Abstract-Child mortality reflects a country’s level of socio-economic development and quality of life. In this paper, Markov chain is used to predict the probability of rural and urban child mortality rate reduction in Ghana

1. International Journal of Scientific& Technology Research,VOL2,ISSUE 11
IJSTR©2013
Using Markov Chain to Predict the Probability of
Rural and Urban Child Mortality Rates Reduction
in Ghana
Patience Pokuaa Gambrah, Yvonne Adzadu
Abstract-Child mortality reflects a country’s levelof socio-economic development and quality of life. In this paper, Markov chain is used to predict the
probability of ruraland urban child mortality rate reduction in Ghana. The probabilities of w hether the rural and urban mortality rates w illincrease was
obtained fromthe current data w here the probability of rates increasing is less than 20%. After applying Markov, it w as realized that the current rates are
not likely to change, that is the reduction rates w illremain the same if proactive measures are not put in place to reduce the CMR drastically. It is
therefore recommended to the government to put in more effort in ensuring that the rates go dow n. This is because if w e depend on the current rates w e
w illnot be able to achieve the Millennium Development Goal (MDG) 4 by 2015.
Keyword- child mortality rate, Ghana mortality rates, Markov chain, mortality rate prediction, ruralmortality, urban mortality
——————————  ——————————
1 INTRODUCTION
HILD mortality,alsoknown as under-5mortality,
refers tothedeath ofinfants and children underthe
age of five.In 2011,6.9 millionchildren underfive
died, down from 7.6 millionin 2010, 8.1 million in 2009, and
12.4 million in 1990.Abouthalfofchild deaths occurin
Sub-SaharanAfrica.Reduction ofchild mortalityis the
fourth oftheUnited Nations’MillenniumDevelopment
Goals.
Child MortalityRateis thehighestin low-incomecountries,
such as most countries in Sub-SaharanAfrica.Achild's
death is emotionallyand physically painful for theparents
and thecountryat large.Manydeaths in the developing
countries gounnoticed sincemanypoor families donot see
theneed toregister theirbabies in thegovernment registry
Thefourth MillenniumDevelopment Goal(MDG 4) aims to
reducethe1990 mortalityrateamongunder-fivechildren
by twothirds.Child mortality is alsocloselylinked toMDG
5- toimprovematernal health.Sincemorethan onethird of
all child deathsoccurwithinthefirst month oflife,
providingskilled caretomothers duringpregnancy,as well
as duringand afterbirth,greatlycontributestochild
survival.MillenniumDevelopmentGoalsadopted bythe
United Nations in 2000aim todecreasechild deaths
worldwideby2015.
1.1 Background of the study
Despitepopulation growth,thenumber ofdeathsin
children under fiveworldwidedeclined from nearly 12
million in 1990to6.9 million in 2011.Theproportionof
under-fivedeaths that occurwithin thefirstmonthoflife
(theneonatalperiod)has increased from36%in 1990to
about 43% in 2011.Therateofdeclinein under five
mortalityhas accelerated from 1.8% a yearover1990-2000
to3.2% a year over 2000-2011.Thehighestlevelsofunder-
fivemortality continuetobefound in Sub-SaharanAfrica,
where1 in 9 childrendiebeforetheageoffive. Under-five
deaths areincreasinglyconcentrated in Sub-SaharanAfrica
and South Asia,whiletheshareoftherest oftheworld
dropped from 31% in 1990 to17%in
2011.
But many morelivescan besaved.Whiletheglobal
numberofunder-fivedeathshas dropped since1990,this
still translates intonearly 19,000 childrendyingeveryday
in 2011.Almosttwothirds ofall under-fivedeathsarethe
result ofinfectiousdiseasesand conditions,suchas
pneumonia,diarrhoea,malaria,measles and AIDS – deaths
which could havebeen prevented.
