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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
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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
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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.
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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
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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.
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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
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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
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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
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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
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ction,
epidemic unless some conditions are met. The treatment
will only help the community if
the
ahempeutic drugs are such that they make the treated humans immediately uninfect;ous to mosquitoes.
n llct
ccine
egree
ssion
with
muia
ment
erms
'of
a
loui
!tion
ot is
this
t€d,
lent
the
the
References:
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Seminar lnternasional dalam Rangk€ Lustrum X Fakulas Kedokteran Hewan Universitas Syiah Kuata,
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201 0
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