Spatio-Temporal Sensitivity of Healthcare Accessibility: Insights from a System Dynamics Model

Abstract

Recent research has increasingly focused on modeling the spatiotemporal dynamics of healthcare accessibility. However, a critical gap remains in understanding the relative influence of underlying factors, such as travel propensity, service availability, and population demand, and particularly how their influence varies across space and time. To address this gap, we proposed an analytic protocol that systematically evaluates these factors through four tiers: general, spatial, temporal, and spatio-temporal global sensitivity analysis (GSA). We demonstrated this framework’s utility through a real-world case study in Florida, USA, integrated with a recently developed system dynamics model. The results revealed that disease rate had the greatest overall influence on variations in health accessibility. The spatial GSA showed clear heterogeneity in factor importance: travel propensity plays a more significant role in rural areas, whereas facility discharge rates have greater influence in urban settings. Furthermore, spatiotemporal GSA indicated that the influence of each factor varied substantially by both week and ZIP code. By quantifying factor influence across multiple scales, this framework offers evidence-based guidance for designing interventions tailored to different planning horizons and geographic contexts—such as short-term versus long-term, and local versus statewide strategies.

1. Introduction

Spatial accessibility to healthcare refers to the ease with which individuals can reach and utilize healthcare services. In public health and geography, estimating this accessibility is a widely studied problem that often involves the modeling of three interacting factors: population demand (people who need care), healthcare supply (availability of health resources), and travel propensity or constraints, such as geographic impedance (Joseph & Phillips, 1984; Luo & Wang, 2003; Neutens, 2015). This problem is further complicated when considering how these factors vary and interact across both space and time. For instance, population demand and healthcare supply may fluctuate across different phases of an epidemic; while individuals’ travel propensity can differ substantially between daytime and nighttime, as well as rural and urban areas.

Recent studies have shown a growing focus on developing models of time-varying (or space-time) healthcare accessibility. Many of them represented time as a discrete variable, measuring the contributing factors and resulting accessibility at specific temporal intervals (Kim, Singh, Speizer, Angeles, & Weiss, 2019; Li, Wang, Kwan, Chen, & Wang, 2022; Xia et al., 2019). More recent efforts, however, adopted a nuanced approach by treating time as a continuous variable, allowing smoother variation in both contributing factors and model outputs (Cassidy et al., 2019; Mao, 2025; Yijie Zhang, Zhang, Hu, & He, 2022). Despite these conceptual advancements, existing spatiotemporal models fail to quantify how the sensitivity of model outputs to each factor varies simultaneously across space and time. As model factors vary and interact over space and time, their influence on accessibility also changes. For example, a decline in supply over time may amplify its influence on accessibility while diminishing the role of travel propensity. For public health planning, it’s essential to know when and where each factor may have the greatest or least effect on the estimation of health accessibility, so that interventions can be tailored to specific times and locations. This spatiotemporal sensitivity analysis remains a critical, understudied frontier in health accessibility research.

To fill this gap, we proposed a spatio-temporal global sensitivity analysis (ST-GSA) protocol to identify key drivers of changes in healthcare accessibility. We demonstrated this framework’s utility through a real-world epidemic scenario in Florida, USA, integrated with a recently developed system dynamics model. In this case study, we evaluated how model factors and their interactions influence estimated accessibility across ZIP codes and weeks.

2. Literature review

2.1. Factors of spatial accessibility to healthcare and their dynamics

Penchansky and Thomas (1981) conceptualizes access to healthcare into five dimensions: availability, accessibility, accommodation, affordability, and acceptability. This conceptual framework has been widely used to guide the selection of factors in modeling studies. Within the health geography literature, many modeling efforts focus predominantly on availability and accessibility due to their pronounced spatial variability, while other dimensions are often simplified or omitted. Availability assesses whether the volume and type of services meet patient needs; Accessibility highlights the geographical location of services in relation to population in demand, including distance and transport (Cromley & McLafferty, 2011).

The foremost factor to consider is individuals’ propensity to travel – how willing they are to make a health seeking trip (Delmelle et al., 2013). This propensity is typically modeled as being inversely proportional to travel costs (e.g., distance or time). Simple accessibility models measure the travel costs by the minimum or average distance to health facilities (Brabyn & Skelly, 2002). More sophisticated models, such as the inversed squared distance, gravity, and Gaussian functions, represent travel propensity as a gradual decay with increasing distance (Guagliardo, 2004; Luo & Qi, 2009; Luo & Wang, 2003). In addition, individuals’ travel propensity can fluctuate over time due to intra-daily traffic patterns (Z. Gan, Liang, & Yang, 2024), disruption of natural hazards (Balomenos, Hu, Padgett, & Shelton, 2019), and other reasons.

