1. Introduction

Population migration is a multifaceted and dynamic process shaped by macroeconomic transformation, institutional design, and regional development imbalances. In the context of China's unprecedented urbanization over the past four decades, internal migration has served as a critical channel through which labor, capital, and human capital are redistributed across space. As documented in the China Statistical Yearbook (2015), the national urbanization rate increased from 17.92% in 1978 to 54.77% by 2014, with the average annual rate accelerating markedly after 1996 [1]. This transformation, however, has not been spatially uniform. While coastal provinces such as Jiangsu, Zhejiang, and Guangdong experienced rapid urban growth due to their early integration into global markets and preferential policy regimes, many inland and western provinces, including Sichuan, remain characterized by relatively slower population growth or even net out-migration [2].

These regional disparities in migration patterns have profound implications for balanced development, social equity, and spatial justice. Metropolitan areas like Chengdu have benefited from agglomeration economies, diversified industrial structures, and strong public service ecosystems, thereby reinforcing their capacity to attract and retain skilled populations. In contrast, smaller inland cities such as Yibin confront structural disadvantages in competing for mobile populations, particularly among younger cohorts and households with higher educational attainment. These challenges are further exacerbated by institutional constraints, most notably China's hukou (household registration) system, which restricts equal access to education, healthcare, and social security for migrants in destination cities [3]. Consequently, the uneven distribution of high-quality public services reinforces the population inertia favoring already-developed urban cores.

Against this backdrop, regional governments in China's western and central provinces have increasingly turned to education investment as a lever for enhancing urban attractiveness and reversing demographic decline. Investment in primary and secondary schools, vocational training centers, and higher education facilities is viewed not only as a driver of human capital accumulation but also as a locational asset that influences household migration preferences. For families with school-aged children, the quality and accessibility of education services can act as a decisive factor in residential decision-making. Although the long-term macroeconomic returns of education are well established in development economics, its short- to medium-term behavioral effects on migration flows—especially within a single province—remain insufficiently quantified and underrepresented in current migration modeling literature.

Existing models of population migration tend to emphasize macro-scale flows, particularly interprovincial or international migration, using static or semi-aggregated econometric approaches that often overlook localized policy variables. These frameworks, while valuable in explaining broad trends, are limited in their capacity to simulate municipal-level dynamics and the impact of place-based interventions such as targeted education investment. Moreover, many of these models do not integrate the feedback mechanisms inherent in spatial migration systems, where population inflows can recursively alter city attractiveness.

To address these gaps, this study develops a mathematical model that links education investment to inter-city migration flows within Sichuan Province. The model employs a system of ordinary differential equations (ODEs) embedded with gravity-based migration logic, in which the population transfer between cities is a function of their relative socioeconomic attractiveness, adjusted by distance and demographic pressure. Education investment is operationalized through measurable proxies—such as per-student funding, school quality indices, and the availability of higher education institutions—and incorporated as a dynamic factor influencing migration attractiveness. The simulation compares two policy scenarios: one in which Yibin receives significant education investment, and one in which it does not. The period of analysis spans 2020 to 2030, with partial empirical calibration based on population data from 2020 to 2024.

The contributions of this study are threefold. First, it introduces a policy-sensitive modeling framework that incorporates education infrastructure as a dynamic, spatially embedded driver of population movement. Second, it contributes to the meso-scale migration literature by focusing on intra-provincial flows and sub-provincial heterogeneity, rather than aggregated national trends. Third, the findings have direct policy implications for small and mid-sized inland cities such as Yibin, offering empirical evidence to support differentiated urban development strategies under conditions of demographic stress.

The structure of the paper is as follows: Section 2 provides a critical review of relevant migration modeling approaches, highlighting the limitations of existing frameworks in capturing localized policy effects. Section 3 outlines the construction of the ODE model, parameter selection, and simulation methodology. Section 4 presents the empirical findings and scenario comparisons. Section 5 discusses the broader policy implications, limitations, and directions for future research. Supplementary materials, including the MATLAB simulation code and detailed parameter tables, are included in the Appendix for replication and extension.

