that the model has a disease-free equilibrium state, denoted by ) ; r" -,s: d and is given as r,i. i:.1,". / ". \;. \ :. t;.,i, ( \ a,'" ;-4t p)'. Pt1 p.to-u\\ lotp.\ .o.o.r. (7) 4-.0. I ^-. u. p- ^!") Let the subscripts U, V, T stand for unvaccinated, vaccinated and treated, respectively. We can show that the expected number ofhumans who (not vaccinated) b€come infectious due to a;ingle infectious mosquiro during il,, entire period of infecriou,ness is {. 4n",= F,ctt 61 N; ". .[""'-""ar pp(1 bz)(t-r)phpe (p,, a"\(o'ht /"" (s) Th€ expe€ted number of vaccinated humans who becom€ infectious due to a single infectious mosquiro during irs entire period ofinlectiou.ness ir 4'rvr Tle = Ac(I - b:Xl r)$e '"'^ l.*n^'4, =FocQ b')(1 . I)ttop9 (tt,+a^\to,1Lr\ N; ' expected numbcr *" (e) of mosquitoes which become infectious due to an infectious human during hisArer period of infectiousness is 1"..,,, sie )tp'e 4' l,.tr-l,r /v{ -- .T eil ' 4 'dt p\\^P,ctt-bz\t p_^,(a t r, a,t p"1 (10) Ifthe human is (i) vaccinated, then, the expected number ofmosquitoes which tr€come infectious is ,i;,, .- p,c(.t a,-r sl . '-'- S "a' !!JJ-J-\,e { "^" ^ " -r!,)'F*tt N. p.,tt,(l t q.-oo t p.t '" (l l) (ii) treated, th€n, the number ofmosquitoes which become infectio$ duo to this human duiing his/her period of infectiousn€ss is Semina. lntemasional dalam Rangka Lustrum X Fakullas Kedokleran Hewan Universitas Syiah Kuata, Darussalam - Banda Aceh,4 dan 5 Oktober20lO 21 s,,,,, = F.r-ttzxt-d\" *,t1, f ""' ,-'Q'|t^'dudl (12) - bz\t - qrke ar !^i^ P.c(t /tr^,(k + \+ar+ !r\<zt, +(t- v)at+ ph) (iii) vaccinated and treated, then, tho number ofmosquitoes which becom€ iltfectious is 4^. -t,nt 6-,(l "i'"'-"'-dd, \, ''I f I'fe'' "' 'nr 4,'i. rll) /r.^^f ^c(t - bzyt - t)(t- 11)k Lr tt"L"k + etr, + lt 4)dh + !,Xtt, + (t v)a r+ &) 4ne 4" and ^-P-P,cze (14) I = n (t-bz)1 then the reproductive numbers from human to human or liom vector to vector between unvaccinated vaccinated, unvaccinated and troated and vaccinated and tr€ated populations are given as , o+ t1,(1 p) \o+ p,t\K+4+a\+ p,) r?' =.4*or4-oD = e phPl /)\1 E) q\ + (t - e)d, + /i' k(l axo+ p"(1 p')) (6+ tt)(k 4.=4',',14",,'.r=e (o+ + rt+,1,+ t|^ = af !x! + 15) phxtt,+(l r)dr+1t)' pk(t ttrllk+8\th+( - r(t - €\t - 4) 0t),1h+ 1t")(nri+l resp€ctively. The rep.oductive number for model sv".ut.n ( + p"Y,k + Qjl v)'zh+ ph) is 4n + qrt ar _ eph)\f,*tr+ltrrrr\a^+ to+ yh ) p' ,/,irr I /,{l-rr " p-rt r1a *.s.,,.tt s-rh) la;. -. ( (16) 'l ') The threshold quantity Rp;vq;vq is the number of secondary infectious cases produced by one primary case introduced into a population in which a proportion p has been vaccinated (Hethcote. 2000; Moghadas, 2004) aod the infectious population has been treated at a mte t. 2. Intervention strategies P€rsonal protection such as the use of protective clothing reduces exposure of human to mosquitoesr which then reduces the transmission of the parasites liom infectious humans to susceptible mosquitoes or from infectious mosquitoes to humans. Vaccination, in general attempts to lower the susceptibility of individuals against particular pathogen. In malaria infection, the three vaccine subunits: (i) reduce susceptibility of the human to infection; (ii) reduce the severity of the disease, thus, conv€.ting a serious life threatening disease to a minor ilhress (Miller et al., 1984); (iii) reduce transmission of the pamsites to mosquitoes. Trcahnent reduces the int'ectiousness of tbe individual by reducing parasite load of th€ treated human, and hence, transmission probabiliry is also reduc€d. These shategies have the effect ofreducing t'he number of infectives in a populalion. In this Seminar lntemasional da'am Rangk€ Lustrum X Fakultas Kedokteran Hewan Universitas Syieh Kuala, Darussalam - Banda Aceh. 4 dan 5 Oktober 2010 22 section, we evaluate the impac! oflhese intervention strategies by determining necessary and sufficient condilions that slow down the progression ofthe disease. 2.1. P€rlsonal protection We will denote the reproductive number without personal protection, treatment, vaccination and the reproductiv€ number with personal protection but without treatment vaccination by /0 and ,o = lqo respectively. 