The second factor is the availability of health supply. The adequacy of supply directly determines whether individuals seeking care can be accommodated, especially during periods of high demand. In modeling, the health supply is commonly quantified by capacity-based metrics such as the number of hospital beds, physicians, or other medical resources. In a time-dependent context, the supply varies with patient admissions and discharges at health facilities. It may also drop to zero when facilities are closed during nighttime hours or due to natural disasters (Yuerong Zhang, Cao, Cheng, Gao, & De Vos, 2022).

The third factor is population demand, which represents the number of individuals needing healthcare services. High demand can strain health supply, leading to longer waiting times, reduced quality of care, or even denial of service. While demand is often quantified as the total population, it can be further specified by demographic or disease status in more targeted studies (Cheng, Yang, De Vos, & Witlox, 2020; Wang & Roisman, 2011; Wigley et al., 2020). Demand for healthcare fluctuates over time for many reasons, such as epidemiological trends (e.g., seasonality), demographic shifts (e.g., population aging), and behavioral patterns (e.g., weekdays vs. weekends).

Together, the three factors form an interconnected healthcare system where changes in one factor can ripple through the others, requiring accessibility models to integrate all three. Classic spatial accessibility models include the container model (Pender, Kuhns, Yu, Larson, & Huck, 2023), Floating Catchment Area (FCA) model (Luo & Wang, 2003) and kernel density model (Guagliardo, 2004). Although widely used across diverse settings, these models are often implemented in static contexts that assume no temporal variation in key factors.

2.2. Recent models for space-time healthcare accessibility

Due to the time-varying nature of these three factors, there has been growing interest in modeling spatio-temporal dynamics of health accessibility. Some dynamic models adopted a discrete-time approach, which measured factors as snapshot values at predetermined time intervals. They then applied static accessibility models to each separate time interval. For instance, studies in Xia et al. (2019) and Li et al. (2022) have modeled changing population demand between daytime and nighttime, and compared accessibility to healthcare between these two time periods. Zhang et al. (2022) considered the supply changes across operational hours during a day and calculated hourly accessibility to general practice services. Gan et al. (2024) focused on travel propensity and showed how accessibility changed across different daily periods—peak, off-peak, and night. This discrete-time approach offers computational convenience, because it can directly use classic accessibility models. It, however, simply assumes temporal independence among the three factors. In other words, each factor evolves separately over time without mutual influence. For example, demand in one period cannot affect supply in the next, overlooking real-world interplay between supply and demand. For this limitation, this approach is generally more suitable for long-term planning scenarios (e.g., spanning multiple years), where factor changes occur gradually rather than abruptly and interactions among factors are minimal.

For improvement, more recent research employs a system dynamics approach, which explicitly represents continuous time and interactions among system components (factors). This approach recognizes that the state of each component in the current period is shaped by its interactions in previous periods. For instance, a surge in demand during one period can reduce supply in the next. This interdependence allows for a more realistic simulation of healthcare accessibility, especially in rapidly evolving scenarios such as epidemics or seasonal outbreaks. Differential equation models (Lattimer et al., 2004; Mao, 2025) and agent-based models (Munir, Hafeez, Rashid, Iqbal, & Javed, 2020; Oh, Trinh, Vang, & Becerra, 2020) have been recently proposed to implement this approach.

Despite growing efforts to advance space-time modeling in health accessibility, limited attention has been given to assessing the influence of key factors on model outputs, particularly how their influences vary across temporal and spatial dimensions. Several studies have used local sensitivity analysis that only focuses on the influence of a single factor across an entire study area, e.g., the threshold of travel time (Luo & Wang, 2003) or distance-decay parameter (Tao, Cheng, Zheng, & Li, 2018). Few studies have incorporated multiple factors and analyzed how their influence vary spatially, temporally, and spatio-temporally. Our study addresses this limitation by evaluating multi-factor spatiotemporal sensitivity.

2.3. Global sensitivity analysis

Sensitivity Analysis is a widely used method to quantify how variability in a model’s input parameters affects its output, providing a measure of each parameter’s influence. In other words, parameters that cause little change in outputs are considered less influential.

