<![CDATA[Japan faces one of the major challenges as its declining birth rate and aging population threaten long-term demographic and economic stability. To address this challenge, a mathematical model with optimal control has been formulated, employing awareness programs and incentives to maximize population growth at minimal policy costs. Along with analyzing the model’s positivity, boundedness, existence of a unique solution, and stability at equilibrium points, the optimal control was characterized using Pontryagin’s Maximum Principle. Using the forward-backward sweep method, the numerical simulation demonstrated that the objective is maximized by applying awareness programs and incentives at full capacity until 2042 and 2046, respectively, before gradually reducing them. Then, a cost-effectiveness analysis was conducted to determine the most efficient approach, revealing that awareness programs are more cost-effective than the alternative strategy. Therefore, the findings of this study provide valuable guidance for policymakers to develop practical, cost-effective strategies that address Japan’s demographic challenges and promote sustainable population growth for society.]]>
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