Introduction

Global public health emergencies (PHEs), such as pandemics, challenge urban healthcare systems1. The recent COVID-19 pandemic exemplified the critical importance of safeguarding healthcare workers and controlling disease spread by ensuring the provision of adequate medical supplies, especially personal protective equipment (PPE)2,3. PPE shortages in many countries adversely affected pandemic prevention and control work4. However, the rapid surge in medical resource demand during such crises often leads to shortages, which exacerbates the already complex situation5,6. PPE scarcity compromises the safety of frontline workers, undermines the effectiveness of public health interventions, and potentially prolongs outbreak duration and severity. Therefore, effective PPE supply is vital for effective urban PHE governance7.

During a pandemic, healthcare workers, patients, and residents all require PPE3. However, effectively allocating PPE to maximize pandemic containment, especially when there are PPE shortages, requires research. O’Leary8 estimated the PPE demand for doctors working in pediatric emergency rooms during the COVID-19 period, which provided a basis for PPE allocation strategies, and Hu et al.9 developed a PPE allocation algorithm that could equitably and effectively distribute PPE during PHEs. However, to date, there has been no research into the prioritization of groups with different virus exposure rates during urban PHEs or on the most effective PPE allocation strategies to gain better control over pandemic spread.

Taking the 2020 COVID-19 outbreak in Wuhan as a case, this study used system dynamics (SD) modeling combined with the susceptible, exposed, infective, and recovered (SEIR) model to explore an optimal PPE allocation strategy for pandemic emergencies.

SD is a widely used pseudo-continuous modeling and simulation approach to holistically analyze complex, interdependent, non-linear systems10. By updating the variables in small time increments, providing positive and negative feedback and time delays, and structuring interactions and control, SD can solve simultaneity (mutual causation) problems. Therefore, because SD can integrate conventional compartmental infectious disease models into more comprehensive structures, it can strategically assess potential policy interventions11.

Many studies have established COVID-19 SD simulation models for infection predictions, policy assessments, and social impacts12. For example, Kumar et al.13 developed an SD model based on SEIR to examine the influence of lockdown and social distancing measures on behavioral conduct, and Abdolhamid et al.14 used an SD simulation to analyze the impacts of citizen behavior, contact reduction, infected isolation, and public quarantine on disease spread.

Therefore, this study extends previous research on the supply and use of PPE to a COVID-19 SEIR model to identify the impacts of various supply and distribution strategies on disease control effects when there is insufficient PPE at the beginning stage of a pandemic, that is, this study provides a test platform for when there is insufficient PPE resources in early urban PHE stages and offers evidence-based PPE allocation and policy development guidance.

Case Study

COVID-19 is a highly transmissible disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)15. Since December 2019, the COVID-19 outbreak rapidly evolved from a regional health issue to a global crisis, which brought extraordinary challenges to city healthcare systems16 and highlighted the lack of global health system readiness to deal with PHEs.

As SARS-CoV-2 2019, which was known globally as COVID-19, spreads from person to person through close contact15, PPE, such as masks, can reduce the risk of infection. Therefore, an adequate PPE supply is essential to curb the early spread of potential pandemic viruses such as COVID-1917,18.

By the beginning of 2020, more than 10,000 Chinese people had become infected with COVID-19, which had initially appeared one month earlier in Wuhan, China19. Because of its sudden appearance, Wuhan was short of needed medical supplies, especially essential PPE such as facemasks20, which meant that many people, especially health workers, did not have appropriate protection21. As COVID-19 can be transmitted by mildly ill or even asymptomatic people (Rothe et al.22), the lack of effective PPE masks significantly increased the spread. This background provided the appropriate research cases and data support for this study. Therefore, this study examined the mask distribution in the 2020 COVID-19 in Wuhan as a case study to establish a SEIR-based SD model to study the PPE distribution problem and simulate the impacts of different PPE allocation strategies on the pandemic development trends.

Data and methods

This section reviews the SD approach and outlines the data collection, analysis procedures, model testing, and model validation.