Unlike local sensitivity analysis, which assesses the influence of a single parameter, global sensitivity analysis (GSA) systematically evaluates all parameters simultaneously. The strength of GSA makes it effective for evaluating nonlinear dynamics models with multiple interdependent inputs, such as complex system dynamics models (Yijie Zhang et al., 2022) and spatially explicit agent-based models (J.-Y. Kang, Aldstadt, Vandewalle, Yin, & Wang, 2020; J. Y. Kang, Michels, Crooks, Aldstadt, & Wang, 2022; Tang & Jia, 2014). However, relatively few studies have examined model sensitivity in both spatial and temporal dimensions. For instance, Zhang et al. (2022) and Tang & Jia (2014) focused on factor influence at the level of the overall system, without accounting for spatio-temporal variability. Kang et al. (2019; 2020) performed GSA on an agent-based model for dengue transmission, but primarily focused on comparing sensitivity across various spatial scales (e.g., micro vs. macro scales; 500 m vs. 1000 m grids) and temporal scales (e.g., weekly, monthly, yearly), rather than at specific spatial locations and continuous time intervals. Our proposed ST-GSA tends to enhance their work.

3. Methods

3.1. The system dynamics model for health accessibility

In our base model to assess spatio-temporal accessibility, the healthcare system is represented by two primary components: populations and health facilities. Each component is characterized by a set of state variables that capture its dynamics over time. (Figure 1).

Figure 1.

Model conceptual design: each circle represents a state variable of a system component. Arrows indicate changes of each variable over time (citation hidden for review).

Each population component (the left panel in Figure 1) has four state variables during a time period t: healthy individuals (H_i,t), infected individuals (I_i,t), individuals demanding healthcare from facility j (D_ij,t), and individuals receiving treatment at facility j (T_ij,t). Transitions between these states were governed by model parameters during time t, including: the disease rate α_i,t, the admission and discharge rates at facility j (AD_ij,t and DIS_j), and the likelihood of population i accessing facility j (β_ij.t). This likelihood β_ij.t is proportional to real-time supply S_j,t and inversely proportional to travel costs that follow a distance-decay function f(d_ij), where d_ij is the distance between population i and facility j. On the other hand, each facility component (the right panel in Figure 1) has two state variables during time t: the current supply (S_j,t) and the number of treated individuals from population i (T_ij,t). The state transitions are determined by the admission rate (AD_j,t) and discharge rate (DIS_j).

The system dynamics were formulated into a set of time-dependent differential equations (see Supplementary file S1 for details) and implemented to simulate daily accessibility to healthcare during a tripledemic, a simultaneous outbreak of Influenza, COVID-19, and Respiratory Syncytial Virus (RSV), in Florida, USA, from October 2022 to September 2023 (a total of 364 days). The model was parameterized using actual ZIP code populations (for population components), hospital bed capacity (for facility components), and epidemiological records (Figure 2). To measure travel costs, we used the road network distance between ZIP code centroids and hospitals. Specifically, we extracted OpenStreetMap drive-service road graph and calculated the shortest path distance from each ZIP code centroid to all hospitals using a single-source Dijkstra algorithm (OpenStreetMap, 2023). The model then estimated daily hospital admissions for each local ZIP code and for the entire state, which were validated against observed hospitalization rates.

Figure 2.

Florida ZIP codes categorized by rural and urban status, based on the 2020 RUCA classification (Urban: codes 1–3; Rural: codes 4–10) (U.S. Department of Agriculture, 2025); Locations of health facilities and supply availability. The line chart shows the observed hospitalization rates (used to validate the baseline scenario) and a key model output showing the percentage of demand being met by week.

3.2. Parameter space and model permutations

To analyze the influence of factors reviewed in Section 2.1, we selected four input parameters to capture variability in population demand, travel propensity, and facility supply (Table 1). Baseline parameter values were derived from and validated against real epidemic data in (citation hidden for review). The lower and upper bounds were defined to encompass plausible ranges observed in real-world practice, as specified in Table 1. Monte Carlo simulations were employed to generate samples from uniform distributions.

Table 1.

