In order to assess the epidemic risk state of hospitals in underdeveloped areas, it is necessary to first sort out the risk indicators that affect the changes in hospital epidemic risk. Therefore, this paper selected medical staff from five hospitals located in underdeveloped areas of China as the interviewees, with a total of 48 interviewees. These interviewees have varying years of work experience, including managers from different hospital departments, front-line medical staff, and epidemic prevention experts involved in COVID-19 prevention and control work between 2019 and 2022. This survey involved three rounds of consultation, with 48 questionnaires issued in each round. The expert positive coefficient of respondents in all three rounds was more significant than 0.9. Apart from the interviews and surveys, this paper also summarizes and analyzes the emergent problems and potential risks that hospitals face during major health events. This analysis draws on relevant literature and media reports of significant health events from the past decade, including literature related to the COVID-19 pandemic, influenza outbreaks, and endemic disease outbreaks; this paper also paid attention to the management announcements and logs released on the official websites of different district and county hospitals during the outbreak period, and sorted out hospitals' relevant internal management information in response to the outbreak. As mentioned above, this paper collected data from multiple sources, which can analyze the risk factors that affect hospital safety from different perspectives, and cross-validate the analysis results.

Through collection, this paper has collected over 30,000 words of various types of raw data. After collecting the above raw data, this paper intends to extract a set of available hospital epidemic risk assessment indicators from the raw data based on Grounded theory. Grounded theory is a qualitative research method aimed at continuously refining core concepts based on experience and data, and ultimately classifying and summarizing relevant concepts to construct a usable theory (27). Based on Grounded theory, this paper first encodes the raw data according to different sources, using the letter Q to identify data from questionnaires, using the letter I to identify data from literature and reports, and using the letter R to identify data from hospital management materials and announcement logs. After encoding, this paper eliminated semantic duplicates through expert discussion and analysis, and sorted out 234 non-duplicate data. This paper randomly selected 170 pieces of data for constructing the epidemic risk indicator system, and the remaining 64 pieces of data were used to test the theoretical saturation of the indicators (28). Next, through semantic extraction and induction, this paper extracted 35 initial concepts with concise semantics and clear descriptions from the selected 170 pieces of data. From the perspective of hospital risk management, these initial concepts were further classified and summarized, resulting in nine categories, namely nine epidemic risk assessment indicators, as shown in Table 1.

Finally, to verify whether the initial concepts and categories extracted are theoretically saturated, this paper extracted and summarized the remaining 64 data, and no new concepts or categories were found, indicating that the epidemic risk assessment indicators constructed in this paper are theoretically saturated.

The common risk assessment usually establishes a risk matrix from two perspectives: the probability of risk occurrence and the severity of risk losses (29, 30), thus defining the level of risk. The results obtained through the above assessment can intuitively and quantitatively describe the size of the risk. However, in practical situations, the epidemic risks faced by hospitals cannot remain unchanged due to the influence of various factors. If a fixed risk level is used to describe the risk, it is obviously insufficient to effectively describe the real hospital epidemic risk environment. Therefore, after sorting out the indicators of hospital epidemic risk through Grounded theory, in order to effectively describe the process of epidemic risk changes and achieve the assessment of risk changes, this paper defines four common discrete states S_n, n = 1, 2, 3, 4 from two aspects: the probability of risk occurrence and the severity of risk losses. The meanings of each state are as follows.

(1) S₁, risk disappearance state. This state is extremely safe, indicating that the risk is almost non-existent and the resulting losses can be ignored.

(2) S₂, risk potential state. This state is relatively safe, indicating that the risk of the epidemic has already existed but has not caused significant damage. At this point, there is a small probability that the risk will occur, and the resulting losses will have a small impact, which can be quickly recovered.

(3) S₃, risk critical state. This is a relatively dangerous state, indicating that the risk has clearly existed and the epidemic is on the verge of outbreak, causing certain losses. At this point, there is a high probability that the risk will occur and cause certain risk losses, which will take a long time to recover.

(4) S₄, risk outbreak state. This state is very dangerous, indicating that the epidemic risk has fully erupted and caused extremely serious losses, and the damage caused is difficult to recover.

