Journal of Womens Health, Issues and Care ISSN: 2325-9795

All submissions of the EM system will be redirected to Online Manuscript Submission System. Authors are requested to submit articles directly to Online Manuscript Submission System of respective journal.

Research Article, J Womens Health Issues Care Vol: 4 Issue: 4

Abortion-Education is Needed: A Markov Decision Process Determination

Stephen EO Ogbonmwan1* and Paul E Ogbonmwan2
1Women & Children Division, Chelsea & Westminster Hospital NHS Foundation Trust Hospital, London
2Mathematics/Computer Department, Benson Idahosa University, PMB 1100, Benin City, Nigeria
Corresponding author : SEO Ogbonmwan
Women & Children Division, Chelsea & Westminster Hospital NHS Foundation Trust Hospital, London
E-mail: [email protected]
Received: June 09, 2015 Accepted: June 23, 2015 Published: June 26, 2015
Citation: Ogbonmwan SEO, Ogbonmwan PE (2015) Abortion-Education is Needed: A Markov Decision Process Determination. J Womens Health, Issues Care 4:4. doi:10.4172/2325-9795.1000190


Abortion-Education is Needed: A Markov Decision Process Determination

The aim of this study is to show the reasons why women procure abortion and use Markov decision process analysis and projections to show that ignorance and non-utilization of the available methods of contraception results in high rate of abortion and its complications; that formal and sex education can reduce abortion rate and the associated complications especially in the developing countries.



Induced abortion; Sub-fertility; Maternal mortality and morbidity; Sex education; Contraception


Abortion is the termination of an ongoing pregnancy. When it is carelessly or illegally induced, it can lead to sub-fertility, maternal morbidity and mortality especially in developing countries. In this paper we aim to show the reasons why women procure abortion and use Markov decision process analysis approach to calculate this effect and make appropriate projections.
Abortion is a very emotive subject from whatever angle one looks at it. Those who are against procurement of abortion are totally against it, so also those who are pro-abortion are completely pro abortion. There seems to be no middle ground although you hear some say they are anti abortion but pro-choice. This may not be possible as one cannot literally serve God and mammoth simultaneously.
Abortion is legal in the home countries of 74.3% of the world population and illegal in nearly seventy nations of the world (25.7% of World’s Population) [1] including Nigeria where abortion contributes about 20-40% of maternal death [2].
It may not be possible to be anti-abortion and be prochoice. There are those who are conscientious objector to procuring abortion and would not like to be associated with the process or facilitate the process either by counseling or assisting or completing legal documents in favor of the process of abortion in any way.
The assumptions to avoid abortion may be based on moral or religious beliefs.
In a paper in 2006, 98.9 % of all cases of abortion in England and Wales were shown to be due to social pleasurable reasons and not from incest or congenital malformation [2].
There are available, effective, long acting, reversible, reliable, and cheap methods of contraception [3-5]. Menstrual regulation in the presence of a positive pregnancy test is a smart clinical but confusing term for abortion because it is not a method of contraception.
Those countries where abortion is said to be legal; when data are critically analyzed, the category under which abortion is carried out, will be found to be mostly social as stated above.
Abortion has ruined many women all over the world as it contributed significantly to the increased maternal mortality in places like India [6,7] and Nigeria [8]. It has been observed that some young women are increasingly becoming sub-fertile in addition to suffering other morbidities and sometimes mortality after procuring abortion and this causes serious worries, concern and embarrassment to their parents and the society at large. This study has been set up to ascertain the reasons for inclination to procuring abortion and use Markov decision process analysis and projections to proffer possible solutions.
Although maternal mortality rate is highest in India in the whole world with Nigeria coming a close second; when one relates maternal mortality as a percentage of the total population, Nigeria becomes the nation with the highest maternal mortality rate in the world. This high maternal mortality rate may be as a result of inadequate investment in healthcare over the years to the detriment of the ordinary citizens in most developing countries.
A change in the law may have no effect on abortion rate and its associated morbidity and mortality as these operations are carried out in the back streets unregulated. We are aware of many laws that are ineffective especially in developing countries where laws are made for those who lack the means to bribe whenever they are caught in wrong doings.
We are proposing mass education especially of the young female folks. In a nation where a single doctor can terminate seventy pregnancies per day in a very small portion of a city like Lagos, one can only imagine how many such pregnancies are terminated daily in the whole of Lagos and even more so in the whole of Nigeria. The figure will be staggering.
In this paper, we aim to utilize Markov models to show the reasons for induced abortion and propose that formal and sex education can reduce the cases of induced abortion and its attendant complications.