C
————————————————
 Patience Pokuaa Gambrah is currently an Asst. Lecturer at the Dept. of
Statistics, Tamale Polytechnic, Tamale. Ghana E-mail:
patiencegambrah@gmail.com
 Yvonne Adzadu(Mrs.) is currently pursuing Masters Degree Programin
Industrial Finance And Investment in Kwame NkrumahUniversityOf
Science And Technology,Kumasi, Ghana. E-mail: yadzadu@hotmail.com

2. International Journal of Scientific& Technology Research,VOL2,ISSUE 11
IJSTR©2013
Figure 1; world underfive mortalityrate, 1990-2011,by
UNICEF region
From theabovefigure,all regionshaveexperienced
marked declinein under-fivemortalityratesince1990.The
highest ratesofunder-fivemortalitycontinuetobe in sub-
Saharan Africa,where1 child in 9 dies beforeagefive.
1.2 Child mortality in Ghana
Accordingto [8],Ghana howeverhasmadephenomenal
progress overtheyears in immunization coverage,from a
national coverageoffour per cent in 1985 to90 per centin
2012.
Furthermore,povertyusually limitsaccess tohealthcare
and restrictsappropriateand balanced diets.Inequities in
exposureand resistanceadd up toinequities in coverageof
availablepreventiveinterventions,accesstoan appropriate
health provider,and care,makingpoor children more
likely tobecomesickthan thebetter-offchildren [7].
Accordingto [9],mostchilddeaths (and70% in developing
countries)which includeGhana.
TheMortalityrate;under-5 (per 1;000)in Ghanawas last
reported at74.40in 2010,accordingtoa WorldBankreport
published in 2012.Under-fivemortalityrateis the
probabilityper 1,000 thata newborn baby willdiebefore
reachingagefive,if subjecttocurrentage-specific mortality
rates.
Below is a historical data chartfor Mortality rate;under-5
(per 1;000)in Ghana.
Figure 2; under five mortalityrate in Ghana, 2002-2010
Ghana is expected toreduceits current child mortalityrate
toabout 40 per 1000 lifebirth in 2015 weshould reach 40.
But our averageannual reduction rateis about2.5%
Table 1; infantand child mortalityrate in Ghana
1.3 Objective
Theobjectiveofthis studyis toadopt Markovmodel for the
prediction oftheprobabilitiesofunder-fivechildmortality
statusin rural and urbanannual mortality ratein Ghana.It
is alsototest whether wecan depend on currentratestobe
ableto achievetheMillenniumDevelopment Goal (MDG)4
by 2015.
2 LITERATURE REVIEW

3. International Journal of Scientific& Technology Research,VOL2,ISSUE 11
IJSTR©2013
[3] developed A"Markov cycletree" cohortmodel wasin
Excel with Visual Basic tocomparethenumberofdeaths
from pneumonia in children aged 1 to59 monthsexpected
under threescenarios:
1. No curativeservices available,
2. Curativeservices provided bya highly-skilled but
intermittentmobileclinic,and
3. Curativeservices provided bya low-skilled
communityhealthpost.
Parametervalueswereinformed byliteratureandexpert
interviews.Probabilisticsensitivityanalyseswere
conducted for several plausiblescenarios.
In [4] model,reductionin child mortalitymay eitherriseor
lower fertility.When thelevel ofchild mortality is high,
reductionin it is likely toraiseboth fertility and survival
enhancingexpenditures on children,becauseit lowersthe
priceofa survivingchild.
[1] Madean attempttoinvestigatetheinteraction between
child mortality and povertyin Pakistan.Theanalysis was
relied on thePakistan Socio-economicSurveyconducted
duringApril toJuly 1999.Thestudyapplied multiple
classificationanalysis that requires dependentvariablenot
tobebadly skewed.Thestudyfound thatmother’s work
participation,household crowding,unadjusted housing
conditions and malnutrition havesignificant negative
impact on thelivelihood ofa child.
A decision analytic model wasdeveloped accordingtothe
stages recommended by [2] byspecifyingthedecision
problem and boundaries ofanalysis,structuringthe
decision model,identifyingappropriateevidence,and
dealingwithuncertainty and heterogeneity.
