A Novel Framework for Forecasting, Evaluation and Early-Warning for the Inﬂuence of PM 10 on Public Health

: PM 2.5 has attracted widespread attention since the public has become aware of it, while attention to PM 10 has started to wane. Considering the signiﬁcance of PM 10 , this study takes PM 10 as the research object and raises a signiﬁcant question: when will the inﬂuence of PM 10 on public health end? To answer the abovementioned question, two promising research areas, i.e., air pollution forecasting and health effects analysis, are employed, and a novel hybrid framework is developed in this study, which consists of one effective model and one evaluation model. More speciﬁcally, this study ﬁrst introduces one advanced optimization algorithm and cycle prediction theory into the grey forecasting model to develop an effective model for multistep forecasting of PM 10 , which can achieve reasonable forecasting of PM 10 . Then, an evaluation model is designed to evaluate the health effects and economic losses caused by PM 10 . Considering the signiﬁcance of providing the future impact of PM 10 on public health, we extend our forecasting results to evaluate future changes in health effects and economic losses based on our proposed health economic losses evaluation model. Accordingly, policymakers can adjust current air pollution prevention plans and formulate new plans according to the results of forecasting, evaluation and early-warning. Empirical research shows that the developed framework is applicable in China and may become a promising technique to enrich the current research and meet the requirements of air quality management and haze governance.


Introduction
The development of China's economy has brought about serious environmental problems, especially smog pollution, which is common in many cities in China, has a pernicious influence on public health and causes great economic losses and confusion in society. With the joint efforts of government, enterprises and the community, air quality can become much better and the influence of air pollution on public health can become increasingly smaller. However, one particular question remains to be answered: When will the influence of air pollution on public health end? PM 2.5 has attracted wide attention since it became known, while the attention paid to PM 10 has started to wane. PM 10 , which is considered as one of the most dangerous air pollutants, is defined as particulate matter with an effective aerodynamic diameter of less than 10 µm [1]. As we all know, particulate matter can infiltrate the respiratory system and cause respiratory diseases [2]. In addition, there is a correlation between PM 10 concentration levels and the number of hospitalizations for lung disease and heart disease [3]. However, due to natural resources, human activities, and chemical composition, some urban and rural areas report PM 10 concentrations above the standard level. Specially, what is more serious is that existing research shows that even if the concentration of PM 10 in the air is small, it will harm human health [4]. Therefore, in this context, to fill this research gap, this study takes PM 10 as the research object and attempts to answer the question-"When will the influence of PM 10 on public health end?"-using air pollution forecasting and health effects analysis, which present an extremely challenging task and can be considered a valuable area for further research.
To address air pollution forecasting issues, several models have been proposed to forecast the main pollutant concentrations and air quality index. For example, Xu et al. [5] proposed a hybrid system for forecasting daily concentrations of six air pollutants in three cities in China. Li and Jin [6] developed a novel forecasting model, which was applied in hourly pollutant concentration forecasting in Beijing, Tianjin, and Shijiazhuang, China. Similarly, Zhu et al. [7] presented a two-step hybrid model for forecasting daily average data of SO 2 and NO 2 in four cities in the region of central China. Liu et al. [8] devised an improved forecasting algorithm for air pollution forecasting based on the ensemble method. Hao and Tian [9] developed a multistep air quality forecasting model, which was applied to seven air quality signals and validated for cities in China. Xu [10] developed a model based on multiple kernel learning and weather data for forecasting air pollution PM 2.5 in Beijing. All the attempts indicate that hybrid models have become mainstream in forecasting air pollution and can be considered a promising tool to solve air pollution forecasting issues.
Furthermore, the review of the abovementioned studies shows that most of the previous studies are focused on air pollutant concentrations and air quality indices centered on hourly and daily data, which can provide the public with early warning information to protect them from the hazards of air pollution. However, the air quality management department cannot adjust their policies according to the forecasting results of a few hours or days in the future. Based on this, further studies focused on yearly data are a promising research direction to provide more valuable information and references for the related management department.
Although artificial intelligence models that exhibit better performance are widely used in many fields, such as mid-short-term load forecasting [11] and agricultural commodity futures prices prediction [12], they are not applicable to this study due to the limited data. In general, many other forecasting models are also not applicable. To develop an effective forecasting model, this study introduces the grey prediction theory into the forecasting model. Specifically, the first-order one-variable grey model, called GM (1,1), is an effective forecasting model that can address forecasting issues with limited data and has been widely employed in many forecasting fields [13]. It has three benefits, namely it is very practical, has convenient operation, and high forecasting accuracy [14]. As a result, the GM (1, 1) model was selected as the basic forecasting engine to solve the forecasting issues with limited data in this paper. However, in addition, the individual grey model not only ignores the significance of optimization but also only performs better in the first step and performs worse as the forecasting horizon increases. Considering the promising potential of hybrid forecasting models and to remedy these limitations, this study introduces one advanced optimization algorithm and cycle prediction theory into the traditional GM (1, 1) model to develop an effective model for multistep forecasting of PM 10 that can successfully obtain future changes in PM 10 , provide guidance for the public to avoid health damage and economic loss, and help policymakers establish efficient policies and determine the proper method to control air pollution.
Another significant issue is the influence of PM 10 on public health. How much losses have it caused in the past and future? To answer this question, the health economic losses assessment model was designed to evaluate the health effects and economic losses of pollution from PM 10 . Specifically, air pollution's health effects and economic losses can be evaluated from the following three aspects: losses from premature death due to illness, medical expenses due to illness, and losses due to lost work. The developed evaluation model not only helps the public understand the basic conditions of health effects and economic losses, but also provides the conditions for the public to avoid damaging health and causing economic losses in the future. Most importantly, politicians can adjust their policies for the future according to the results of the evaluation.
In summary, in this paper, by combining the newly proposed forecasting model and evaluation model, a novel hybrid framework is developed for forecasting, evaluation, and early-warning for the influence of PM 10 on public health. To verify the effectiveness of the developed hybrid framework of addressing air pollution issues and answering the research question, the PM 10 concentration data in Xi'an, China is employed in this case study. Empirical research shows that the developed framework is applicable in China and may become a promising technique to enrich the current research and meet the requirements of air quality management and haze governance.
The remainder of this study is organized as follows. Section 2 develops the proposed hybrid framework for forecasting, evaluation, and early-warning. Section 3 conducts an empirical study. Discussion of the influence of the threshold value of PM 10 is presented in Section 4. Finally, Section 5 concludes this paper.