Many models of Markov chains have been formulated and applied to many areas of human endeavor [9,10] Applications of Markov models have been used to solve some health problems as Markov Chains were used by some to model the spread of epidemic diseases. This can be seen in the work of Gani 2003 [11].
Random allocation model came up normally in sharing of needles among intravenous drug users (IVDU), and was developed to model the growth of ineffective IVDUS [12-16].
It is assumed that; ‘I’, hypodermic needles are used by IVDU who could be infected with a virus, such as hepatitis or HIV. The needles, which are shared among ‘n’ susceptible IVDU, infect 1 ≤ s ≥ min (i, n) of them.
In another paper attention was paid to Manpower Planning, the area which is generally referred to as population mobility. Grinod and Valliant and Milkovich also did some work on manpower planning using similar principles [17,18].

Model Development and Results

A large number of sub-fertile individuals were interviewed to determine if the cause of their sub-fertility was related to a prior history of illegal abortion.
We employed the long time steady state probabilities using the Markov Chain process to reach the long run effect of this problem on the society. Markov Chain process (MCP) named after Andrey Markov provides a mathematical frame work for modeling decisionmaking in situations where outcomes are partially random and partially under the control of the decision maker.
Strictly speaking a MCP is a discreet stochastic control process characterized by a set of states, in each state there are several actions from which decision Maker must choose. For a state ‘S’ an action ‘a’, a state transition function Pa(s) determines the transition probabilities to the next state. The state transition of a MDP posses the Markov property: given the state of the MDP at time‘t’, time t+1 are independent of all previous state of action. Markov Decision Process is an extension of Markov Chains; the difference is the addition of action (allowing a choice) and rewards (giving motivation). If there was only one action or, if the action to take were fixed for each state a Markov Decision Process would reduce to a Markov Chain process.
The study of the long run influence of peers or lack of knowledge of methods of contraception on an individual’s inclination to abortion was carried out in three clinics in Nigeria. Two hundred females of 14 - 42 years old were interviewed on why they procured abortion along the following line of questioning.
1. Peer effect.
2. Fear of being a single mother
3. Lack of knowledge of the fact that sexual intercourse could leads to pregnancy.
4. Lack of knowledge of available methods of contraception.
Three of the above factors led to higher level of abortions shown in the Figures 1:a-c would be used for the model.
Figure 1a: Age Range.
Figure 1b: Educational Attainment of Women .
Figure 1c: Reasons for abortion.
We assume the followings for our computation of the long time effect of abortion on the society.
Assumption of the model
(a) The stationarity property of Markov Chain holds.
(b) Time period of study is one calendar year.
The model: Let ‘S’ respondent be due for abortion at time (i+1) and let the number of respondent in respective cadre add up to ‘n’. It follows at time (i+1), that S respondents have had an abortion, if at time i deadline, S respondent were found to have procured abortion and the one additional respondent that came in late was already among the counted abortion procuring respondent and the probability of those aborting or (s-1) respondent with probability and the additional name that came in was among the aborting respondent. Here we use representation similar in spirit to Factored MDP’S, but focusing on the state space partitions involved (Boutniler et al, 1999).
Let Ps(i,n)=P(S respondent at time i/n were initially in the given cadre)
We have the following recursive equation for the probability.
Ps(i+1,n)=Ps(i,n)s/n+Ps-1(i,n) (1) With S=1,2,… min(i+1,n) and in general the recursive equation for the Markov model is given by Ps(i+1,n) = Ps(i+n)hs+ Ps-1(i,n)gs-1 with hs + ge = 1, since hs = s/n, gs = (1-s/h) and gs-1 = (2)
The various values of the probability hs have also been considered.
Rutherford (1954) studied the case where hs = P + Cs with 0 < C < (1-P)/n in which hs may now be a single linear function of S and P
Recall (2)
Ps(i+1,n) = Ps(i+n)hs+ Ps-1(i,n)gs-1 (3)
Let hs = P + CS
=> gs = 1 - hs = 1 - P – CS
gs = 1 - P – CS
gs - 1 = 1 - P – C(S – 1)
= q – C(S - 1) (4)
Where 1 – P = q
Substituting (4) and (3) in (2) we have
Ps(i+1,n) = Ps(i,n) (P + CS) + Ps-1(i,n) [q – C (S - 1)] (5)
Deriving the model transition matrix using PGF
To deal with (5), we use the probability generating function (pgf) (Rinu) of the probabilities Ps (i, u) i.e.
We rewrite 5 in the form of
which reduces to the form
Substituting (6) and (7) into (8), we have
Is further reduced to the form
Thus to solve (12), let’s consider the first few Pgfs for S ≤ Min (i, n).
This is so because when i = 1,2 and 3, and considering the summation
in (6) where S ≤ Min (i, n) and by probability S ≤ n , then n ≥ 3
We now seek a recursion equation for the coefficients of the various powers of U
Let us write for
We now substitute (11) into (10) to obtain
(12) Putting the coefficient of U in (12) in matrix form, we have,
Computation of the model algorithm:
In the system (13) the transpose of the square matrix is a transpose matrix which satisfies the constant unit sum of every row to be n probabilities. This transition matrix in (13) also satisfies the model assumptions stated earlier in this section. We now apply the model in the following section. Note that if a Markov Chain with transition matrix P is initiated in state Si, then after one step it is in state Sj the overall transition can be worked out as follows. Let the probability that the state is in Sk after one step is Pjk Summing over all possible
steps we obtained (14)
This calculation shows that the probability is equal to the ijth element of the matrix P2 i.e. while this is the same result got from the diagonal of a square matrix as expounded in (13)
Using the model
The study carried out in three Clinics in Nigeria to determine the reasons for and the long run effect of abortion on the society and the following were re-coded. Here ‘a’ stands for ‘Influence of peer group’, b stands for fear of bringing up fatherless children while c stands for ignorance of methods of contraception.
  A b C
 Clinic 1 .1 .2 .3
Clinic 2 .4 .5 .6
Clinic 3 .7 .8 .0
An analysis of this finding using the Markov Decision process method yield the steady state probability below with a, b and c as given above.
So at the steady state position, we have that 7.301% females interviewed were influenced by their peer group while 8.26% do not know that there are reliable and available methods of contraception. Fear of bringing fatherless plays almost a zero role.