[6] Did a study who’s analysiswas based on microdata
from the2005 Demographic and healthSurvey.Bayesian
Semi Parametric Probit Model for discretetimesurvival
data and Markov-Chain MonteCarlomethods (MCMC),
revealed several variables,includingthe ageofthemother
and thebreastfeedingduration whoseeffects exhibited
distinctage-dependencies.In thecaseofbreastfeeding,age
dependency wasintimatelylinked with thereasons for
stoppingbreastfeeding
3 METHODOLOGY
Markov Chain Definition
A stochastic process {Xn }is called a Markov chain if
Pr{Xn+1 = j | X0 = k0, . . . , Xn-1 = kn-1, Xn = i }
= Pr{Xn+1 = j | Xn = i }  transitionprobabilities
for every i, j, k0, . . . , kn-1 and for every n.
Discretetimemeans nN = { 0, 1,2, . . . }.
Thefuturebehaviorofthesystemdepends onlyon the
currentstateiand not on any ofthepreviousstates.
Pr{Xn+1 = j | Xn = i } = Pr{X1 = j |X0 = i } for all n
(They don’t changeover time)
Wewill only considerstationary Markovchains.
Theone-step transition matrix for a Markovchain
with states S= { 0,1, 2 } is
P=[
P00 P01 P02
P10 P11 P12
P20 P21 P22
]
wherepij = Pr{X1 = j | X0 = i }
3.1 Data presentation and analysis
Thetablebelow was extractedfrom table 1
Area 1988 1993 1998 2003 2008
Rural 162.5 149.2 122.0 118.0 90.0
Urban 131.1 89.9 76.8 93.0 75.0
Assumptions fromtheabovetable
Theprobability thattheruralmortality ratewill increaseis
0 as over theyearstherehas beena decreasein therates.
Theprobability thattheurbanmortalityratewill riseis
about 0.2 sinceit was oneout ofthefiveyears thatwent
up(that was2003)
It could thereforebeassumed that theprobabilitythatboth
rates will increasein a particular yearis verysmall.
Thereforethefollowing area (Rural and urban)prediction
can beused;

4. International Journal of Scientific& Technology Research,VOL2,ISSUE 11
IJSTR©2013
• Two areas (rural and urban) areused todetermine
national child mortality rate.
• When bothare used in a year,thereis a 10%
chancethat onewill goup and a 5% chancethat
both willgoup.
• If only onearea will godown at thebeginningof
theyear,thereis a 10% chancethatit will goup by
theend of theyear.
• If neither will godown at thebeginningofthe
year,measures areput in placetolet it godown
that is moreeffort areput into ensuringthat it go
down by theend oftheyear.
• Areas thatgoup duringthe year aremonitored to
makesureit is minimizeby thecloseoftheyear.
• Thesystem is observed afterthe measureshave
been put in placetoensurethatit does not riseby
theend of theyear.
States for rural and urbanarea
Table2; states forruraland urban areas
Index State Statedefinitions
0 s = (0) Non went up. The
year started with
all areas having
reduced mortality
rateas compared
with theprevious
year.
1 s = (1) One went up. The
year started with
one area goingup.
2 s = (2) Both areas went
down.
Events and Probabilities for rural and urbanareas
Table 3; probabilities for each state
Index Current
state
Events Probability Next
state
0 s0 = (0) Neither
areas went
up
0.85 s' = (0)
One area
went up
0.10 s' = (1)
Both areas
went up
0.05 s' = (2)
1 s1 = (1) Remaining
area does
not go up
and the
other went
down
0.9 s' = (0)
Remaining
area goes
up and the
other area
goes down.
0.1 s' = (1)
2 S2 = (2) Both areas
went down
when
measures
areput in
placeto
ensurethey
all go
down.
1 s' = (0)
State-TransitionMatrixand Network for CMR in Ghana
Theevents associatedwitha Markov chaincan be
describedby the m m matrix:P = (pij).