These above four states cover the entire process of changes in epidemic risk. The probability that the epidemic risk belongs to state S_n is represented by P(S_n), and the epidemic risk state at time t can be expressed as Pt(Sn)={Pt(S1),Pt(S2),Pt(S3),Pt(S4)},∑i=02Pt(Sn)=1. It is known that in practical situations, the epidemic risk is always constantly changing due to the impacts of various risk indicators. It will randomly transition between the 4 states mentioned above, as shown in Figure 1.

In Figure 1, the four risk states are mutually reachable, together forming the random state space of epidemic risk (31). Under the influence of various indicators, the actual epidemic risk in the actual situation will be randomly changing, and the entire transformation process is a random change process. Therefore, in order to effectively measure the changes in the epidemic risk state, this paper intends to adopt the Markov chain prediction method to assess the epidemic risk state and its change. Markov chain have a mathematical definition and are classic theories in probability theory and mathematical statistics. It can effectively describe the random state of things and is suitable for predicting changes in the random state of things (32).

In order to effectively assess the random transition process of the epidemic risk state under the comprehensive influence of various indicators, this paper intends to use matrix to describe the random transition process of the epidemic based on Markov chain theory. As shown below.

The element S_n→m in the matrix represents the process of the epidemic risk transition from state S_n to S_m. The meanings of each element S_n→m are shown in Table 2.

After defining the epidemic risk state and its random state space, this paper will comprehensively assess the impact of each indicator on the epidemic risk state from two aspects: the probability of risk occurrence and risk loss. The level definition of the risk occurrence probability P(a_j) and risk loss L(a_j) for each indicator a_j are shown in Table 3.

Next, based on the definition of the four states of epidemic risk in this paper, the probability level P(a_j) and risk loss level L(a_j) of the risk occurrence are substituted into the risk matrix (33), which can intuitively and effectively distinguish different epidemic states, as shown in Table 4.

As shown in Table 4, the higher the P(a_j) and L(a_j), the higher the probability of risk occurrence and the greater the loss caused by the indicator. This indicator a_j will lead the hospital risk state to transition toward a more dangerous risk state. As mentioned above, it is only necessary to assess the probability level P(a_j) and risk loss level L(a_j) of each indicator, the comprehensive impact of each indicator a_j on the hospital's epidemic risk state can be determined. However, during the assessment process, due to the lack of expert experience, it is difficult to provide accurate judgments on P(a_j) and L(a_j) of a certain indicator, which can easily lead to inaccurate assessment results. To reduce the difficulty of expert assessment and ensure the accuracy of the assessment results, this paper proposes an epidemic risk state assessment method based on a risk matrix. As shown in Figure 2, experts only need to provide the value range of P(a_j) and the value range of L(a_j), thus the impact of indicator a_j on risk state can be assessed.

In Figure 2, P_max(a_j) represents the maximum level of risk occurrence probability for a_j, while P_min(a_j) represents the minimum level of risk occurrence probability for a_j.L_max(a_j) represents the maximum level of risk loss for a_j, while L_min(a_j) represents the minimum level of risk loss for a_j. The following concepts can be derived from Figure 2.

According to the above concepts, dividing the intersection of Square(a_j) and Square(S_n) by Square(a_j) can calculate the probability that a_j belongs to the risk state S_n, as shown in Formula (1).

In Formula (1), μSn(aj) represents the probability that a_j belongs to the risk state S_n. The larger its value, the greater the probability that a_j belongs to S_n, indicating a higher probability of the epidemic risk state transitioning to S_n under the influence of a_j.

As mentioned above, through the method proposed in this paper, experts do not need to provide an exact numerical value for the frequency level or loss severity level of each risk indicator a_j in the assessment process. Experts only need to provide the value range [P_min(a_j), P_max(a_j)] and [L_min(a_j), L_max(a_j)] for each indicator according to the definition in Table 3, thus can calculate the value of μSn(aj) according to Formula (1). μSn(aj) effectively reflects the impact of indicator a_j on the risk state of the epidemic. This method reduces the difficulty of expert assessment and effectively achieves the assessment of the impact of each indicator on the epidemic risk state.

It is known that μSn(aj) represents the probability that indicator a_j belongs to the risk state S_n. When μSn(aj) > 0, it indicates that under the influence of a_j, the epidemic risk state of the hospital may transition to S_n. Therefore, this paper intends to comprehensively assess the impact of a_j on the epidemic risk state of hospitals, and further assess the changes in the overall epidemic risk state of hospitals. As shown in Formula (2).