The Developed Hybrid Framework for Forecasting, Evaluation, and Early-Warning
In this section, the hybrid framework for forecasting, evaluation and early-warning for the influence of PM 10 on public health is developed, which consists of two parts: a novel forecasting model for PM 10 and a novel assessment model for health economic loss.
2.1. Part I: A Novel Forecasting Model for PM 10

Grey Prediction Theory
Given a nonnegative time series where n ≥ 4, the detailed procedure of GM (1, 1) is summarized as follows: Step 1: The first-order accumulated generating operator is employed to obtain the 1-order accumulation sequence X (1) : Step 2: The background value array Z (1) is where Step 3: The GM (1, 1) model is where a is the developing coefficient and b is the grey action.
Step 4: The parametersâ andb can be obtained by the least-square algorithm and written as: (2) . . .
Step 5: The winterization equation of Equation (5) can be written as Equation (8), and its solution, i.e., the time response function, can be written as Equation (9).
Step 6: The forecasting results can be obtained based on the inverse accumulated generating operator, which can be written aŝ

Artificial Intelligence Optimization Arithmetic
The artificial intelligence optimization arithmetic called manta ray foraging optimization (MRFO), proposed by Zhao et al. [15] in 2020, was developed based on chain foraging, cyclone foraging, and somersault foraging strategies. Definition 1. Chain Foraging. Manta rays can identify plankton's position and swim to it. In the foraging process, manta rays form a foraging chain by lining up head-to-tail. All individual manta rays, except the first one, are updated according to the position of food and the ray in front of it, while the first ray is only updated according to the position of the food. The chain foraging can be described as follows: α = 2·r· |log(r)| (12) where X d i (t + 1) is the ith individual manta ray's position in the dth dimension at time t, X d best (t) is the position of the best solution thus far in the dth dimension at time t, r is a random vector in [0, 1], and α is a weight coefficient. Definition 2. Cyclone Foraging. In the cyclone foraging strategy, the individual manta ray not only swims towards the food along a spiral path, but also follows the one in front of it. The cyclone foraging can be described as follows: where β is a weight coefficient, r 1 is a random vector in [0, 1], and T is the maximum iteration number.
In addition, by randomly defining a new position as the reference position, the individual manta ray is forced to find a new position far from the current best position, which is designed to improve the exploration and enable MRFO to perform an extensive global search. The corresponding mathematical model can be described as follows: where X d rand is the reference position randomly defined in the entire search space and Ub d and Lb d are the upper and lower bounds in the dth dimension, respectively. Definition 3. Somersault Foraging. In the somersault foraging strategy, the food's position is considered a pivot. The individual manta ray tends to swim to and from, and around the pivot and somersault to a new position. As a result, they usually update their positions around the best position thus far. The somersault foraging can be described as follows: where r 2 and r 3 are random numbers in [0, 1], and S is the somersault factor that is equal to 2, which is defined to decide the manta rays' somersault range.
Pseudocode of the MRFO Algorithm 1.