In this paper we have deduced that the long term effect of subfertility, psychological trauma and other morbidities associated with abortion in the female population in our society result from ignorance and non-utilization of effective methods of contraception and this can be reduced with formal and sex education rather than making more laws.
Using the Markov decision process approach to calculate this effect and making appropriate projections, we observed that 15.56% i.e. (8.26 + 7.30) of the population are either unaware of reliable methods of contraception or procure abortion due to peer group pressure effect. This is highly significant. A reduction is suggested by way of purposeful sex education and teaching about the availability and effectiveness of methods of contraception.
Many articles in literature support the role of education in reducing maternal morbidity and mortality. The commonest associations with maternal morbidity and mortality are lack of education, low literacy rate and high poverty [19,20]. Evidence is available about the utility of web-based health education for students in low resource settings, which showed modest results, were due to inadequate exposure to educational materials and this was reversed with intervention which focused on teen’s purposeful searching for health information when they are in personal circumstances of unmet health needs. Other studies have shown that abortion education is acceptable and valued by medical students and should be integrated into the curricula of all medical schools [21,22].
In the Norwegian study, they showed conclusively that in Norwegian women, low education was associated with lower frequency of child delivery but higher frequency of induced abortion. In Pakistani women, child delivery was not related to education, but induced abortion tended to be more frequent in those with a university education. However university education is not synonymous with sex education and knowledge of contraception [23].
Abortion education has been shown to be deficient in Nurse Practitioner, Physician Assistant and Certified Nurse Midwifery programs in the United States. As integral components of women’s health care, abortion, pregnancy options, counseling and family planning merit incorporation into routine didactic and clinical education [24]. Even more importantly, abortion education and knowledge of effective methods of contraception needs to be more available to all especially the female population in the developing countries where there is a very high maternal mortality rate.
Abortion education is limited in US medical schools. As an integral part of women’s reproductive health services, abortion education deserves a place in the curricula of all medical schools anywhere in the world so that physicians can be prepared to answer pertinent questions especially about available methods of effective, reversible and long acting methods of contraception [25].
There is low literacy rate generally in developing countries and those who are literate may be uneducated with respect to available and effective methods of contraception. The attitude of most abortionist and those women who seek induced abortion smacks of lack of general sex education. The greed for money by the backstreet abortionists, the lack of knowledge of the numerous available methods of reliable, effective, long term, cheap and reversible methods of contraception all play a role.
We propose the need to educate our teaming masses that there are effective, cheap, and available, long acting and reversible methods of contraception as advances in the area of contraception in the last two decades has been overwhelming. In the 21st century, no one needs to procure an abortion as most methods of contraception have over 99.5% effectiveness if used correctly. Using an effective method of contraception correctly can only come by way of sex education.
There are oral contraceptive pills, sub-dermal implants, injectable or depot preparations, intra-uterine devices, fem-shield for intravaginal use, condoms to wear on the phallus and above all abstinence, which is the safest of all methods of preventing pregnancy and the associated sexually transmissible infections.


We need an effective sex educational system to teach our female population that pregnancy is preventable and one need not procure abortion as effective methods of preventing abortions abound.
It is reasonable to assume that we do not need more legislations but rather education of the at risk population
In some countries there are adequate facilities for caring for fatherless children and single mothers, some babies are adopted and in others, fatherless children find their way into children’s homes where volunteers or the state cares for them; unfortunately such care facilities are not available in developing countries.
This study can be repeated on a larger scale to validate these findings and projections.


We hereby acknowledge with thanks the help of the clinic staff and junior trainees who carried out the interviews and the women who took part in this research study.


Track Your Manuscript

Media Partners