SD model development

As shown in Fig. 1, empirical SD research comprises four consecutive steps23): (1) systems analysis; (2) development of the causal loop diagram (CLD); (3) creating a stock and flow diagram (SFD); and (4) conducting a simulated system analysis.

Fig. 1
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Model development algorithm.

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System analysis

The traditional SEIR model is suitable for modeling the COVID-19 pandemic spread13. SEIR is a compartmentally-based model that was developed to study the spread of infectious diseases24. The model divides the population into four compartments: (i) susceptible, (ii) exposed, (iii) infectious, and (iv) recovered25.

People in the infected class can infect other people. Based on the SEIR model, the COVID-19 transmission changes that occur in populations are shown in Fig. 2. As the Wuhan policy at the beginning of the COVID-19 outbreak involved population isolation, we also included this in the model.

Fig. 2
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SEIR COVID-19 transmission.

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Casual loop diagram (CLD)

To provide easier interpretation by development communities, the first step in SD analysis is to develop a CLD or ‘system map’, which shows the important variables and their respective causal links26. In this study, the variables we included were actor behaviors, actor relationships, system conditions or states, and interventions that could change the system27.

The high-level model causal loop diagram is shown in Fig. 3, in which the resource variable ‘masks’ was added to the traditional SEIR model to consider the interactions between mask availability and the other variables.

Fig. 3
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Wuhan COVID-19 SEIR model CLD.

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The CLD feedback loops are a simplified representation of the relationships between the key variables28. There are two fundamental feedback loops: reinforcing loops (marked R) and balancing loops (marked B). In a reinforcing loop, a small deviation in one variable becomes amplified through the loop, which results in exponential growth or decay, while in the balancing loop, a small deviation in one variable becomes reduced through the loop, which results in behaviors that approach equilibrium29.

The CLD shown in Fig. 3 has one balancing loop and one self-reinforcing loop. The self-reinforcing loops reflect the increase in the infected; as the infected proportion increases, the contact rate between the susceptible and infected also increases, which leads to a further increase in the infected. The balancing loop indicates that when mask wearing increases, mask consumption increases, and infection decreases, which reduces the number of exposed and infected.

This model, which was developed from a PPE distribution perspective, has several variables and constants that holistically characterize the system behavior. The model boundaries were set so that the model incorporated the impact of PPE on the spread of infectious diseases. Based on the model boundaries, the model variables were classified into three main groups: endogenous, exogenous, and excluded. The endogenous variables influence system behavior and are also influenced by it, and the exogenous variables influence system behavior but cannot be influenced by it; however, because the effects of the excluded variables on the model were negligible, these were not considered.

Stock and flow diagram (SFD)

The SFD distinguishes each variable and describes the system elements and overall framework. Intuitive symbols depict the logical relationships between the elements and explore the system’s feedback and control rules30. Based on the CLD, the resulting SFD is shown in Fig. 4.

Fig. 4
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Wuhan COVID-19 SEIR model SFD.

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COVID-19 appeared in Wuhan, China, at the end of 201919. To curb the pandemic spread, Wuhan City implemented a lockdown from January 23 to April 8, 202031. During this period, there was a serious PPE shortage of masks, goggles, and protective clothing. Based on Wuhan’s prevention and control strategy, we classified the urban residents into three categories: (i) medical staff, for whom the shortage of masks greatly increased their infection risk; (ii) out-of-home citizens who had to maintain the basic city functions and had to work outside, such as water and electricity company and logistics employees; and (iii) citizens who had to stay at home in compliance with the pandemic prevention and control policies.

Because COVID-19-diagnosed patients were promptly isolated in separate hospital wards until they recovered, the risk of infection for categories (ii) and (iii) was mainly latent patients and the risk of infection for category (i) was primarily from infected individuals. Due to the weak impact, this model did not consider any cross infections between the suspected cases and hospital patients.

The differences in the way masks were worn (such as correctly distinguishing the front and back, and strictly covering the mouth and nose) also had a significant impact on the protective effect32. Therefore, medical staff wearing masks were deemed to have better protection than the two resident types. These factors were considered in the parameter settings.