Description and value ranges of input parameters for GSA

Factors	Parameters	Description	Lower value	Baseline value	Upper value	Justification
Demand	Disease rate (αi)	Likelihood of disease infection in population i	αi *0.5	α i	αi *1.5	Empirical studies estimate the R0 of COVID-19 to range from 2 to 6, whereas influenza and RSV demonstrate narrower ranges (Achaiah, Subbarajasetty, & Shetty, 2020; Alimohamadi, Taghdir, & Sepandi, 2020). This study adopted the maximum possible range (a threefold difference).
Propensity to travel	Frictional coefficient (b)	Distance decay effect as $f\left(d_{ij}\right)=(1/d_{ij}^b)$	1	2	3	The range of 1 to 3 is frequently cited as the empirical observation for human travel behavior (Chen, 2015; Liu, Sui, Kang, & Gao, 2014).
Supply	Capacity (Sj)	The number of hospital beds at facility j	1* Sj	S j	1.5* Sj	Florida hospital association reported that the ICU capacity surged ~40% during COVID (FHA, 2021)
	Discharge rate (DISj)	Likelihood of being discharged from facility j	DISj *0.5=1/14	DIS j =1/7	DISj *1.5≈1/5	For influenza, COVID, and RSV, the length of stay at hospitals is estimated to range between 5 and 14 days (Madad et al., 2023; Xing & Bahl, 2025)

3.3. Space-time global sensitivity analysis (ST-GSA)

To analyze factors’ influence, we conceptualized a 3D cube where the X, Y and Z axis indicate spatial locations, time intervals, and output values (Figure 3). In this structure, each cell has a model output value at a specific location and time. A ‘space slice’ includes model outputs at a given location across the entire temporal domain. Likewise, a ‘time slice’ contains model outputs across all locations for a specific time interval. The GSA is then conducted at four tiers: the entire cube, space slices, time slices, and space-time cells.

Figure 3.

A conceptual framework for space-time global sensitivity analysis

General GSA

We first conducted a basic global sensitivity analysis (GSA) to assess the overall impact of each parameter on the model output, regardless of space and time (i.e., analyzing the entire cube in Figure 3). The model output was defined as the 10^th percentile of demand met percentages across the entire study area and simulation period. This percentile was chosen to capture a worst-case scenario, in which only a very small fraction of demand was met. This scenario would be particularly relevant for policymakers due to its severity. This metric was calculated by first estimating the daily percentage of demand met for the entire study area, computed as the ratio of total admissions to total demand for each day (Figure 2). The 10^th percentile was then determined among these daily values over the entire 364-day simulation period. Finally, we assessed the influence of each parameter on the variation of this metric.

Spatial GSA

We designed a spatial GSA to examine how the influence of each parameter varies across different ZIP code areas (i.e., analyzing each space slice in Figure 3). The model output was defined as the 10th percentile of demand- met percentages for each ZIP code over the 364- day period. First, the daily percentage of demand met within each ZIP code was calculated as the ratio of daily admissions to daily demand. The 10th percentile was then derived from these 364 daily values for each ZIP code. Using this metric, we assessed the influence of each parameter in each ZIP code.

Temporal GSA

We further added a temporal GSA to investigate how the influence of each parameter changed over time periods (i.e., analyzing each time slice in Figure 3). We first divided the entire simulation period into 26 consecutive bi-weekly intervals, starting from October 8, 2022. We selected a two-week interval to smooth short-term fluctuations and highlight more consistent patterns. The model output was defined as the 10^th percentile of demand-met percentages across the entire study area for each time interval. This metric was calculated by first computing the daily percentage of demand met for the entire study area, i.e., the total admissions divided by total demand for each day. The 10^th percentile was then estimated from those daily values within each time interval. Upon this model output, we estimated the influence of each parameter and plotted them as time series over the bi-weekly periods.

Spatiotemporal GSA

At last, we performed a spatiotemporal GSA to evaluate the influence of each parameter within a specific ZIP code and time interval (i.e., analyzing each space-time cell in Figure 3). At this finest spatio-temporal scale, the model output was defined as the 10^th percentile of demand-met percentages within each biweekly period for every ZIP code, which was derived from daily percentage of demand met by ZIP code. Then, the influence of each parameter was estimated for each specific ZIP code and time interval.

Sobol’s sensitivity analysis

To implement the ST-GSA described above, several methodological options are available, for example, Sobol, Shapley, and Kucherenko methods. The Sobol method is relatively straightforward to interpret and implement; however, it relies on the assumption of independent model inputs, which may bias the estimation of their effects when dependencies are present. In contrast, Shapley and Kucherenko methods can accommodate correlated inputs and yield more robust estimation. However, these approaches are more computationally intensive, particularly for complex spatio-temporal dynamic models.