In Formula (2), P ′(Sn→m) represents the total probability of the epidemic risk state transitioning from S_n to S_m due to the comprehensive impact of indicator a_j. total represents the total number of risk indicators a_j. For example, when n = 1, the values of P ′(S1→1), P ′(S1→2),P ′(S1→3), and P ′(S1→4) can be calculated sequentially according to Formula (2). Finally, according to Formula (2, the following matrix can be calculated.

This matrix corresponds to the random state space of epidemic risk proposed in Section 2.2 of this paper, which describes the random transition probability of the epidemic risk state under the influence of various indicators. Next, normalize the elements in each row of the above matrix, and the Markov chain transition matrix of the epidemic state can be obtained. The matrix is shown below.

STM is the state transition matrix of epidemic risk. According to Markov chain theory, once the state transition matrix of epidemic risk is established, the stable state of things in long-term random changes can be predicted (34). The calculation formula is as follows.

In Formula 3, Pt(Sn) represents the epidemic risk state at time t, and Pt+k(Sn) represents the epidemic risk state at time t+k. k is the number of state transitions, and k > 0. According to Markov chain theory, when the value of k is sufficiently large or approaches infinity, Pt+∞(Sn) will tend to stabilize and no longer change. The risk state at this time is called the stable state of epidemic risk, denoted as P^(Sn). P^(Sn) is the state where the epidemic risk state is most likely to transition. It represents the change trend of the epidemic risk state under the comprehensive influence of various indicators in a long-term risk environment. Therefore, by calculating the P^(Sn), it will be possible to grasp the future risk trends of hospitals and effectively predict the future hospital epidemic risk state.

At this point, this paper proposes the concept of epidemic risk state, and combines risk matrix and Markov chain to propose an assessment method for epidemic risk state and its change trend. In subsequent chapters, this paper will use this method to assess the risk state and its change trend of hospitals in underdeveloped areas. The above methods were carried out in accordance with relevant guidelines and regulations, and did not involve experiments on humans and/or the use of human tissue samples.

It can be inferred from the assessment results of the risk state and its change trend in the three stages mentioned above.

(1) In stage t0, the value of P^t0(S2) is significantly highest, indicating that there is a high probability that the epidemic risk state of hospitals in the region will transition toward S₂ during non-epidemic stage. In the non-epidemic stage, these hospitals are in a relatively safe risk state, but there is already a relatively small epidemic risk in these hospitals.

(2) In stage t1, the high values of P^t1(S2) and P^t1(S4) indicate a high probability that these hospitals' risk state will transition toward S₂ or S₄ in the early epidemic stage. In the early epidemic stage, hospitals in the region faced significant risks and hidden dangers. The values of P^t1(S2) and P^t1(S4) are relatively close, indicating that these hospitals may transition toward the high-risk state of S₄ if there is a slight mistake at this stage.

(3) In stage t2, the P^t2(S4) value is significantly highest, indicating a high probability that these hospitals' risk state will transition toward S₄ during the epidemic outbreak stage. During the epidemic outbreak stage, hospitals in the region are facing extremely serious risks, with a high probability of suffering serious losses. The values of P^t0(S1) and P^t0(S2) are both small, indicating that if hospitals in the region do not make timely adjustments at this stage, there is only a small probability that they can recover to a safe state.

As mentioned above, in the t0 stage, hospitals in the region are in a relatively safe state, but there is always a potential small risk of the epidemic. In stages t1 and t2, there is a high probability that the epidemic risk state will transition toward a more dangerous state.

Next, in order to assist the hospital in reasonable risk management in different stages, this paper intends to use the proposed assessment method to compare the effectiveness of different risk management plans, identify key risk indicators that affect these hospitals' risk state change, and provide priority reference for risk management.

In stages t1 and t2, considering that the impact of risk loss in the short term is not easily changed in the actual risk control process, hospitals can only reduce the risk occurrence probability to a certain extent. Therefore, in the assessment process of each indicator control plan, this paper intends to reduce the minimum occurrence probability level P_min(a_j) and the maximum occurrence probability level P_max(a_j) by one level, respectively, to simulate different risk indicator control plans.