Data collection and parameter settings

Both partial and full model calibration require time series data for several variables33; therefore, precise time series data were needed to develop an effective COVID-19 SEIR SD model and test the model parameter accuracies. The required data were:

  1. (i)

    Time series data on the number of infections, the recovered cases, and deaths;

  2. (ii)

    The number of urban residents, medical staff, out-of-home citizens, and at-home citizens;

  3. (iii)

    Relevant COVID-19 pandemic SEIR model parameters, such as infection rates, recovered rates, and death rates;

  4. (iv)

    Mask inventory and supply speeds.

To obtain the needed data for (i), we used a web crawler to crawl the number of COVID-19 infections, recoveries, and deaths in Wuhan each day from January 23, 2020, on the DXY website (URL: https://open.dxy.cn/ ), which is China’s authoritative medical data service and support platform that provided real-time pandemic data updates from the beginning of the COVID-19 outbreak. In July 2020, the research team was invited to review the PPE supply activities in Wuhan, which provided us with a rare opportunity to examine the COVID-19 SEIR system and obtain primary data for (ii) and (iv). To gather the data for (iii), we reviewed existing research. He et al.34 applied particle swarm optimization to estimate the COVID-19 SEIR system parameters34 and to estimate the parameters, Saikia et al.35 fitted the COVID-19 diffusion trend in India using a SEIR model combined with historical data. Based on these research findings, we determined the parameters for the data for (iii).

Other data in the model (such as urban population and medical staff) were obtained by consulting government websites and statistical yearbooks. The model took 0:00 on January 23, 2020, as the simulation starting point, with each simulation step being 1 day. The initial values of the external variables after preprocessing in this model are shown in Table 1.

Table 1 External variables.
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Model validation and testing

Several test methods have been proposed to evaluate SD model validity36,37,26. This section discusses the tests most used in SD literature and presents the proposed model’s application results38,39,40,41.

The key model test assumptions were as follows.

  1. (1)

    The city is locked down, and the total number of people remains unchanged during the simulation period. All infected in the city are treated in isolation, and no cases are exported or imported. Due to the lockdowns implemented in many cities around the world during the COVID-19 pandemic period42,43, this assumption is also universally applicable.

  2. (2)

    Since the COVID-19 vaccine began to be approved for use at the end of 2020, this model does not consider vaccines or immunity.

  3. (3)

    Wuhan established many COVID-19 isolation wards and makeshift hospitals and had strict testing and isolation measures. Therefore, this model does not consider the cross-infection of suspected patients in hospitals.

Behavior reproduction test

We used model calibration to test the ability of the model to replicate observed behavior by comparing the simulated model behavior against actual available time series data44,45. Model calibration drives the real-time series input data through the model structure and compares the simulated output behavior with the associated time series data for the output, which is an essential step in the empirical analyses of SD models. In this study, the simulated results, in which the infected population and number of deaths were taken as the core index, were compared with the actual data obtained by the web crawlers.

Fig. 5
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Comparison between the model output for reported and simulated infected population count.

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Fig. 6
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Comparison between the model output for reported and simulated deaths.

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Figures 5 and 6 show that the curve trends for both the simulated and reported results were roughly the same, which indicated that the simulation results were consistent with the actual results and within an acceptable error range. About two weeks after the COVID-19 outbreak, the Chinese Health Commission confirmed the human-to-human transmission, after which Wuhan’s prevention and control efforts were strengthened. We designed a table function to quantify the prevention and control effort factor; however, due to quantification subjectivity, there was a slight error between the simulation and reported results, but this was deemed to be within an acceptable range.

Extreme conditions test

To determine whether the model behaved properly when extreme values, such as zero or infinity, were assigned to a given variable, an extreme condition test was conducted to evaluate the model’s capability in extreme conditions37. Extreme condition tests can be implemented by directly inspecting the model equations or by running a simulation model46. In this case, we implemented both approaches.

Fig. 7
figure 7

Extreme conditions test for 0 contact rate.

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Fig. 8
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Extreme conditions test for ∞ contact rate.