For illustration purposes, we selected the Sobol method because two of our four model inputs, including discharge rate and the travel friction coefficient, were treated as constants. In addition, the correlation between disease rates and hospital capacity across ZIP codes was found to be weak and not statistically significant (correlation = 0.04), supporting the assumption of negligible interdependence among the inputs. Further, the Sobol method allows the evaluation of first and second order effects, providing clear insights into the individual contributions of each factor as well as their combined interactions.

Mathematically, Sobol method decomposes the total variance in model output and measures the proportion of output variance caused by individual parameters and their combinations (Saltelli et al., 2008). Specifically, for a model output Y = f(X₁, X₂, …, X_k), where X_i are the input parameters, the total variance V (Y) in the model output can be decomposed as:

$$V(Y)={\sum }_i{V}_i+{\sum }_{i<j}{V}_{ij}+{\sum }_{i<j<l}{V}_{ijl}+\cdots +V_{\mathit{12}\dots k}$$

where V_i =V(E(Y|X_i)) is the variance in model output due to the variability of parameter X_i, also referred to as the first-order effect of parameter X_i. V_ij = [V(E(Y|X_i,X_j)) − V_i − V_j] is the variance in model output due to the interaction between two parameters X_i and X_j, referred to as the second-order effect of X_i and X_j, and so on. This decomposition clearly divides the contribution of each input parameter into its first order (direct) effect (S_i) and its interactions with other parameters (S_T,i). Mathematically, the first-order index (S_i) measures the main effect of parameter X_i on the output variance, independent of other parameters, and can be calculated as:

$$S_i=\frac{V_i}{V\left(Y\right)}$$

Likewise, the second-order index (S_ij) measures the interaction effects between parameters X_i and X_j, expressed as:

$$S_{ij}=\frac{V_{ij}}{V\left(Y\right)}$$

The total index (ST_i) computes the total effect of parameter X_i on the output variance, including its first-order effect and all higher-order interactions involving X_i.…

$$S{T}_i=S_i+{\sum }_{j\ne i}{S}_{ij}+{\sum }_{j\ne i,k\ne i,j<k}{S}_{ijk}+\dots$$

For a model with k input parameters, the Sobol analysis requires N × (2k + 2) model permutations (Menberg, Heo, & Choudhary, 2016), where the sample size N is recommended to be at least 1,050 for robust results (Y. Gan et al., 2014). In this study, we set the sample size (N) to 3,000 and the number of parameters (k) to 4, resulting in a total number of 30,000 (= 3,000× (2× 4 + 2)) model permutations. We used the SALib library in Python to generate random samples and calculate sensitivity indices (Herman & Usher, 2017; Iwanaga, Usher, & Herman, 2022). To handle the large number of model permutations, we used parallel processing on Google’s V6e TPU equipped with 172.9 GB of system RAM and 225.3 GB of disk storage. Each permutation took approximately 2.5 hours. The codes and data are available through the journal’s designated repository.

4. Results and Discussion

4.1. General GSA

Figure 4 provides a system-level perspective on how each parameter influenced the variability of model outputs. Based on the first-order sensitivity indices, disease rate emerged as the most influential parameter, accounting for approximately 40% of total variance in model outputs. The discharge rate was the second most influential, contributing to about 28% of total variance. In contrast, facility supply and travel propensity of individuals exert comparatively limited effects. The ranking suggests that, within the ranges considered, changes in supply capacity and travel propensity did not substantially alter overall system performance compared to epidemiological dynamics (disease rate) and patient flow processes (discharge rate). The 2^nd order sensitivity indices show that the disease rate had the most significant interactions with other inputs, which accounted for 15% of total variance. Therefore, the impact of disease rate on model outputs depended, to some degree, on the values of other parameters. For all parameters, the total sensitivity index substantially exceeded the first-order index, indicating that interactions among parameters played a significant role in shaping the model output. However, these interactions were not strong enough to alter the overall ranking of parameter influence.

Figure 4.

The first order (S1), second order (S2), and total sensitivity (ST) indices of each parameter, along with their 95% confidence intervals.