2. Literature review

2.1. Theoretical foundations of migration modeling

Migration has become a classical theory in the research of populations, and this theory concerns the economic rationality of the research and the spatial behavior. Ravenstein's seminal Laws of Migration provided one of the earliest systematic accounts of migratory behavior, highlighting trends such as rural-to-urban flows and the dominance of short-distance moves [4,5]. These ideas were further formalized in Sjaastad's Human Capital Model , which conceptualizes migration as an investment decision: individuals weigh long-term gains from relocation, such as better job prospects or education, against costs like emotional strain or financial expense [6]. This model became a landmark in the field of the advancement of the rational choice of the individual in migration decisions.

Building on this perspective, Lee's Push-Pull Theory introduced a more structured analysis by classifying migration drivers into push factors (e.g., poverty, unemployment at origin), pull factors (e.g., better services or opportunities at destination), and intervening obstacles (e.g., policy or distance) [7]. These foundational theories were extended by Todaro, who argued that expected, not actual, income differences drive urban migration. Being migrants, they can take up informal or low-waged work in their cities and hope that in the long-term course they will be able to advance upwards. This is a more probabilistic perspective of employment as a subtle correction to the simple-minded wage comparison [8]. Finally, Zelinsky's Mobility Transition Theory emphasized that migration patterns correlate with demographic and economic development stages, situating population movement within broader modernization processes [9].

In the 1970s, there was the emergence of the gravity models, pioneering quantitative modeling. In these models, the flow of migration is assumed to be directly proportional to the population of two places, and the distance between them has an inverse relationship. In the contemporary approaches to modeling on the basis of gravity, there is a tendency to add to the general model some socioeconomic and institutional characteristics in order to represent the degree of destination attractiveness. Though elegant theoretically, gravity models generally intuitively suppose symmetry of interactions and possibly fail to represent the full effects of a specific policy intervention course of action.

2.2. Education and migration dynamics in China

The Chinese scenario makes an interesting case, where all of the institutional reforms, demographic shifts, and spatial policy influence the internal migration. Recent empirical studies underscore how China's hukou system, while gradually relaxed in small and medium cities, continues to limit mobility by tying access to public services such as schooling, healthcare, and housing subsidies to one's place of registration [3]. This structural limitation has staggeringly impacts on the rural-to-urban migrants and it has lasting impacts on the redistribution of the human capital in regions.

Regional differences in educational quality and public investment are other forces influencing migration in China. While tier-one cities like Beijing and Shanghai attract high-skilled labor through concentrated resources and elite universities, inland cities struggle with talent outflow, particularly among younger, college-educated cohorts [2]. The policies that are concerned with attracting talent tend to concentrate on monetary incentives or recruitment of the elite, but they can fail to consider the presence of area-wide structural factors that determine the mobility choices of the whole population, such as school quality, family services, or infrastructure. The key point is that education investment is not only a long-term strategy to increase productivity but also a short-to-medium term indicator of the competitiveness of the city. This qualifies it as an influential dynamic migration variable, particularly when taking into consideration local adaptational reactions regarding demographic strains.

Although there is rich literature on inter-provincial or national migration, less has been researched about intra-provincial population movements and the influence of localized education policy on migration behavior. The city of Yibin is representative of the requirement to realize regionalized models taking into consideration the local heterogeneity, infrastructural disparities, and policy interventions. The details of such dynamics cannot be brought out using traditional models, which makes the argument for simulation strategies at the sub-provincial level solid.

2.3. ODE-based simulation models for migration analysis

Given the continuous and interdependent nature of migration flows, Ordinary Differential Equations (ODEs) offer a suitable mathematical framework for simulating population dynamics. ODEs describe how the state of a system evolves, allowing for the modeling of interactions between multiple variables—such as population stocks, education levels, and migration incentives—under varying policy regimes.

In a basic form, an ODE relates the derivative of a variable (e.g., population) to its current state and influencing factors. In more complex systems, this relationship is generalized into a set of coupled equations governing multiple state variables simultaneously. These systems are particularly relevant when exploring feedback loops, such as how rising population inflows affect local resources and, in turn, influence future migration trends. Because most real-world systems are nonlinear and do not admit closed-form analytical solutions, numerical methods are required to solve ODEs over a given period.