Algorithm 1 MRFO
Output: X*-X with the best fitness Parameters: T-the maximum number of iterations N-the number of population F i -the fitness of i-th manta ray [L i , U i ] -the boundaries of the i-th variable X i -the position of i-th manta ray t-the current iterations d-the dimension of the optimized problem. 1 /*Set the basic parameters of MRFO algorithm. */ 2 /*Initialize the manta ray X i (i = 1, 2 . . . N) randomly. */ 3 FOR EACH i: Calculate the fitness F i for each manta ray 5 END FOR 6 /*Determine the best solution found so far X*. */ 7 WHILE (t < Iter Max ) DO 8 FOR EACH i: 1 ≤ i ≤ N DO 9 IF rand < 0.5 DO 10 /* Cyclone foraging strategy. */ 11 IF t/T > rand DO 12  IF F (X i (t + 1)) < F (X best ) DO 26 /* Update the position of X best, i.e., X best = X i (t + 1). */ 27 END IF 28 FOR EACH i: Although the traditional GM (1, 1) can directly provide multistep forecasting results, it may only perform better in the first step and performs worse as the forecasting horizon increases, which could ultimately lead to a poor forecasting performance. It is worth noting that the most recent data can describe the latest development trend and study the object's characteristics [16]. As a result, this study introduces the cycle prediction theory into the traditional GM (1, 1) model to develop an effective model for multistep forecasting, which can capture the latest development trends and features of the studied object and consequently improve the forecasting performance to a considerable extent. The detailed procedure of the GM (1, 1) model based on cycle prediction theory, denoted as C-GM (1, 1) model, is described as follows: Step 1: The first-order accumulated generating operator is employed to obtain the 1-order accumulation sequence X (1) as shown in Equation (1); Step 2: The background value array Z (1) as shown in Equation (3); Step 3: The parametersâ andb can be obtained by the least-square algorithm, and then the winterization equation and its solution, i.e., the time response function, can be obtained as shown in Equations (8) and (9), respectively; Step 4: The forecasting model can be obtained based on the inverse accumulated generating operator, which can be written as shown in Equation (10); Step 5: Cycle prediction theory is introduced to develop an effective model for multistep forecasting. Specifically, the developed forecasting model is applied to forecast the n + 1 th data point, denoted as y n+1 . Then, to utilize the most recent data to predict future data points, the first data point in X (0) is removed, and the forecasting results of the n + 1 th data point, i.e., y n + 1 , are appended into X (0) to reconstruct a new sequence, denoted as X n+1 : Accordingly, the reconstructed sequence can be considered as a new nonnegative original time series, and Steps 1 to 5 are repeated to obtain the forecasting results: Step 6: Determine if the termination conditions are met. If n + N ≥ m, the cycle prediction is terminated, and then forecasting results are output y i , i = n + 1, n + 2, m, where m is the length of the forecasted point. Otherwise, Steps 1-5 should be repeated until the termination conditions are reached. The proposed C-GM (1, 1) model is applicable and effective for multistep forecasting. However, there are two main parameters in the GM (1, 1) model, i.e., a and b, that are usually determined by the least square estimation method that may directly affect the forecasting performance. Most importantly, the solution of the least square estimation method might not be the optimal solution and may result in a poor forecasting performance or inability to obtain the optimal forecasting performance. An artificial intelligence optimization algorithm, inspired by Du et al. [17], Hao et al. [18], Tian and Hao [19] and Yang et al. [20], may be a promising approach for determining the optimal parameters that play a vital role in the development of an optimal model. Accordingly, the MRFO algorithm was employed to determine the optimal parameters in the GM (1, 1) model in the cycle prediction process, i.e., a and b, which can enhance the forecasting model's effectiveness. To obtain improvements in the forecasting performance, the commonly used evaluation metric, mean absolute percentage error (MAPE), was considered the optimization target to improve the forecasting accuracy.

