Mathematical Modeling and Analysis on the Population Birth Rate Trends in Japan

Japan faces a significant demographic challenge with far-reaching social, economic, and political ramifications due to its declining birth rate and rapidly rising aging population. Addressing the intricate aspects of these serious emergent phenomena, this study has proposed a mathematical model using a system of ordinary differential equations that has been observed analytically and numerically. As part of the analytical solution, we have verified the model’s existence and uniqueness, investigated its stability at the equilibrium points, and explored its characteristics concerning different state variables. Besides, a sensitivity analysis has been conducted to identify the sensitive parameters based on the estimated parameters. Additionally, the Runge–Kutta fourth-order approach has been used to find the numerical solutions. This study’s findings have been investigated using a newly proposed mathematical model to highlight the demand for a broad awareness campaign in Japan to address the possible effects of a declining birth rate on social structure and the country’s economy, as well as concerns about rising prices influencing family planning decisions. To sustain population growth in Japan, the government should provide proper initiatives to boost the birth rate.