Common numerical solvers include Euler's Method, which provides first-order approximations, and more advanced Runge-Kutta methods, especially the fourth-order RK4, which balances accuracy with computational efficiency. For stiff systems—where changes occur at vastly different rates—implicit methods and adaptive step-size controls are often necessary. MATLAB's ode45 solver, based on the Runge-Kutta (4,5) scheme, is especially well-suited for non-stiff systems like migration dynamics, where variables such as population and education evolve smoothly over time. The flexibility of MATLAB's suite of solvers (e.g., ode15s, ode23, ode113) allows researchers to tailor simulation strategies to specific modeling needs.

Critically, the success of ODE-based migration models depends not just on computational implementation but on careful model formulation, empirical calibration, and sensitivity analysis. Initial conditions must reflect real-world data, parameters should be grounded in historical or theoretical justification, and results should be interpreted with attention to stability, feedback effects, and robustness under uncertainty.

By bridging theoretical migration models with empirical education-policy dynamics and computational ODE tools, this review highlights the interdisciplinary basis for developing a regional migration simulation. Such an approach is particularly relevant for understanding how localized education investment—often neglected in national-level models—can influence population redistribution within provinces like Sichuan.

3. Modeling framework

To examine intra-provincial population dynamics in Sichuan and evaluate the influence of education investment in Yibin, we construct a deterministic, multi-city migration model based on Ordinary Differential Equations (ODEs). The model integrates demographic evolution and socio-economic migration behavior across four key cities: Chengdu, Mianyang, Yibin, and Aba. The objective is to simulate how educational investment, as an urban policy tool, can influence population flows and regional demographic balance over time.

3.1. Model structure: a coupled population-migration system

Let the population vector at time  $$ \mathrm{t}$$  be denoted by  $$ \mathrm{P}\left(\mathrm{t}\right)=\left[{\mathrm{P}}_1\right(\mathrm{t}),{\mathrm{P}}_2(\mathrm{t}),\dots ,{\mathrm{P}}_{\mathrm{N}}(\mathrm{t}){]}^{\mathrm{\top }}$$ , where  $$ \mathrm{N}$$  is the number of cities and  $$ {\mathrm{P}}_{\mathrm{i}}\left(\mathrm{t}\right)$$  represents the population of city  $$ \mathrm{i}$$ . The time evolution of  $$ {\mathrm{P}}_{\mathrm{i}}\left(\mathrm{t}\right)$$  is modeled as (see Equation 1):

$$ \frac{d{P}_i}{dt}=B_i\cdot P_i-D_i\cdot P_i+\sum _{j\ne i} M_{ji}-\sum _{j\ne i} M_{ij}$$(1)

Here,  $$ {\mathrm{B}}_{\mathrm{i}}$$  and  $$ {\mathrm{D}}_{\mathrm{i}}$$  are the birth and death rates of city  $$ \mathrm{i}$$ , and  $$ {\mathrm{M}}_{\mathrm{i}\mathrm{j}}\left(\mathrm{t}\right)$$  denotes the migration rate from city  $$ \mathrm{i}$$  to city  $$ \mathrm{j}$$  at time  $$ \mathrm{t}$$ . The model thus accounts for natural growth and net migration.

3.2. Migration mechanism: attractiveness and resistance

Migration decisions are conceptualized as driven by attractiveness differentials among cities, modulated by resistance factors that impede movement. We define a potential function to quantify migration incentives between any city pair (i,j).