Selection of Pollution Factors, Exposure Populations and Health Effects
Economic losses can be calculated after defining the pollution factors, exposure populations, and health effects. In this paper, the research object, i.e., PM 10 , is considered as pollution factor. The year-end permanent population were used as the exposed populations to haze pollution. Based on the data availability, the death mortality, respiratory disease outpatient rate, increase of emergency cases, restricted activity days, increase of cases of lower respiratory tract infection/asthma in children, increase of asthma cases and increased cases of chronic bronchitis are considered the health effects in this study.

The Newly Proposed Health Economic Losses Assessment Model
The economic losses caused by air pollution to human health include the following three aspects: losses from premature death due to illness, medical expenses due to illness, and losses due to lost work. The detailed calculation model can be defined as follows:

Definition 4. Losses from Premature Death Due to Illness
where N is the number of exposure populations, P is the change in premature death caused by increasing one unit of air pollutant concentration, n is the difference between the actual value and reference value of the pollutant concentration, a is the labor force ratio, S is the mean residual life, which is defined as 5 according to Zeng et al. [21], and G is the per capita annual salary.

Definition 5. Medical Expenses Due to Illness
where X i is the change value of ith disease due to the variation of pollutant concentration, C i is the average medical charge of ith disease, and r i is the morbidity of ith disease caused by increasing one unit of air pollutant concentration.
Definition 6. Losses Due to Lost Work. The losses due to lost work refers to economic losses caused by certain restrictions on work activities due to air pollution. Based on the research results in Cai [22], one restricted activity day is equivalent to 1/4 days of absence due to illness. The losses due to lost work can be calculated as follows: where A is the days of lost work due to pollution, G d is per capita daily wage, and D is the changes in restricted activity days caused by increasing one unit of air pollutant concentration.

Definition 7.
Total Health Economic Losses. According to the change value of the public health effect due to the variety of pollutant concentrations, the health economic losses caused by air pollutants can be assessed and the detailed model can be defined as follows: where L is the total health economic losses due to the current condition of air pollutants, L i is the health economic losses value of the ith public health effect, and n is the number of public health effects.

Study Area and Data Description
Xi'an, the capital of Shaanxi and the eastern gateway to China's ancient Silk Road, is a national historic and cultural city and is northwest China's largest central city. Its location is shown in Figure 1. Monthly PM 10 concentration data of Xi'an collected from March 2014 to February 2019 were used in this study, and were retrieved from the website of the China Air Quality Online Monitoring and Analysis platform (https://www.aqistudy.cn accessed on 1 October 2019). In general, the season has a large impact on the concentration of atmospheric pollutants. Therefore, in this paper, one year (i.e., four seasons) was divided according to the general division of the Northern Hemisphere and the actual climate change in China as follows: spring (March-May), summer (June-August), autumn (September-November), and winter (December-February).