Finally, the proposed method was used to assess the risk state after different controls, and the results are shown in Tables 8, 9.

According to the assessment data shown in Table 8, if Pt1(S1)+Pt1(S2)>0.389, it indicates that the control of indicator C_j is effective in stage t1, which can enable the hospital to transition toward a safety risk state, as shown in Figure 4. By comparison, the following conclusions can be drawn.

(1) In the early epidemic stage, risk indicators that can improve these hospitals' risk state include: C₂, C₃, C₈, andC₉.

(2) In the early epidemic stage, risk control for C₁, C₄, C₅, C₆, or C₇ will not effectively improve these hospitals' epidemic risk state.

(3) In the early epidemic stage, compared to other risk indicators, risk control for C₂ and C₈ is the most effective way to improve the hospital's epidemic risk state. This indicates that in the early epidemic stage, hospitals should prioritize the training of epidemic prevention skills for medical staff and the management of public health in hospitals. Secondly, it is the risk control for C₃, namely the management of work rights, work responsibilities and performance assessment during the epidemic period. Finally, it is the risk control for C₉, namely strengthening the epidemic supervision and management in hospitals.

According to the assessment data shown in Table 9, if Pt2(S1)+Pt2(S2)>0.261, it indicates that the control of indicator C_j is effective in stage t2, which can enable these hospitals to transition toward a safety risk state, as shown in Figure 5. By comparison, the following conclusions can be drawn.

(1) In the epidemic outbreak stage, risk indicators that can improve these hospitals' risk state include: C₁, C₂, C₃, C₄, C₆, C₇, and C₉.

(2) In the epidemic outbreak stage, risk control for C₅ or C₈ will not effectively improve these hospitals' epidemic risk state.

(3) In the epidemic outbreak stage, hospitals in the region first need to carry out risk control for C₂ and C₁, that is, prioritize training on epidemic prevention skills and psychological awareness for medical staff. Secondly, it is necessary to carry out risk control for the C₃, namely strengthen the management of work rights, responsibilities, and performance evaluation during the epidemic period. Finally, it is also necessary to pay attention to the supply of emergency supplies in hospitals C₄, the preparation of emergency personnel C₆, and the management of public service facilities in hospitals C₇.

The next step is to analyze the risk control plan for non-epidemic stage t0. In order to provide a priority reference for the risk control of hospitals in the region, this paper uses the same method to reduce the minimum probability level P_min(a_j) and maximum probability level P_max(a_j) of each risk indicator by one level. In this stage, if the P_min(a_j) of a certain risk indicator is already level 1, it will not decrease. Finally, by assessing the risk state after different controls, the results are shown in Table 10.

According to the assessment data shown in Table 10, if Pt0(S1)+Pt0(S2)>0.688, it indicates that the control of indicator C_j is effective in stage t0, which can enable these hospitals to transition toward a safety risk state, as shown in Figure 6. By comparison, the following conclusions can be drawn.

(1) In the non-epidemic stage, risk indicators that can improve these hospitals' risk state include: C₁, C₂, C₃, C₄, C₅, C₆, C₇, C₈, andC₉.

(2) In the non-epidemic stage, risk control for C₅ is the most effective, indicating that in the non-epidemic stage, the preparation of emergency funds in hospitals is the most important for ensuring hospital safety. In addition, training on the psychology and awareness of medical staff C₁, the supply of emergency supplies C₄, and the preparation of emergency personnel C₆ are also important for ensuring hospital safety.

In summary, hospitals in underdeveloped areas should have different control strategies at different epidemic stages, that is, risk control for each indicator should have different priorities. By assessing the epidemic risk state and its change trend in different stages, scientific and reasonable risk control can be carried out (35). On the contrary, in the absence of effective assessment data, blind risk control may not be efficient and may even lead epidemic risk state to transition toward more dangerous state.

The method proposed in this paper takes into account the randomness and uncertainty of epidemic risk (36), viewing epidemic risk as a stochastic process under the influence of various risk indicators, and defining four random states of epidemic risk, achieving dynamic assessment of epidemic risk status and its change trend. Compared to general static risk assessment methods, this method establishes a random risk state space for the epidemic based on Markov theory, which is closer to the real epidemic risk environment. The assessment results can more effectively reflect the real epidemic risk situation in different periods, and the assessment results provided have higher support for decision-making.