3.2.1. Attractiveness score

The composite attractiveness score of city iii, denoted A_i, aggregates four key components (see Equation 2):

$$ {\mathrm{A}}_{\mathrm{i}}={\mathrm{\beta }}_1{\mathrm{E}}_{\mathrm{i}}+{\mathrm{\beta }}_2{\mathrm{W}}_{\mathrm{i}}+{\mathrm{\beta }}_3{\mathrm{L}}_{\mathrm{i}}+{\mathrm{\beta }}_4{\mathrm{U}}_{\mathrm{i}}$$(2)

where:

E_iis the Education Quality Index, including average school ratings, teacher-student ratio, and educational attainment,

W_i is the Wage Level, e.g., average annual income,

U_i is the Urban Utility Index, combining infrastructure indicators such as healthcare beds and transport coverage,

I_i is the Education Investment, quantified via per capita public education expenditure,

This multi-dimensional measure reflects both short-term (e.g., wages) and long-term (e.g., education) migratory incentives.

3.2.2. Resistance score

We define resistance to migration from city i to city j as (see Equation 3):

$$ {\mathrm{R}}_{\mathrm{i}\mathrm{j}}=\mathrm{\alpha }{\mathrm{S}}_{\mathrm{j}}+\mathrm{\beta }{\mathrm{D}}_{\mathrm{i}\mathrm{j}}$$(3)

where:

S_j is the population saturation in city j, measured as the current population relative to carrying capacity,

D_ij is the geographic distance between cities i and j,

α and β are coefficients representing sensitivity to saturation and distance, respectively.

Saturation reflects the diminished marginal utility of inflow in crowded urban cores, while geographic distance captures frictional and psychological costs of relocation.

3.3. Gravity-style migration flow

To model inter-city migration flows, we combine attractiveness and resistance factors into a unified migration potential function. The net migration potential from city i to city j, denoted Φ_ij, is defined as (see Equation 4):

$$ {\mathrm{\Phi }}_{\mathrm{i}\mathrm{j}}\left(\mathrm{t}\right)={\mathrm{A}}_{\mathrm{j}}\left(\mathrm{t}\right)-{\mathrm{A}}_{\mathrm{i}}\left(\mathrm{t}\right)-{\mathrm{R}}_{\mathrm{i}\mathrm{j}}$$(4)

where A_j(t) and A_i(t) represent the time-varying composite attractiveness scores of the destination and origin cities respectively, and R_ij captures fixed resistance—such as institutional barriers, cultural friction, or administrative distance. Only when this net potential is positive do we expect meaningful population movement.

$$ {\mathrm{M}}_{\mathrm{i}\mathrm{j}}\left(\mathrm{t}\right)=\mathrm{\gamma }\cdot {\mathrm{P}}_{\mathrm{i}}\left(\mathrm{t}\right)\cdot \frac{\mathrm{m}\mathrm{a}\mathrm{x}\left({\mathrm{\Phi }}_{\mathrm{i}\mathrm{j}}\right(\mathrm{t}),0)}{1+\mathrm{\delta }{\mathrm{D}}_{\mathrm{i}\mathrm{j}}}$$(5)

Here, γ is a global migration sensitivity parameter controlling the responsiveness of population movement to potential differences, P_i(t) is the source city's population at time t, and D_ij is the physical or infrastructural distance between cities i and j. The term max(Φ_ij(t),0) ensures that migration flows only occur when the net potential is positive, while the denominator 1+δD_ij imposes a distance decay effect, scaled by δ. This structure reflects standard assumptions in regional migration theory while embedding time dynamics and local heterogeneity (see Equation 5).

3.4. Scenario design: modeling education investment in Yibin

In order to analyze the possible effect of educational investment on regional migration, especially in Yibin we pose two comparative simulation situations. Scenario A (Investment Case) assumes a proactive public policy aimed at increasing Y_i education investment, I₃(t), beginning in 2020. To realistically represent the delayed and nonlinear effect of policy implementation, I₃(t) is modeled using a sigmoid function (see Equation 6):

$$ I_3\left(t\right)=I_{\mathrm{3,0}}+\Delta I\cdot \frac{1}{1+e^{-k(t-t_0)}}$$(6)

In this expression, I_3,0 denotes the baseline investment level, I is the increment in investment intensity due to the policy, k is the diffusion rate representing the pace at which policy effects diffuse through the system, and t₀ is the policy onset year. This functional form reflects how steady is the growth of investment and its saturation with time.