Study Area and Data Description
Xi'an, the capital of Shaanxi and the eastern gateway to China's ancient Silk Road, is a national historic and cultural city and is northwest China's largest central city. Its location is shown in Figure 1. Monthly PM10 concentration data of Xi'an collected from March 2014 to February 2019 were used in this study, and were retrieved from the website of the China Air Quality Online Monitoring and Analysis platform (https://www.aqistudy.cn accessed on 1 October 2019). In general, the season has a large impact on the concentration of atmospheric pollutants. Therefore, in this paper, one year (i.e., four seasons) was divided according to the general division of the Northern Hemisphere and the actual climate change in China as follows: spring (March-May), summer (June-August), autumn (September-November), and winter (December-February). Based on this, the annual average value of the air pollutant concentration from 2014 to 2018 was calculated and is shown in Table 1. Meanwhile, the limit value of the air pollutant concentration in the national ambient air quality standards (GB 3095-2012) and the exceeding standard rate (ESR) are also presented in Table 1. Level 2 of the pollutant concentration limit was selected for PM10 in this study. The annual average concentration of PM10 exhibits a roughly decreasing trend year by year with an increase in 2016. The concentration of PM10 is the largest in the past five years (2014-2018), which indicates that PM10 was not effectively controlled in 2016. Fortunately, the concentration of PM10 was effectively controlled after 2016, dropping to 110.67 ug/m 3 and 99.17 ug/m 3 in 2018, respectively. However, the concentration of PM10 is still higher than the national standard annual average concentration. Specifically, the ESR value exhibits a roughly decreasing trend year by year but still exceeds the standard limit. As a result, Xi'an needs to continue to strengthen the control of PM10 emissions, while the public also needs to strengthen pollution prevention and health protection. Based on this, the annual average value of the air pollutant concentration from 2014 to 2018 was calculated and is shown in Table 1. Meanwhile, the limit value of the air pollutant concentration in the national ambient air quality standards (GB 3095-2012) and the exceeding standard rate (ESR) are also presented in Table 1. Level 2 of the pollutant concentration limit was selected for PM 10 in this study. The annual average concentration of PM 10 exhibits a roughly decreasing trend year by year with an increase in 2016. The concentration of PM 10 is the largest in the past five years (2014-2018), which indicates that PM 10 was not effectively controlled in 2016. Fortunately, the concentration of PM 10 was effectively controlled after 2016, dropping to 110.67 ug/m 3 and 99.17 ug/m 3 in 2018, respectively. However, the concentration of PM 10 is still higher than the national standard annual average concentration. Specifically, the ESR value exhibits a roughly decreasing trend year by year but still exceeds the standard limit. As a result, Xi'an needs to continue to strengthen the control of PM 10 emissions, while the public also needs to strengthen pollution prevention and health protection.  To develop an effective air pollution forecasting model, the grey prediction theory was used because of its desirable performance with forecasting issues with limited data. To date, the grey model has developed with many variants proposed based on similar modeling procedures of GM (1, 1), such as NDGM (1, 1) [23], NGBM (1, 1) [24], Grey Verhulst [25] and FANGBM [26]. The classical GM (1,1) model and its variants are widely employed in many fields, such as energy consumption [27,28], wind turbine capacity [29], and CO 2 emissions [30]. Since there are so many grey models, the selection of a basic forecasting engine is important for the effectiveness of the developed forecasting model. As a result, in this study, the GM (1, 1), NDGM [23], NGBM (1, 1) [24], Grey Verhulst [25], OP-NGBM (NGBM optimized by MRFO), and OP-FANGBM (FANGBM optimized by MRFO) were considered candidates for basic forecasting engines.
To evaluate the performance of the candidate models, the absolute percentage error (APE) and MAPE were selected, and are defined as follows: where x (0) (k) is the kth data in the original time series,x (0) (k) is the corresponding fitted or predicted value and n is the length of the time series. The benchmark of modeling accuracy evaluation by Lewis [31], which has been widely used in different forecasting fields, was employed in this study, and is presented in Table 2.  Table 3 provides the fitted results and predicted results of GM, NDGM, NGBM, Grey Verhulst, OP-NGBM, and OP-FANGBM for forecasting PM 10 . The MAPE values of GM, NDGM, NGBM, Grey Verhulst, OP-NGBM, and OP-FANGBM are lower than 10%, which indicates that the modeling accuracy evaluation results of all the models are highly accurate. Table 3 shows that the OP-FANGBM model obtains the best fitting performance for PM 10 . However, it does not follow that the OP-FANGBM model is more applicable than other grey models for forecasting PM 10 . In general, the forecasting performance of one model is evaluated based on the forecasting results of the out-sample. However, on the one hand, there are no out-sample data for model forecasting performance evaluation; on the other hand, this study focuses on developing an effective forecasting model for forecasting the future changes in PM 10 in the next few years. Therefore, in this study, the selection of a basic forecasting engine depends on the rationality of forecasting trends in the next few years, and the MAPE values of the fitted results were introduced as auxiliary means for the models with rational forecasting trends. For example, from the forecasting results of the different models in Table 3, the NGBM, Grey Verhulst, OP-NGBM and OP-FANGBM models present a clear downward trend with a high rate of decline. Combined with the actual situation of air quality, this is inconsistent with the actual trend of change. In addition, the NDGM forecast that the concentration of PM 10 will remain at 90 ug/m 3 is unrealistic. As a result, the NDGM, NGBM, Grey Verhulst, OP-NGBM and OP-FANGBM models are not applicable for forecasting future changes in PM 10 . Meanwhile, it can be seen in Table 3 that although it does not achieve the best fitting performance, the GM model not only obtains rational forecasting trends but was also evaluated as highly accurate according to Lewis' benchmark of modeling accuracy evaluation. In addition, comparison of the NGBM model and OP-NGBM model shows that the forecasting result of the OP-NGBM model is more rational than the individual NGBM model. That is, the basic forecasting model can be further improved to develop an effective model that will obtain more rational forecasting results. Finally, we can reasonably conclude that the GM (1, 1) model was more applicable than the other models. As a result, the GM (1, 1) model was selected as the basic forecasting engine and will be combined with other advanced techniques to develop an effective forecasting model for solving forecasting issues in this paper.