4.2. Spatial GSA

Maps from spatial GSA revealed distinct spatial gradients of parameter influence across ZIP codes. The first-order indices (Figure 5a) showed that disease rates had the greatest impact (above 50%) on total variance of demand met in most ZIP codes. The discharge rate exerted a consistently moderate impact (20 −30%) and the supply posed a lower impact (10–20%). Travel propensity exhibited a more spatially heterogeneous impact: it contributed less than 10% in most urban ZIP codes but became more influential in rural areas, where it explained roughly 10–30% of the variance.

Figure 5.

Sensitivity indices of four model parameters by ZIP code area: a) the first-order index; and b) the total sensitivity index. The maps for 2^nd order index can be found in the supplementary file.

The total sensitivity indices (Figure 5b) reinforced these patterns. Notably, increased total effect of discharge rate became concentrated primarily in urban ZIP codes, with a much weaker influence in rural areas. In contrast, the effect of travel propensity rose noticeably in rural ZIP codes. This suggests that interactive effects further amplified travel propensity’s influence in rural contexts, making it a more critical driver of the model’s output in those regions (see the 2^nd order effect map in Figure S2 in Supplementary file).

While the spatial GSA shows similar patterns of the general GSA (Figure 4)—identifying disease and discharge rates as the dominant parameters—it provides a more nuanced view by uncovering geographic heterogeneity across the urban-rural divide. The discharge rate has a stronger impact in urban areas than in rural ones, primarily because health facilities are more densely concentrated in cities. Even a modest improvement in the discharge rate can free up a substantial amount of health resources, resulting in a significant increase in the level of demand that can be met. This spatial limitation compels individuals to place greater weight on travel costs when making decisions about seeking care. As a result, even a slight easing of travel barriers can enable rural residents to access substantially more healthcare resources, leading to meaningful improvements in service accessibility.

4.3. Temporal GSA

Using the statewide level of demand met as the model output, Figure 5 illustrates how the influence of each parameter evolved over two-week intervals. First, the disease rate consistently emerged as the dominant parameter in most time intervals because it directly controlled the magnitude of demand for healthcare, making it the primary driver of whether demand can be met. This is consistent with findings from both the general and spatial GSA.

Second, at the early phase of epidemic (prior to week 4 in Figure 2), the travel propensity, discharge rate and supply all had low first order effects but much higher total effects. At this phase, demand was still relatively modest and hospital supply was far from saturation. Consequently, no single parameter strongly governed system behavior; instead, model outputs were driven more by their combined interactions, particularly in conjunction with the disease rate (see the second-order effects in Figure S3 of the Supplementary file). For example, available beds (supply capacity) only matter if patients can reach them (travel), and discharge only matters if facilities begin to fill by demand (the disease rate).

As the epidemic accelerated and approached its peak (week 4–10 in Figure 2), the system moved toward saturation as demand continued to rise. At this phase, the discharge rate became far more influential than travel propensity and hospital supply capacity because it determined how quickly occupied beds could be turned over and made available for new demands. When facilities were nearly full, even small improvements in discharge could significantly increase effective capacity. In contrast, increasing travel mainly redistributed patients among already strained facilities, offering limited support to meet demand.

Following week 10, as the epidemic began to subside (Figure 2), demand declined while available healthcare capacity recovered. This shift provided individuals with greater flexibility in accessing services, leading to a renewed increase in the influence of travel propensity and a corresponding decline in the importance of disease and discharge rates.

4.4. Spatio-temporal GSA

This type of GSA allows researchers to examine parameters’ influence within specific local ZIP codes and short time periods. For clarity, we only visualized the parameter with the greatest influence as the primary driver of output variability. Figure 7 presents four representative time intervals that capture major pattern changes, while complete results for all intervals are provided in Figure S4 in the supplementary file.

Figure 7.

The most influential parameter by ZIP code for four representative time intervals. Color hue indicates the dominant factor, while the saturation represents the magnitude of its total sensitivity index.

During the early phase of the epidemic (Weeks 3–4), the discharge and disease rates had little impact. Instead, travel propensity was the primary driver because demand remained below facility capacity and individuals had flexibility to choose facilities for healthcare. The mobility-driven phase was brief: as the epidemic approached its peak (around weeks 5–6), its influence was quickly overtaken by the disease and discharge rates, which became comparably critical in the system. During this time period, demand for hospitalization surged substantially, and facility capacities were nearly fully utilized, reducing the relative importance of both travel propensity and supply. The disease-discharge pattern persisted through week 16, as the epidemic gradually waned, the influence of both disease and discharge rates had diminished. After week 16, the disease rate became the dominant factor in most rural areas, while the discharge rate continued to prevail in a few urban areas. The shift observed in rural areas likely reflected a slowdown in demand growth alongside a stable discharge rate, which together eased capacity constraints. As a result, even small changes in the disease rate could highly influence how effectively demand could be met. This pattern changed after week 35–36, when the epidemic was approaching its end. At this late stage, demand for hospitalization had stabilized or begun to decline. Consequently, the system was no longer driven mainly by new demand, but by how fast existing demand could be cleared. Therefore, discharge rate emerged as the most critical factor and maintained its leading influence through the end of the simulation.