In contrast, Scenario B (Baseline Case) maintains a static education investment level for Yibin throughout the simulation horizon, effectively simulating the absence of any additional policy efforts. The rest of the structural parameters i.e. the birth and death rates, inter-city distances, initial population distributions, and the socio-economic weights are kept constant, across the two different scenarios, to isolate the causal role played by educational investment.

3.5. Key assumptions

First, birth and death rates are stationary and uniform across all cities during the simulation period (2020–2030), excluding the effects of fertility or mortality shocks. Second, we assume symmetric geography, such that distance values satisfy D_ij=D_ji, and are treated as exogenous and invariant. Third, policy feedback loops are excluded: the simulation assumes no endogenous policy adjustment in response to migration outcomes (e.g., no reactive expansion of services in response to inflow). Fourth, migration preferences are homogeneous, implying a uniform global sensitivity parameter γ across all origin-destination pairs. Lastly, saturation levels S_j(t) are used as proxies for urban carrying capacity and are modeled as a function of infrastructural constraints and land availability, not dynamically recalibrated with real-time population stress.

These assumptions are designed to foreground the effects of educational policy changes while holding constant broader macroeconomic or institutional dynamics that are beyond the scope of this analysis.

3.6. Implementation and numerical solution

The system of ordinary differential equations defined by the migration and demographic dynamics is implemented in MATLAB using the built-in ode45 solver. This function applies the adaptive Runge–Kutta (4,5) method, which is particularly effective for non-stiff, moderately coupled systems like ours. The simulation time horizon spans from 2020 to 2030, with annual resolution. Initial conditions for population vectors P_i(2020) are calibrated using real demographic data from the Sichuan Statistical Yearbook and the China Population Census. Policy shocks in Scenario A are introduced beginning in 2022, with observable effects emerging gradually due to the sigmoid investment function.

The numerical outputs include: (i) time-series data on city-level population P_i(t); (ii) bilateral net migration flows M_ij(t); (iii) time-varying attractiveness indices A_i(t); and (iv) saturation constraints S_j(t). Key comparative indicators—such as Yibin’s net brain gain, migration retention rate, and cumulative inflow—are then extracted to evaluate the long-term demographic impact of educational investment.

4. Simulation and results

This chapter presents the numerical simulation outcomes of the population migration model described in Chapter 3. The model examines the impact of education investment on population flows between four key cities in Sichuan Province: Chengdu, Mianyang, Yibin, and Aba. Two policy scenarios are analyzed—high education investment in Yibin (Scenario A) and low investment (Scenario B)—to evaluate their influence on population dynamics during 2020–2030.

4.1. Population trajectories under policy scenarios

Figure 4.1 illustrates population trajectories for each city across the two scenarios. Under Scenario A, Yibin experiences steady population growth, increasing from 4.1 million in 2020 to approximately 5.3 million by 2030, representing a 29% rise. In contrast, Scenario B results in near stagnation, with population hovering around 4.1 to 4.3 million. Chengdu, as the provincial capital, maintains consistent growth (~1.5% annually) in both scenarios, increasing from 16.5 million to nearly 19 million by 2030. Meanwhile, Mianyang and Aba show mild declines or stabilization, with Scenario A slightly mitigating decline due to regional redistribution effects (Table 4.1). These patterns demonstrate that increased education investment positively affects Yibin’s demographic growth, consistent with theories that human capital enhancement attracts migration.

4.2. Net migration inflows to Yibin

Figure 4.2 tracks the net migration inflow to Yibin annually. The inflow remains near zero before 2023 due to lagging policy effects. Post-2023, Scenario A shows a marked increase, peaking around 70,000 persons per year by 2028, while Scenario B remains flat, reflecting minimal migration attraction. Most migration originates from Mianyang and Aba, indicating regional labor redistribution rather than loss from Chengdu, which remains a stable population hub. This aligns with the migration cost-benefit framework where education investment raises a city’s pull factor over time.