Forecasting Results and Analysis of the Developed Forecasting Model
To provide effective forecasting results of PM 10 in the future, this study developed a forecasting model based on the GM (1, 1), MRFO algorithm, and cycle prediction strategy. The fitting and forecasting results of GM (1, 1) and the developed model for forecasting PM 10 are listed in Table 4. Table 4 shows that the developed model obtains the best fitting performance for PM 10 . Specifically, the MAPE values of GM (1, 1) and the developed model for modeling PM 10 are 6.0324% and 4.2546%, respectively. As a result, we can reasonably conclude that the developed model performs better than the individual GM (1, 1) model in the fitting performance and forecasting future changes of PM 10 .  Figure 2. It shows a slightly decreasing trend from 2019 to 2025. According to the abovementioned analysis, the concentration of PM 10 is beyond the limit values from 2019 to 2021, which indicates that the influence of PM 10 on public health may end in 2022. As a result, Xi'an city should adopt more effective and persistent air quality control measures to control the emissions of PM 10 and try their best to end the influence before 2022.   Figure 2. It shows a slightly decreasing trend from 2019 to 2025. According to the abovementioned analysis, the concentration of PM10 is beyond the limit values from 2019 to 2021, which indicates that the influence of PM10 on public health may end in 2022. As a result, Xi'an city should adopt more effective and persistent air quality control measures to control the emissions of PM10 and try their best to end the influence before 2022.

Remark for the Performance of Different Models
The applicability of the GM (1, 1) model is discussed and approved by comparing the forecasting results of GM (1, 1) model with NDGM, NGBM, Grey Verhulst, OP-NGBM, and OP-FANGBM model. It should be noted that, under the optimistic situation of air pollution control, the annual average concentration of PM10 will decrease year by year, and the rate of decrease will become slower and slower. In other words, the annual average concentration level of PM10 is unlikely to drop rapidly, and it is also unlikely that it

Remark for the Performance of Different Models
The applicability of the GM (1, 1) model is discussed and approved by comparing the forecasting results of GM (1, 1) model with NDGM, NGBM, Grey Verhulst, OP-NGBM, and OP-FANGBM model. It should be noted that, under the optimistic situation of air pollution control, the annual average concentration of PM 10 will decrease year by year, and the rate of decrease will become slower and slower. In other words, the annual average concentration level of PM 10 is unlikely to drop rapidly, and it is also unlikely that it will remain almost unchanged for many years. Therefore, at the stage of selecting the basic forecasting model, the first consideration should be given to whether the model captures the possible and reasonable future change trend of PM 10 . Based on analysis in Section 3.2.1, only the GM (1, 1) model provides the reasonable trend in the future, which is selected as the basic model of the developed model. On the premise that the GM (1, 1) model can provide a reasonable trend, the research goal of this paper has changed from the rationality of forecasting trend to the superiority of forecasting performance. As a result, the C-MRFO-GM (1, 1) model is developed to forecast the annual average concentration of PM 10 from 2019 to 2025. Then the fitting and forecasting results of GM (1, 1) and the developed model are compared in Section 3.2.2. By comparing the GM (1, 1) model and the developed model, it can be observed that the developed model achieves the best results in terms of MAPE. Based on abovementioned analysis, we can safely draw the conclusion that the developed model can achieve effective forecasting of PM 10 from 2019 to 2025, which not only performs better than GM (1, 1) model in terms of forecasting results' accuracy but also exhibits significant superiority compared with NDGM, NGBM, Grey Verhulst, OP-NGBM, and OP-FANGBM model in terms of the forecasting trend's rationality.

Results of the Designed Health Economic Losses Evaluation Model
In this section, the evaluation of the health effects of PM 10 and the corresponding economic losses are divided into two parts as follows: evaluation for the past and evaluation for the future. This can help the public understand the basic conditions of the health effects and economic losses, and provide the conditions for the public to avoid damages to health and economic losses in the future. Most importantly, politicians can adjust their policies according to the results of the evaluation for the future.