For rural and urbanareas,wehave:P=[
0.85 0.10 0.05
0.9 0.1 0
1 0 0
]
State-TransitionNetwork
• Nodefor each state

5. International Journal of Scientific& Technology Research,VOL2,ISSUE 11
IJSTR©2013
• Arc from node i tonode j if pij > 0.
Multi-step (n-step)Transitions
TheP matrixis for onestep: nton + 1.
states: s0 = 0 (non went up), s1 = 1 (one went up) s2=2 (both
went up)
Transition matrix:P=[
0.85 0.10 0.05
0.9 0.1 0
1 0 0
]
Interpretation: p01 = 0.1, is conditionalprobabilityof
mortalityrate in onearea goingup next yeargiven that
non went up thisyear.
Two-step Transition Probabilities
Let pij beprobabilityofgoingfrom i toj in twotransitions.
In matrix form,P(2) = P  P, sofor IRS examplewehave
P2=[
0.85 0.10 0.05
0.9 0.1 0
1 0 0
]×[
0.85 0.10 0.05
0.9 0.1 0
1 0 0
]=
[
0.8625 0.095 0.0425
0.855 0.1 0.045
0.85 0.1 0.05
]
Theresultantmatrixindicates,for example,thatthe
probabilityofrates notincreasing 2 years fromnow given
that thecurrentyear therewas no increaseis p00 = 0.8625
n-Step Transition Matrix for CMR
Table 4; results of n-step transition matrix
Time,n Transition matrix, P(n)
1
[
0.85 0.10 0.05
0.9 0.1 0
1 0 0
]
2
[
0.8625 0.095 0.0425
0.855 0.1 0.045
0.85 0.1 0.05
]
3
[
0.861125 0.09575 0.043125
0.86175 0.0955 0.04275
0.8625 0.095 0.0425
]
4
[
0.861256 0.095688 0.043056
0.861188 0.095725 0.043088
0.861125 0.09575 0.043125
]
5
[
0.861243 0.095694 0.043063
0.861249 0.095691 0.043059
0.861256 0.095688 0.043056
]
4 INTERPRETATION OF RESULTS AND
CONCLUSION
For P(2) that is in twoyears timewhen wearetoreach the
MDG as countrythisis the probabilities wetoexpect given
thecurrent child mortalityrates.
(0.1)
2
0
1
(1)
(0.85)
(0.1)(0.05)
(0.1)
(0.9)
2
0
1
(0.85)
(0.8625)
(0.095)(0.0425)
(0.1)
(0.855)
(0.045)
(0.1)
(0.0.05)

6. International Journal of Scientific& Technology Research,VOL2,ISSUE 11
IJSTR©2013
Table5: analysis of results
Index Current
state
Events Probability Next
state
0 s0 = (0) Neither
areas went
up
0.8625 s' = (0)
One area
went up
0.095 s' = (1)
Both areas
went up
0.0425 s' = (2)
1 s1 = (1) Remaining
area does
not go up
and the
other went
down
0.855 s' = (0)
Remaining
area goes
up and the
other area
goes down.
0.1 s' = (1)
Remaining
area goes
up and the
other area
goes up.
0.045 s' = (2)
2 S2 = (2) Both areas
went down
when
measures
areput in
placeto
ensurethey
all go
down.
0.85 s' = (0)
One area
will goup
0.1 s' = (1)
Both areas
will goup
0.05 s' = (2)
From theaboveresultsit could besaid that Ghana is still
not safesinceit still havethepotential ofchild mortality
rateincreasingin years ahead.That is for exampleifwe
take2 years (P(2))tocomewhich is theMDG westill have
86%(P00)chanceofnot increasingthecurrentrates.Wehave
a 10% chanceofonearea goingup. This means wearestill
not certain or 100% surewhethertherates will bereduced
or not.Even if our rates will not increaseit means as for
reachingthetargetis out ofthe question.Sincewearestill
battlingwith thereduction rates.Thereis thereforethe
need for governments and stakeholders toputin more
efforts in makingsurethat weareabletoget 100% certainty
that our mortalityrateswill not increasein theyearsahead
and then battlewithhow toreducethemortalityrates
drasticallyin ordertoreach our targetofMillennium
Development Goalson child mortality.