9 *o {t Vt Where y4 = rb + 0r, + !r, "= and and Wc have (r7) r"(l - bz)? - In order to analyse the effects of personal protection, we show under what circumstances r0 - & > 0 ana ed, p<0,$<0. The irs! and second inequalities ar€ all satisfied if 0 < bz < 1. we therefore conclude that prolcction always reduces the number of secondary infections. Due to climate €hange the valu€ ofr0 will increase, therefore we n€ed rnore pe.sonal protection. 2.2. Ef(€cts oftreatment only We first analyse the effects of treatm€nt in the absence of vaccination. The reproductive number when treatment is implemented as a conaol strategy in the population without vaccination is a- = a l"-.*a,1" . = **) #('. (r8) In order to analyse the effect of heatment, we need to determine urder what conditions :x- rxrr >o un6 941.g ( 1e) ak two inequalities are satisfred if (1 - 4) < l/4/?,r. This means that for treatment to b€nefit an individual as well as fie population at large (where there is no vaccination), the treatment induced r€duction factor for infectivity should be less than the factor by which treatment reduces the infectious period of a human. We note that if ? = 1, (that is if the heated humans immediately become uninfectious), then, treatment will always slow down the progression of the disease. Setting the troatment induced basic reproductive number in the unvaccinated population 4ur = I and solving for * gives the threshold treatment rate ofmalaria in that community, and is given as These ,- v,,v'.@, -1) - q) (20) "'- ,/-,/(I^\l lo to which exists when I < .{ < ffi . This means that malaria can be cont.olled iftreatment rate rt> rt. 2.3. Eff€cts ofvaccination only In the absence oftreatment, the discase reproductive number becomes i) =4 " "-& 4''^(hr j4lt P .1t :r1l \ otph v- 111-c1 | (21) ) is Seminar lnlernasional dalam Rangka Luslrum X Fakullas Kedokte.an Hewan Univercitas Syiah Kuala, Darussalam - Banda Aceh.4 dan 5 Oklober2010 21 a combined deSr€e of protecdr' 4uu is for coverage 2 with a vaccine that offers wares with average duration of protection I ' (l t( - /\(l - E)) L20l and induced immlnity that that for a perfect vacri!' in a population with average life exp€ctancy 1/A' The expression (2ll shows The exprcssion for that offer a complete degr€' = 1t - p;,t4 . tt also shows that a vaccine (1 = l) or transmissi:! of protection, that is either a pre-er,'throcytic subunit that is looyo ef{ective = l), with immunity that wanes at tie same rate *iri blocking subunit that is 100o% eflective (o: 0)' but only of{ers averag;eath rate (d: l4) is only as good as a vaccine that does not wear ptz)g" ftom the formu]€ 50% Iegree of protection (1 -1)(l -e) ytq4=Vz'inthis(jase:d' in the absence of heatnec for 4uv , we deduce that a measure of the vaccine impad f;or the model offers life long protection, 4"" (t : =(l- can be defined as see I22.231 ' . 4,) o o.&ptth\lt vt!1 ,, ,rr. ,tl---4Llt ) d t Ph\ 'lh (22) ,. t in tenni ifand oniy if O>O,and 4ouv >!?oifandonlyifO<0 This means that ifthe reproduction number ola ofreducing malaria transmission, a vaccine will have a positive impact *t.rttv ua"ccinatea Dopuladon is greater than the ionesponding reproduction nrtmber witlrour ru..ii"ri.". fftft" *o ieproductive iumber, are equal lhen lhe vaccine ha' no impact Note that 4ouv <4 Tofindthelevelofvaccinationthatisnecessaryfordiseaseemdication'w€solvetheequation p >p"(critical 4ur = t for p. It can be shown that for {uu < t, (, , ) o+t, P'= , trt - 'tl\'- !x" ) i,\' - vaccination coverage level) where (21) "-* p" €xists for Ro > 1 and (1 - f)(1 - €) < vh I//1. 2.4. Effects of treatment in the vaccinated population when treatment is Following the same method as above we see that th€ reproductive number implemented in the vaccinated population only is ,". It -.4. , /- -! rrl!q',.q{.r. can be shown that the conditions +irl g. d- r0 *d #<out" (24) satisfied if (l-t)<fr This are vaccinated, imnlies lhal for irealmenl lo be etleclive in a population where all susceptibles which treatment by factor t elrment indrccd reduclion factor for inlectiviD should be less than the reduces the infectious period ofa vaccinated human' Conclusions decrease the The analysis shows that vaccination and personal protectior can effectively the development of the development of malaria in a community' whercas teatment may increase Hewan Univelsitas Syiah Kuala Seminar lnternasional dalam Rangka Lustrum X Fakultas Kedokteran _ 4dan5Oktober2ol0 Aceh Daruss;bm Banda 24 ction, epidemic unless some conditions are met. 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