Data Sources for Health Economic Losses Assessment
For the empirical study for Xi'an, China, the data source for the proposed health economic losses assessment model are as follows: (1)

Selection of Threshold Value of PM 10 's Health Effects
To evaluate the health effect of air pollution and the corresponding economic losses, the concentration threshold value of PM 10 should be determined. However, there is no standard for the threshold of air pollutant concentration in the research. In some studies, such as Li et al. [32], the standard is selected from the World Health Organization [33]. According to the related studies conducted by Li et al. [34][35][36], four baseline values of the annual concentration of PM 10 are considered as the background value and shown in Table 5. Interim target-1 (IT-1) equals the limit value of air pollutant concentration in the national ambient air quality standards (GB 3095-2012). Therefore, in the current situation in which interim target-1 (IT-1) is still not achieved, 70 ug/m 3 is selected as the threshold value of PM 10 . Table 5. Four annual mean concentration baseline levels of PM 10 .

Level PM 10 (ug/m 3 )
Interim target-1 (IT-1) 70 Interim target-2 (IT-2) 50 Interim target-3 (IT-3) The public health effects caused by air pollution and the corresponding economic losses from 2014 to 2018 were estimated based on the dose-response functions between the changes in PM 10 concentration and the health effects shown in Table 6 [21], and the final evaluation results are presented in Table 7. According to the evaluated results shown in Table 7, the detailed analysis is as follows: Table 6. Dose-response functions between the changes in PM 10 concentration and the health effects.

Heath Effect Ends
Changed (2) Under the baseline levels of PM 10 , the change values of the public health effects in 2018 were lower than those in the other four years. Furthermore, the total health economic losses caused by PM 10 from 2014 to 2018 were 16.9444, 16.3875, 23.4475, 15.2293, and 12.4900 hundred million Yuan, respectively. More specifically, the health economic losses in the past five years were 84.4987 hundred million Yuan. More details about the influence of PM 10 on public health can be seen in Table 7. The public health effects caused by air pollution and the corresponding economic losses from 2019 to 2021 were estimated and are presented in Table 8. In Table 8, Total I is the total public health effects and corresponding health economic losses from 2016 to 2020, which can be used to present the health damage from air pollution and the health economic losses conditions from 2016 to 2020. In addition, relevant decision makers can make policy adjustments according to the planning targets and the predicted values for the next two years to ensure the successful completion of the 13th Five-Year Plan (i.e., the plan, objectives, and their implementation for national economic and social development over five years from 2016 to 2020, here is the environmental protection related goals). Total II is the total public health effects and corresponding health economic losses from 2021 to 2025, which can be used to present the health damage from air pollution and the health economic losses conditions in China's 14th Five Year Plan (i.e., the plan, objectives, and their implementation for national economic and social development over five years from 2021 to 2025). Similarly, relevant decision makers can formulate a reasonable 14th Five Year Plan according to the forecasting results of public health effects and corresponding health economic losses from 2021 to 2025 to ensure the continuous improvement of air quality in the period of the 14th Five Year Plan. Total III is the total public health effects and corresponding health economic losses from 2019 to 2025, which can be used to present the health damage from air pollution and the health economic losses condition in the next few years.
The change values of the public health effects in 2019 show that the number of premature deaths was the smallest (1331), while the number of days of lost work was the largest (1,997,420); from the corresponding economic losses in 2019, it can be observed that the health economic losses caused by medical expenses was the smallest (1.5121 hundred million Yuan) and the health economic losses caused by delayed wages was the largest (5.1228 hundred million Yuan). The total health economic losses in 2019 were 10.5373 hundred million Yuan. Similar findings and analyses can be performed and determined for other years. The detailed evaluation results of each year can be seen in Table 8. Under the baseline levels of PM 10 , the change values of the public health effects and corresponding health economic losses in 2021 were lower than those in other years. Specifically, the results showed that the total health economic losses caused by PM 10 from 2019 to 2021 are 10.5373, 7.3338, and 3.2058 hundred million Yuan, respectively. In addition, it is worth noting that it is expected that there may be no health damages or health economic losses from PM 10 after 2021. In other words, the influence of PM 10 on public health may end in 2022.

Discussion of the Influence of the Threshold Value of PM 10
Under the baseline of the national standard limited concentration values, the influence of PM 10 on public health may end in 2022. However, if we select the baseline levels of PM 10 with lower concentrations, the average annual concentration of PM 10 will still impact human health and cause health economic losses. For example, by selecting four annual mean concentrations of PM 10 shown in Table 5 as the baseline, the total health economic losses caused by PM 10 10 show that under the baseline of IT-2, the influence of PM 10 on public health may end in 2026, while under the baseline of IT-3 and AQG, PM 10 will still pose a negative impact on public health and cause economic losses from 2019 to 2025.