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Figures 7 and 8 show the infected population count when we respectively set the contact rate to zero and infinity. Figure 7 shows that when the contact rate is 0, the existing infected recover (or die), and as the other citizens do not come into contact with these infected individuals, there are no new infections. The results in Fig. 7 are consistent with this inference. Figure 8 shows that when the contact rate is infinite, the pandemic rapidly spreads, and all residents eventually become infected. As the infected recover (or die), the numbers gradually decrease. Therefore, the results shown in Fig. 8 are consistent with this inference.

In summary, the model developed in this article passed the extreme condition testing.

Results and discussion

Simulation results under different priority strategies

This section discusses the simulation results for the number of COVID-19 infections and deaths during the Wuhan closure period (January 23 to April 8, 2020) under different PPE supply priorities, each of which is shown in Table 2. Due to the much lower virus exposure rate for at-home citizens compared to the other populations in the system, we set the PPE supply priority for at-home citizens to the lowest level to reduce the required number of simulations.

Table 2 Simulation results for different PPE supply priority strategies.
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The simulation results for the currently infected population are shown in Fig. 9. The results show that when masks are prioritized for out-of-home citizens (strategies 5 and 6), the number of infections and deaths significantly increase, which may be due to insufficient medical protection for medical staff, resulting in a large number of medical staff infections.

Fig. 9
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Simulation results for the currently infected population.

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Fig. 10
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Simulation results for infection rate I.

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The results in Figs. 10 and 11 confirm this point. Infection rate I and infection rate II respectively represent the number of medical staff with masks and those without masks who become infected with COVID-19. The strategy 5 and 6 curves are significantly higher than those of the other strategies.

Fig. 11
figure 11

Simulation results for infection rate II.

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With the strict implementation of pandemic prevention measures, as confirmed patients are quarantined, only medical staff come into contact with them. Therefore, prioritizing mask allocations to both medical staff and infected patients can significantly reduce the number of medical staff infections and reduce the total number of infections. As can be seen from the Figs. 10 and 11, strategies 1 and 3 prioritize mask supply to medical staff and patients, which significantly reduces the number of medical staff infections and minimizes the number of infections. Therefore, reducing the number of medical staff infections is crucial in controlling the total number of infections. Strategy 4 also prioritizes healthcare worker mask supply, which also results in a relatively low number of infections; however, the effectiveness is slightly worse than strategies 1 and 3.

However, as medical staff also come into contact with out-of-home citizens and suspected infectious patients, the medical staff incubation period can increase their risk of infection. Therefore, prioritizing medical staff mask supply followed by infected individuals and out-of-home citizens (strategy 3) can reduce this risk and ensure that infected medical staff have a lower risk of infection before diagnosis. Therefore, the final number of infections and deaths in strategy 3 is the lowest.

Simulation results for different mask replacement frequencies

This section examines optimal mask supply priorities for strategy 3; medical staff – infected individuals –out-of-home citizens; and sets three different mask replacement frequencies: (1) best frequency - replace every four hours; (2) general frequency - replace every eight hours; (3) worst frequency - replace once a day. With a decrease in the mask replacement frequency, the effectiveness of masks in preventing the spread of COVID-19 reduces from 91% to about 69%15.

Based on the different mask replacement frequencies, we set three strategies: (1) optimal mask replacement frequency; (2) general replacement frequency; if there is a mask inventory surplus, increase the mask replacement frequency to the optimal level first for medical staff, then for infected individuals, and finally for out-of-home citizens; and (3) supply masks at the worst replacement frequency; if there is a mask inventory surplus, increase the mask replacement frequency to the general frequency first for medical staff, then for infected individuals, and finally for out-of-home citizens, and if there is still a mask inventory surplus, increase the mask replacement frequency to the optimal level in the same order.

The simulation results are shown in Figs. 12 and 13. The effect of strategy 2 is significantly better than the effect of strategy 1, and the effect of strategy 3 is slightly better than the effect of strategy 2. Therefore, in the early stages of a pandemic outbreak, prioritizing the availability of PPE for every susceptible individual is more important than ensuring the most scientific and effective PPE replacement rate.

