A Novel Nonlinear Fertility Catastrophe Model Based on Thom's Differential Equations of Morphogenesis and a Topological Alternative to the Micro-Macro Divide in Demography

Abstract

This paper introduces a novel fertility model grounded in Thom's nonlinear differential equations of morphogenesis. Through a three-dimensional catastrophe surface - representing the interaction between latent, continuous fertility determinants and abrupt catastrophic shocks - the model incorporates key socioeconomic and environmental variables that explain demographic patterns across macro-, meso-, and micro-levels, including the global fertility decline, regional population disparities, and localized phenomena such as teenage pregnancy. To demonstrate the model's practical utility, an agent-based simulation is presented to show how latent factors - education, contraceptive use, and parental involvement - interact with disruptive influences such as socioeconomic deprivation, violence, and substance abuse. A bifurcation set analysis further reveals how minor shifts in socioeconomic conditions can trigger significant fertility changes and critical transition points in demographic dynamics. By unifying Thom's morphogenetic framework with classical fertility theory, this study advances a pioneering approach to multi-layered demographic analysis and provides a morphogenetic topological alternative to the rigid micro-macro divide in demography. The results offer actionable insights for public health policy, equipping stakeholders to address both gradual trends and sudden demographic shifts.