Conclusions
This study began by posing the following question: When will the influence of PM 10 on public health end? To answer this question, by combining the newly proposed forecasting model and evaluation model, a novel hybrid framework is developed for forecasting, evaluation and early-warning for the influence of PM 10 on public health. These are the main contributions of this study. To verify the effectiveness of the developed hybrid framework to address air pollution issues and answer the research question, the PM 10 concentration data in Xi'an, China was employed in the case study. Furthermore, the results demonstrated that the developed hybrid framework is applicable in China and may become a promising technique that enriches the current research and meets the requirements of air quality management and haze governance. It should be noted that this study mainly focused on answering the question in China. As a result, the "replicability" of our work in the international context is not considered in this study. However, the empirical results prove the validity of the established research framework in forecasting, evaluation, and early-warning for the influence of PM 10 on public health. Therefore, we can safely draw the conclusion that the developed framework can be considered as an effective tool in the international context. Furthermore, considering the availability of data and the significance of internationalization, the international context research can be the subject of our future studies, which will be a worthwhile studying direction for the whole society.
Specifically, the new findings from this study that are different from the literature can be summarized as follows: (1) Based on the results of the empirical study, the question "When will the influence of PM10 on public health end?" can be answered as follows: The influence of PM 10 on public health may end in 2022 under the baseline of the national standard limited concentration values, but it will still pose a negative impact on public health and cause economic losses from 2019 to 2025 under the baseline of IT-2, IT-3 and AQG. Overall, the current situation is not very good, and Xi'an city should adopt more effective and persistent air quality control measures to control PM 10 emissions. (2) Different from most previous air pollution health economic losses studies that focused on PM 2.5 , the present study focused on PM 10 , which has been neglected in previous studies and can bridge the research gap in air pollution health economic losses. The experimental results show that the changes in health effects and health economic losses caused by PM 10 cannot be ignored, and people should consider emissions reduction and control of PM 10 .
(3) This study contributes forecasting, evaluation and early-warning to the research, which are new ideas and a new research framework. Specifically, forecasting can provide future changes in PM 10 , while evaluation can help the public understand the basic conditions of health effects and economic losses and also predict the future conditions for the public. Most importantly, politicians can adjust their policies according to the results of the evaluation for the future. To the best of our knowledge, most previous economic losses assessment studies only focused on assessing the economic costs of past disasters while ignoring the significance of evaluating the economic losses for the past and future. As a result, the presented research framework and ideas provide a theoretical reference and academic reference for future research.
In the future, the research framework and ideas based on forecasting, evaluation and early-warning can be extended and applied in other fields, such as storm surge disaster losses [38], e-commerce precision poverty alleviation benefit assessment [39], rainstorm disaster losses [40], earthquakes and flood losses [41] and impacts of haze pollution on the tourism industry [42]. (4) Most previous studies focused on health economic losses caused by air pollution in different areas and at different times. On the positive side, assessing past economic losses provides support for air pollution prevention and control. However, when will the influence of air pollution on public health end? This is a significant and neglected issue, which can be considered a new research direction. As a result, this study takes PM 10 as the research object and first poses the question: "When will the influence of PM 10 on public health end?" The answer is provided based on forecasting, evaluation and early-warning. (5) Another interesting finding is that the traditional grey model is more applicable than other grey models for forecasting PM 10 in Xi'an, China. In general, in the air quality forecasting field and other related forecasting fields, variants of the traditional grey model may perform better than the traditional grey model. For example, in Wu et al. [43], the GM (1, 1) model with fractional order accumulation performs better than the GM (1, 1) model alone. Different from previous studies, this study not only considers the fitting accuracy but also the rationality of the future development trend of things. It should be noted that the prediction of the future development trend needs to conform to the development law of things, which is obviously different from the training and testing process of the prediction model. (6) Wu and Zhao (2019) [44] employed an individual model named the fractional order accumulation GM (1, 1) model to forecast the number of lightly polluted days from 2017-2020, which proves the forecasting power of grey forecasting theory. Cycle prediction theory can capture the latest development trend and features of the studied object, while optimization can obtain the model's optimal parameters. As a result, cycle prediction theory and optimization can improve the forecasting performance to a large extent. Considering the advantages and disadvantages of grey forecasting theory, this study further develops the findings of Wu and Zhao (2019) and introduces cycle prediction theory and optimization into air pollution's health economic losses assessment and forecasting.

Data Availability Statement:
Publicly available datasets were analyzed in this study. Detailed data sources can be found in Sections 3.1 and 3.3.1.