TITLE:
Mathematical Modelling of Family Planning Interventions: A Compartmental Approach to Population Growth Control
AUTHORS:
Lukman Olalekan Ahmed, Abdullahi Muhammed Ayinde, Adeoye Seun, Musa Kabiru, Ene Christiana Agbo, Hassan Abdulrahman
KEYWORDS:
Family Planning, Population Growth, Mathematical Modelling, Compartmental Model, Reproductive Health, Differential Equations, Basic Reproductive, Numerical Simulation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.9,
September
17,
2025
ABSTRACT: This study presents a mathematical modelling approach to analyze the impact of family planning interventions on population growth dynamics. Using a compartmental model, the population is divided into six groups: Susceptible, Informed, Sexually Active Non-Users, Contraceptive Users, Non-Users and General Population. The model incorporates differential equations to describe transitions among these compartments, influenced by factors such as sexual behavior, contraceptive adoption, and public health education. Analytical techniques, including equilibrium analysis and the computation of the basic reproductive number were used to evaluate the model’s behavior and stability. Numerical simulations conducted in MATLAB revealed that increased contraceptive usage and awareness significantly reduce the number of high-risk individuals while stabilizing overall population growth. The reproductive number was shown to decrease as contraceptive uptake increased, confirming the effectiveness of intervention strategies. The findings highlight the importance of reproductive health education and contraceptive access in managing population growth, providing valuable insights for policymakers and public health planners. This study demonstrates the potential of mathematical modelling as a predictive and policy-support tool in reproductive health and demographic planning.