4.3. Attractiveness and resistance scores

4.3.1. Attractiveness score evolution

Figure 4.3 shows composite attractiveness scores A_i(t) or each city, capturing socio-economic pull factors weighted by education quality, employment opportunities, amenities, and infrastructure. Yibin’s attractiveness significantly increases under Scenario A, rising from 0.45 in 2020 to 0.78 by 2030. This sharp increase contrasts with minimal changes in other cities and Scenario B, demonstrating education investment as a critical driver of urban attractiveness (Table 4.2). These findings support the premise that human capital development boosts endogenous city growth potential [10,11].

4.3.2. Resistance scores and saturation effects

Resistance scores R_ij, representing migration friction mainly due to geographic distance and infrastructural limits, remain relatively stable across scenarios. However, Figure 4.4 shows that population saturation indices S_j(t) which measure population relative to city carrying capacity, increase for Yibin from 0.60 to 0.85 under Scenario A. Chengdu approaches saturation near 0.95, indicating limited further absorption capacity. The saturation rise in Yibin signals growing pressure on urban infrastructure and services, which may moderate future migration inflows unless capacity is expanded [3,12].

4.4. Sensitivity analysis

In Table 4.3, sensitivity tests on parameter of key concern to the model are summarized. By selecting the value of 20 percent increase in migration sensitivity, the population growth becomes two years faster in Yibin when compared to the scenario when the migration sensitivity remains unchanged, revealing existence of responsiveness between migration flows mobilized and migration incentives. Still, since doubling the weight on the quality of education to w₁ increased the population growth rate by a margin of 10%, another such increase will have an identical average increase. Major differences between the diffusion rate k, i.e. the speed of adoption of the policy, do not influence the scale of growth, but only its timing. These robustness checks confirm the critical role of education investment in migration dynamics and validate the model's reliability under parameter uncertainties [9,13].

4.5. Summary of key results

Overall, the simulation results demonstrate that targeted education investment in Yibin substantially increases the city's attractiveness and triggers significant net migration inflows. The favorable demographic change is a slow process, which identifies the education policy as a long-term capacity-building tool, not as a short-term growth driver. Moderate population redistribution is seen around neighboring cities as per intra provincial redistribution of labour. Moreover, population saturation effect shows that it is equally necessary to coordinate education policies with infrastructure and urban capacity enlargement so that sustainable growth can be ensured.

5. Conclusion and discussion

5.1. Summary of findings

This study develops a deterministic multi-city migration model based on a system of coupled ordinary differential equations (ODEs) to assess the impact of public education investment on population dynamics in Sichuan Province, with a focus on the mid-sized city of Yibin. The simulation contrasts two policy scenarios: one in which per capita education investment in Yibin increases significantly after 2022 (Scenario A), and a static baseline (Scenario B). The model captures population evolution across four cities—Chengdu, Mianyang, Yibin, and Aba—by integrating both natural growth and intercity migration driven by time-varying attractiveness differentials.

Simulation results reveal that increased education investment in Yibin, modeled via a sigmoid function I₃(t), progressively elevates its overall attractiveness score A₃(t). This growth in attractiveness feeds into the migration flow function M_ij(t), resulting in a sustained net inflow into Yibin beginning in 2025. Compared to the baseline scenario (Scenario B), where attractiveness remains static, Scenario A demonstrates a gradual but definitive demographic shift favoring Yibin.

The model shows that the relationship between I₃(t) and A₃(t) is non-linear, and the effects of education policy act with a delayed onset due to the time lag inherent in human capital formation. Population growth in Yibin does not spike abruptly; instead, it accumulates steadily, with yearly net migration increasing at an average rate of 2.1% between 2025 and 2030. This supports the notion that education investment serves primarily as a long-term structural driver rather than a short-term population lever. The results corroborate theoretical expectations from migration models such as Lee’s push-pull theory, Todaro’s expected income framework, and the more recent work by Beine et al. on skill-selective migration [7,8,11].

5.2. Education as a conditional lever for endogenous growth

While rising education levels increase Yibin’s attractiveness A_i, the simulation reveals this factor alone is insufficient to sustain net population growth beyond a certain threshold. Specifically, in Scenario A, the population gains a plateau by 2029, constrained by the saturation function S_i(t) and labor-market mismatches. These findings indicate that educational inputs must be paired with corresponding demand-side absorptive capacity in the economy.

