Modeling Survival Dynamics of Women at Child Birth Using Delay Differential Equation

Abstract

A numerical simulation analysis of a time delay differential equations model involving human population dynamics was carried out to quantify the impact of probability of survival of women to child bearing age on the dynamical system. The study assumed that there are three population of women of child bearing class which include the juvenile women (J w ), child bearing class of women ( ) and the menopause women ( ). A computational approach was adopted in the study which involved the numerical simulation of the human population dynamics using ODE 45 numerical scheme. Result predicted a decrease in the population of juvenile women and fluctuation in the population class of child bearing women and menopause women for a varying value of the probability of survival of women to child bearing age. Result further showed a decrease in the population of juvenile women and an increase in the population of class of child bearing women and a fluctuation in the population of menopause at t=20. However, predominantly unstable dynamical system was predicted leading to unstable steady state solution of the time delayed differential equation involving human population dynamics. The study recommended that women of menopause age should stop child bearing in order to enhance their longevity and women of juvenile age and women of child bearing age should adopt antenatal and post-natal facilities domiciled in the public health centers to curtail the death of women during child bearing.

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