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A Novel Nonlinear Fertility Catastrophe Model Based on Thom's Differential Equations of Morphogenesis

Rolando Gonzales Martinez

TL;DR

The paper addresses the challenge of explaining global fertility declines and abrupt demographic shifts by integrating Thom's nonlinear morphogenesis with catastrophe theory. It proposes a three-dimensional cusp catastrophe surface to model interactions between latent fertility determinants and catastrophic shocks, extended to macro-, meso-, and micro-demography. An ABM of teenage pregnancy embeds cusp catastrophe dynamics, showing how individual factors and peer/regional influences can trigger sudden transitions in pregnancy status. The work introduces a stochastic extension, bifurcation analysis, and policy-relevant insights for anticipating tipping points and informing resilient reproductive health policies.

Abstract

A novel fertility model based on Thom's nonlinear differential equations of morphogenesis is presented, utilizing a three-dimensional catastrophe surface to capture the interaction between latent non-catastrophic fertility factors and catastrophic shocks. The model incorporates key socioeconomic and environmental variables and is applicable at macro-, meso-, and micro-demographic levels, addressing global fertility declines, regional population disparities, and micro-level phenomena such as teenage pregnancies. This approach enables a comprehensive analysis of reproductive health at aggregate, sub-national, and age-group-specific levels. An agent-based model for teenage pregnancy is described to illustrate how latent factors -- such as education, contraceptive use, and parental guidance -- interact with catastrophic shocks like socioeconomic deprivation, violence, and substance abuse. The bifurcation set analysis shows how minor shifts in socioeconomic conditions can lead to significant changes in fertility rates, revealing critical points in fertility transitions. By integrating Thom's morphogenesis equations with traditional fertility theory, this paper proposes a groundbreaking approach to understanding fertility dynamics, offering valuable insights for the development of public health policies that address both stable fertility patterns and abrupt demographic shifts.

A Novel Nonlinear Fertility Catastrophe Model Based on Thom's Differential Equations of Morphogenesis

TL;DR

The paper addresses the challenge of explaining global fertility declines and abrupt demographic shifts by integrating Thom's nonlinear morphogenesis with catastrophe theory. It proposes a three-dimensional cusp catastrophe surface to model interactions between latent fertility determinants and catastrophic shocks, extended to macro-, meso-, and micro-demography. An ABM of teenage pregnancy embeds cusp catastrophe dynamics, showing how individual factors and peer/regional influences can trigger sudden transitions in pregnancy status. The work introduces a stochastic extension, bifurcation analysis, and policy-relevant insights for anticipating tipping points and informing resilient reproductive health policies.

Abstract

A novel fertility model based on Thom's nonlinear differential equations of morphogenesis is presented, utilizing a three-dimensional catastrophe surface to capture the interaction between latent non-catastrophic fertility factors and catastrophic shocks. The model incorporates key socioeconomic and environmental variables and is applicable at macro-, meso-, and micro-demographic levels, addressing global fertility declines, regional population disparities, and micro-level phenomena such as teenage pregnancies. This approach enables a comprehensive analysis of reproductive health at aggregate, sub-national, and age-group-specific levels. An agent-based model for teenage pregnancy is described to illustrate how latent factors -- such as education, contraceptive use, and parental guidance -- interact with catastrophic shocks like socioeconomic deprivation, violence, and substance abuse. The bifurcation set analysis shows how minor shifts in socioeconomic conditions can lead to significant changes in fertility rates, revealing critical points in fertility transitions. By integrating Thom's morphogenesis equations with traditional fertility theory, this paper proposes a groundbreaking approach to understanding fertility dynamics, offering valuable insights for the development of public health policies that address both stable fertility patterns and abrupt demographic shifts.

Paper Structure

This paper contains 7 sections, 21 equations, 2 figures.

Table of Contents

  1. Introduction
  2. A Nonlinear Fertility Catastrophe Model
  3. A Cusp Catastrophe-Agent Based Mathematical Model of Teenage Pregnancy
  4. Agents and Social Networks
  5. Discussion
  6. Conclusion
  7. Python Code of to replicate the simulations of the Cusp Catastrophe-Agent Based Mathematical Model of Teenage Pregnancy

Figures (2)

  • Figure 1: Left: Response surface of the fertility model based on catastrophic morphogenesis. The model takes into account the effects of $X$ traditional fertility factors, as well as catastrophic shocks ($Z$). Right: state-space of control parameters of the model: $\alpha$ and $\beta$.
  • Figure 2: Simulation of teenage pregnancy in an agent-based model using a cusp catastrophe surface. Left: all agents (represented as blue markers) are in a non-pregnant state, positioned according to non-catastrophic fertility factors (X-axis) and catastrophic shocks (Z-axis), such as deprivation and violence. Right: After the ABM simulation, some agents (red markers) have transitioned into a pregnant state, triggered by an increase in catastrophic shocks (Z-axis) or decreases in non-catastrophic factors (X-axis).