Best practice scientific mask replacement frequency is often based on laboratory conditions and assumptions. The effectiveness of masks in blocking pathogens decreases over time and wearing masks for an extended time can lead to microbial accumulation and increased humidity, which reduces the mask’s protective effectiveness. However, in real situations, especially when resources are limited, these best practices need to be adapted. Early in a pandemic when masks are in short supply, ensuring everyone has access to at least some level of protection may be more important than strictly adhering to replacement frequency. The logic behind this strategy is to reduce the overall transmission risk across the community rather than only maximizing the protective effects for single individuals.

The strategy’s effectiveness depends on a variety of factors, such as public knowledge about mask reuse, cleaning methods, and the actual community spread of the virus. However, the results in Fig. 13 show that flexible adjustments to supply replacement can reduce the number of pandemic deaths by more than 20%. In any case, this trade-off underscores the importance of having a flexible response and optimal resource allocation during a public health crisis.

Fig. 12
figure 12

Simulation results for the infected population with different mask replacement strategies.

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Fig. 13
figure 13

Simulation results for the accumulated number of deaths with different mask replacement strategies.

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Conclusions

This study explored the impact of different PPE supply strategies on the effectiveness of pandemic prevention and control in the early stages of a pandemic when the PPE is scarce. The following conclusions were made based on the results.

  1. 1)

    The PPE supply strategy during a pandemic can be modeled using an SD model. The SD model developed in this work allowed for pandemic prevention and control forecasting and measurement under different supply strategies. The proposed SD modeling approach was developed for a real-world case study; the 2020 COVID-19 situation in Wuhan, China.

  2. 2)

    Ensuring that medical staff are not infected is vital to curbing the early spread of a pandemic. Therefore, to minimize the number of infections and deaths, priority should be given to distributing PPE to medical staff, followed by infected individuals, out-of-home citizens, and finally at-home citizens.

  3. 3)

    When PPE is insufficient, priority should be given to ensuring every resident has available PPE, rather than ensuring the most effective PPE replacement frequency for medical staff or infected individuals.

Based on the above-mentioned simulation results, some policy suggestions are given to provide a PPE supply reference in similar pandemic situations. The SD model can also be employed to simulate changing conditions for other parameters, such as infection rate changes.

  1. (1)

    To effectively reduce pandemic transmission speeds and alleviate medical protection material supply pressures in the early stages of a pandemic, government medical departments should prepare contingency plans and strengthen medical protection material reserves.

  2. (2)

    To ensure the most effective supply strategies during a pandemic, real-time inventory and in-transit PPE statistics are needed.

  3. (3)

    When there are PPE shortages, ensure that every susceptible individual has PPE available and increase the surplus PPE replacement frequency based on the priorities outlined in conclusion (2).

This SD simulation for PPE allocation strategies has implications for urban resilience governance during PHEs. First, SD simulations can be employed to assess and optimize emergency medical supplies to ensure that emergency supply distribution is rationally prioritized. To achieve this, policymakers could develop effective emergency material reserve plans with certain redundancies. Second, after formulating optimal material distribution strategies, public participation, non-governmental organization involvement, and pandemic prevention and control policies could also be optimized and adjusted. Third, PPE priority allocation strategies also have reference value for medical staff, civil servants, volunteer deployment strategies, and dynamic urban pandemic governance systems during PHEs.

To the best of our knowledge, this research is the first to apply SD modeling to investigate the impact of the PPE allocation on pandemic prevention effectiveness. However, as this was exploratory research, there were several limitations. First, to simplify the model, we only considered the scarcest PPE materials in the 2020 COVID-19 in Wuhan, which were masks. Other PPE, such as protective clothing and goggles, were not included in the model. In addition, the SD model masks were not classified, primarily because it is still controversial whether the N95 mask is better than surgical medical masks in preventing COVID-19 infections47. Third, this study took initial-stage COVID-19 outbreak data from Wuhan as an example. As Wuhan had adopted a strict policy of closing the city at this stage, whether the conclusions of this study can be applied to a wider range of pandemic outbreaks needs further confirmation.