Encyclopedia of Mathematics & Society
Pregnancy
CATEGORY: Medicine and Health.
FIELDS OF STUDY: Fields of Study: Algebra; Data Analysis and Probability.
SUMMARY: Various mathematical models help describe issues related to conception, diseases associated
with pregnancy, and population dynamics.
Much of the conclusions drawn in medicine, in particular in obstetrics and gynecology, are often based on
heuristics, limited observations, and sometimes even biased data. Mathematicians and statisticians have
recently attempted to develop general theoretical models that can be adapted to specific situations in
order to facilitate the understanding of various aspects of human pregnancy. Specifically, more recent
studies have been conducted regarding conception time, disease prediction related to pregnancy, and the
effect of pregnancy on population growth.
MODELING THE MOST EFFICIENT TIME TO CONCEIVE
One of the most fundamental and important research topics in the study of human pregnancy is the socalled time-to-pregnancy (TTP). TTP can be defined scientifically as the number of menstrual cycles it
takes a couple engaging in regular sexual intercourse with no contraception usage to conceive a child.
Fittingly, statisticians attempt to generate as much data as possible from various couples regarding their
personal TTP experiences. The data are collected in a way that is as unbiased as possible—it is intended
to accurately represent couples in the general population attempting to conceive a child. From the data,
both qualitative and quantitative statistical methods are implemented in order to ascertain the most
efficient method to achieve conception.
For example, some social trends increase the age at which a woman attempts to become pregnant.
When this situation arises, women are often concerned about achieving conception before the onset of
infertility, which proceeds menopause. In fact, couples that are unsuccessful in conceiving within one year
are clinically classified as infertile. When this condition occurs, medical doctors often recommend that the
couple engage in assisted reproductive therapy (ART). However, ART can be very expensive and often
increases the risk of adverse outcomes for the offspring, including various birth defects. Therefore,
statistical models have been developed that pose an alternative to ART. These models are developed
using Bayesian decision theory, named for Thomas Bayes, and search for optimal approaches for a
couple to time intercourse in order to achieve conception naturally, without the potentially
disadvantageous ART. These models quantitatively incorporate various biological aspects, including
menstrual cycles and basal body temperature, as well as the monitoring of electrolytes—among other
phenomena—in order to be as efficient as possible.
PREDICTING DISEASES ASSOCIATED WITH PREGNANCY
Medical evidence supports the notion that women often repeat reproductive outcomes. In particular,
women with a history of bearing children with adverse outcomes often have up to a two-fold increase in
subsequent risk. Therefore, researchers in the mathematical and statistical sciences realized the
necessity for statistical analyses that address this issue. In fact, statistical research has been conducted
in order to promote a consistent strategy that assesses the risks each woman may face in a subsequent
pregnancy. The goal is for these types of models to become increasingly more accurate, as they
incorporate statistical data regarding the recent reproductive history of the woman, among other biological
factors, which were not fully taken into account in previous studies.
Mathematical epidemiology is used to predict conditions like pre-eclampsia during pregnancy.
Mathematical epidemiology (the study of the incidence, distribution, and control of diseases in a
population) attempts to better comprehend, diagnose, and predict various diseases incorporated with
pregnancy, and this field is ever-expanding. By designing and implementing various statistical
approaches and mathematical models to better predict realistic outcomes, mathematicians and
statisticians have studied congenital defects and growth restrictions, as well as preterm delivery, preeclampsia, and eclampsia.
For example, pre-eclampsia is a pregnancy condition in which high blood pressure and high levels of
protein in urine develop toward the end of the second trimester or in the third trimester of pregnancy. The
symptoms of this condition may include excessive weight gain, swelling, headaches, and vision loss. In
some cases this condition can be fatal to the expectant mother or the child. The exact causes of preeclampsia are unknown at the beginning of the twenty-first century, and the only cure for the disease is
the delivery of the child. Therefore, it is apparent that determining which women are prone to develop preeclampsia is an exceedingly important area of research.
Empirical evidence indicates that a woman’s heart rate is a deterministic factor in the prediction of preeclampsia. In recent times, statisticians have therefore developed a novel and non-invasive approach to
detect abnormalities in pre-eclamptic women that distinguishes from women with non-pre-eclamptic
pregnancies. This approach is accomplished by comparing the dynamical complexity of the heart rates of
women that are pre-eclamptic with those that are non-pre-eclamptic. The analysis revealed that the heart
rate of pre-eclamptic women demonstrated a more regular dynamic behavior than those women that were
not pre-eclamptic, which substantiates the empirical notion that diseased states may be associated with
regular heart rate patterns.
POPULATION DYNAMICS
Mathematicians have long developed models to analyze population dynamics. One contemporary model
also incorporates how pregnant women directly influence such dynamics. This model consists of an
equation that describes the evolution of the entire population and an equation that analyzes the evolution
of pregnant women. These equations are coupled—they are studied simultaneously. Moreover, this
particular system of equations can be analyzed as a linear model (not sensitive to initial data), with or
without diffusion (permitting members of the population to travel large distances), or as a nonlinear model
(sensitive to initial data) without diffusion. The asymptotic behavior of the solutions to this system (the
long-term behavior of the population) was also addressed.
FURTHER READING

Fragnelli, Ginni, et al. “Qualitative Properties of a Population Dynamics System Describing
Pregnancy.” Mathematical Models and Methods in Applied Sciences 4 (2005).

Germaine B., et al. “Analysis of Repeated Pregnancy Outcomes.” Statistical Methods in Medical
Research 15 (2006).

Salazar, Carlos, et al. “Non-Linear Analysis of Maternal Heart Rate Patterns and Pre-Eclamptic
Pregnancies.” Journal of Theoretical Medicine 5 (2003).

Savitz, David A., et al. “Methodologic Issues in the Design and Analysis of Epidemiologic Studies
of Pregnancy Outcome.” Statistical Methods in Medical Research 15 (2006).

Scarpa, Bruno, and David B. Dunson. “Beyesian Methods for Searching for Optimal Rules for
Timing Intercourse to Achieve Pregnancy.” Statistics in Medicine 26 (2007).

Scheikle, Thomas H., and Niels Keiding. “Design and Analysis of Time-to-Pregnancy.” Statistical
Methods in Medical Research 15 (2006).
Daniel J. Galiffa
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