Without industrial sectors capable of employing the newly educated workforce, the marginal gains from additional investment diminish. In the model, when E_i exceeds 0.65 but W_i (wage opportunity) remains below the regional average, net inflows begin to taper. This aligns with Lucas’s endogenous growth theory: human capital generates long-term growth only when embedded in productive ecosystems [12]. If the mismatch persists, the city risks “migration leakage” — a loss of talent to nearby cities with more developed economic environments.

5.3. Asymmetric intercity competition and strategic differentiation

Yibin competes under structural disadvantage compared to Chengdu and Mianyang. Chengdu, with a large labor market and cultural centrality, maintains high baseline attractiveness A₁(t), while Mianyang's research-intensive economy draws STEM talent. Yibin lacks both agglomeration and industrial prestige.

The model reveals that cities like Yibin can only break demographic equilibrium if their relative attractiveness A_i(t) crosses a behavioral threshold — influenced by intercity distance D_ij, housing availability, and employment potential. Specifically, if A₃(t) - A₂(t) > 0.15 and D₃₂<200 km, significant migration flow redirection becomes feasible. This implies that a differentiated strategy, not imitation, is key.

Yibin’s optimal trajectory lies in exploiting its geographical advantage — as a river-port city on the Yangtze logistics chain — and reinforcing sectoral niches such as green manufacturing, smart logistics, and vocational education. These can attract skilled returnees and young professionals priced out of tier-1 urban centers.

5.4. Policy recommendations informed by model dynamics

1. Prioritize Targeted Education InvestmentRather than uniformly increasing education budgets, governments should focus on strategically enhancing areas that directly impact local employability and innovation. Investments in vocational training programs can equip young residents with practical skills aligned with regional industries. Simultaneously, teacher training and professional development are essential to improve education quality. Building partnerships between educational institutions and local industries can ensure that curricula remain relevant and responsive to market needs, creating a stronger pipeline from education to employment.

2. Match Talent Development with Industrial StrategyEducational planning should be closely aligned with regional industrial development. Encouraging synergy between local universities, technical colleges, and high-growth sectors—such as renewable energy, biotechnology, or smart manufacturing—can help ensure a steady supply of job-ready talent. Policies should support the physical co-location of training institutions and industrial parks, which fosters collaboration, innovation, and knowledge exchange, making the region more attractive to skilled professionals.

3. Improve Retention Through Housing and Job GuaranteesTo reduce the outmigration of educated youth, governments should implement measures that increase the perceived and actual benefits of staying. Affordable housing schemes, especially for first-time renters or young professionals, can significantly improve post-graduation retention. In addition, job guarantee programs or local employment quotas for new graduates can enhance stability and confidence in regional opportunities, reducing the incentive to migrate elsewhere.

4. Invest in Livability and Social InfrastructureUrban amenities such as efficient public transport, accessible healthcare, green spaces, and cultural venues are crucial for attracting and retaining skilled populations. Policies that support holistic urban development contribute to a higher quality of life, which is increasingly a key factor in migration decisions among younger and mobile workers.

5. Integrate Yibin into Broader Regional DevelopmentEmbedding Yibin within wider regional economic strategies, such as Sichuan’s "One Zone, Two Corridors" initiative, is essential. Active participation in cross-city innovation corridors can enhance Yibin’s visibility, connectivity, and access to funding. This regional integration not only brings in more capital but also strengthens institutional linkages, making Yibin a more viable and attractive option for both talent and investment.

5.5. Final remarks

This study provides quantitative and strategic evidence that educational investment—when modeled as a time-dependent sigmoid shock to attractiveness—can meaningfully alter the demographic trajectory of mid-sized cities like Yibin. However, its impact is contingent upon coordination with labor market absorption, urban livability, and provincial-scale economic alignment. The modeling framework, grounded in ODE-based migration dynamics, offers a replicable and scalable tool for policymakers seeking to anticipate population movement under targeted public investment strategies. The findings highlight that education is not an isolated variable, but part of an ecosystem requiring coherent multi-sectoral planning to unlock its full demographic dividends.