5 RECOMMENDATIONS
Thegovernmentneeds toeducatecitizen moreon how to
curb thismortalitybecausemost ofthecausesofdeath in
under-fivearepreventable.Soif governments are
committed in educatingtheircitizens on thepreventive
measurestotakeor torushchildren tohospital for early
treatment thiscould help reducetheratedrastically.They
should alsoseetoit thatthelongqueues for children
under-fiveat thehospitalsis alsoreducesincethisis what
prevents most peoplefromsendingtheirchildrento
hospitals.
Alsofamilies especiallymothers should beeducated on the
effects of under-fivemortalityon thefamily,community
and country atlarge.They should treatunder-fivedeath
cases as criminal cases ifthefault is fromtheparent,to
deter othersfrom delayingwhentheyseethattheir
children areindisposed.Again thereshouldbefreehealth
carefor all childrenunder-fiveas mostparentscannot
afford thebasic health carefor their wards.
Citizens should bemadetoknow thatthey arethosewho
arenot helpingin the MDG.When you seeother countries
recording90% reductionrateand Ghanarecordingless
than 50% then citizensshould bealarmed and thereforesee
toit that theirbehavioral patterns will helps in the
reduction.
Researchers should research moreintothe reasons why
Ghana is not reachingabout50%reduction rateand find
solutionstotheproblem for us tousetheresearch findings.
Children under-fivearedyingevery year,downfrom over
12 million in 1990.Most ofthesechildren aredyingin
developingcountries frompreventablecausesfor which
thereareknown andcost-effectiveinterventions.Unless

7. International Journal of Scientific& Technology Research,VOL2,ISSUE 11
IJSTR©2013
efforts areincreased therewill belittlehopeofavertingthe
additional 5.4 millionchild deaths per year,or a reduction
of two-thirds,needed toachieveMillenniumDevelopment
Goal (MDG) 4 by 2015.
REFERENCE
[1] Ali, S. “Povertyand Child Mortalityin Pakistan,
MicroImpact ofMacroeconomicAdjustment
Policies (MIMAP)”, TechnicalPaperSeriesNo.6.
Jan 2001.
[2] Briggs,A.H., Claxton,K.,Sculpher,M.J: “Decision
modelling forhealth economic evaluation”.Oxford:
Oxford UniversityPress; 17 Aug2006
[3] CatherinePitt,Bayard Roberts and Francesco
Checchi.“Treatingchildhood pneumonia in hard-
to-reach areas:Amodel-based comparisonof
mobileclinics and community-based care”.
http://www.biomedcentral.com/1472-
6963/12/9/prepub Jan 10,2012
[4] Cingo,A. “Fertility Decisions WhenInfant
Survivalis Endogenous”,Journal of Population
Economics; 11:21-28.(1998).
[5] Ghana Health Services(2010). “Facts And Figures”;
TheHealth Sector In Ghana
[6] Jimma,TesfayeAbera: “ModelingMortalityof
Children UnderFivein EthiopiaUsingBayesian
Approach”(2011).Availableat SSRN:
http://ssrn.com/abstract=1772616or
http://dx.doi.org/10.2139/ssrn.1772616
[7] VictoraC.G., WagstaffA.,SchellenbergJ.A.,
Gwatkin D.,Claeson M., Habicht J.-P.“Applying
an Equity Lens toChild Health Mortality:Moreof
theSameIs Not Enough”.Lancet.2003;362:233–41..
[PubMed]
[8] World Health Organization. WorldHealth Statistics
2010.World HealthOrganization.2010,Geneva.
[9] UNICEF, “CommittingtoChild Survival:A
PromiseRenewed – Progress Report2012”,New
York,2012.