4.5. Policy implications

In general, sensitivity analysis identifies which parameters are most influential to model outputs under uncertainty and thus suggests candidates for prioritization in resource allocation. Relevant to this research, different GSAs allow policymakers to optimize resource allocation over different locations and time periods.

The results from the general GSA indicate that the disease rate had the greatest impact on meeting healthcare demand and showed strong interaction with other model inputs across the state and throughout the study period. Therefore, statewide strategies should consistently prioritize resources to reduce transmission, such as vaccination programs and early detection, as these are likely to yield the largest overall impact. Moreover, the strong interactions between the disease rate and other parameters highlight the need for coordinated policies; for instance, investments in supply capacity or improvement in mobility are only effective when aligned with a certain level of disease spread.

Additionally, the spatial heterogeneity revealed by the spatial GSA implies that a one-size-fits-all approach is suboptimal. In urban areas, improving hospital discharge processes and care transitions may significantly enhance system performance. While in rural areas, encouraging travel propensity, e.g., converting schools, civic centers, or stadiums into temporary healthcare sites and providing free or subsidized transportation to hospitals, becomes more critical to controlling outcomes.

Unlike spatial GSA, temporal GSA provides guidance for short-term, rapid-response interventions because its findings are tied to specific time windows. The findings imply that the first four weeks might be the best time to improve mobility, given that travel propensity had a much higher total effect within this period compared to later periods. Similarly, the map series from spatio-temporal GSA enables local health agencies to tailor interventions for specific locations and time periods, supporting more precise and context-sensitive decision-making.

4.6. Limitations and future research

This study has several limitations. First, the proposed sensitivity analysis was only demonstrated with a system dynamics model, but it is independent of base models and can be adapted to any other space-time accessibility models, such as agent-based models. Second, the sensitivity analysis was limited to supply, demand, and travel-related factors. However, access to healthcare is a multidimensional system where many other factors also play important roles, such as income, ethnicity, and quality of services. Future research should include these factors into the system dynamics model to evaluate their specific impacts. Third, this study computed sensitivity indices independently across spatial slices, temporal slices, and spatio-temporal cells. We recognize that our estimation did not account for potential spatio-temporal autocorrelation in the model outputs, such as influences from neighboring ZIP codes or prior time steps. Future work can incorporate spatial lag and temporal lag variables into our analysis. Lastly, the findings are geographically and contextually specific to Florida, USA, and to acute disease outbreaks. Nevertheless, the methodology is scalable to other regions and medical contexts, such as chronic disease management, provided that disease incidence and facility discharge rates are parameterized accordingly. In short, while these limitations suggest avenues for more sophisticated research, they do not diminish the fundamental significance of the methodology presented.

5. Conclusions

Although population demand, facility supply, and travel propensity are widely recognized as key determinants of healthcare accessibility, their individual and combined influence remains insufficiently explored, particularly across different spatial and temporal contexts. The major contribution of this work is the development of a space-time GSA protocol for healthcare accessibility, implemented across four tiers: general, spatial, temporal, and spatio-temporal. This protocol is an extension of traditional GSA methods to the spatiotemporal domain, and is particularly suited for models with non-stationary outputs that vary over space and time. The case study demonstrated that no single factor universally dominated healthcare accessibility; instead, dominant drivers varied by location and phase of the epidemic. The proposed GSA protocol thus provides evidence-based guidance for designing interventions tailored to different planning horizons and geographic contexts (e.g., short-term versus long-term, local versus statewide).

Figure 6.

Bi-weekly sensitivity indices of four model parameters: a) the first-order index; and b) the total sensitivity index. The 2^nd order index can be found in the supplementary file.

Data Availability Statement

The data, codes, and instructions that support the findings of this study are publicly available at https://doi.org/10.6084/m9.figshare.31505704