The impact of understaffing on delaying early-stage SARS-CoV-2 outbreak detection

Background Having a minimum number of workers in medical services is widely regarded as a key component of disease prevention. However, with the delay in confirming cases of SARS-CoV-2, the understaffed medical providers informed late and the virus has rapidly spread nationally. This study, based on the Dempster-Shafer theory method and Evidential Reasoning, assesses the risks posed by understaffing for the SARS-CoV-2 outbreak. The findings examine six (6) factor risks and show that the understaffing risk in 2019 was 0.14% in magnitude in Wuhan, compared to 0.27% in Shenzhen. When ranking understaffing risks from low to high, the findings show that they increased from 3.979 to 3.983% and from 3.998 to 4.002% in Wuhan and Shenzhen, respectively. risk

Introduction SARS-CoV-2, which includes similar symptoms of SARS-CoV-1, was discovered in Wuhan at the end of 2019 [1]. Before medical workers officially informed China's population, the World Health Organization (WHO), and the rest of the world, the disease had already spread from Hubei province to other parts of China. The delayed response in Wuhan allowed the infection to spread and death count to rise. Once Chinese authorities acknowledged the severity of the outbreak, the government began to train 35.000 medical workers, include military health workers to assist in Shenzhen and Wuhan city, the epicenter of the outbreak.
Seven thousand other medical workers from (16) provinces assisted in 16 other cities and prefectures in Hubei. On March 16, Ruiyun Li. et al., [2] highlighted the importance of detecting asymptomatic SARs S-CoV-2. This outbreak is similar to 2002-2003 pandemic, where hospitals in Guangdong province were understaffed and the health care system in other cities in China was collapsing. 1 Limited medical services will not protect the population.
Instead, are dealing with secondary challenges such as complacency and; low morale. Therefore, it is time to learn from our mistakes so that we can improve conditions in hospitals to ensure the safety of populations in China. During the 2002 SARS-CoV-1 outbreak, people experienced similar symptoms, including fever, cough, and respiratory [3,4]. It is not surprising that there are similar challenges with SARS-CoV-2, as there were in 2002. Now as then, understaffed medical facilities continue to be a crutch to the healthcare system in the majority of Chinese cities. With schools, universities, childcare centers, supermarkets, stadiums, and other places for mass gathering closed, many of China's cities became ghost towns. And, the population relies on the hard work of health workers to cure the virus and allow them to return to normal life. This study following philosophy who states that [5]: There is no longer the feeling of being working where burnout governs human being.
Under workload must be respect instead of over workload. If not, multiple errors in work and injuries or disasters occur. And, the consequences are considerable.
Therefore, we will estimate how understaffed hospitals increase the risk of spread in Wuhan and Shenzhen by using the Dempster Shafer Theory (DST) and its Evidence Reasoning approach (ER).
Understaffing increases the risk of workplace injury Scholars highlighted the fact that the lack of staff at work leads to incapacity of doctors or other workers in the hospitals. 5 However, not having enough people on duty can be hazardous in a variety of public hospitals and clinics [6]. Employee does gets rewards for overloaded work. In case the rewards monetary may not satisfy the requirement of workers, work conflicts could also rise [7]. All these working conditions put workers into psychological problems and then potential disasters are no longer well controlled by workers in services, which in turn could cause injuries [8]. As an example, the decrease in disease prevention is observed in Iraq while understaffing is sustained, with population and immigration growing up [9]. Especially, in SARS-CoV-1, 40% of understaffing was not able to prevent disease [10].
On the other hand, understaffing leads to certain health workers fear-driven absenteeism [11], patients health workers virus transmission [12,13,14], and succumbing of staff during their duty [15]. Additionally, medication errors occurred in hospitals are mainly caused by lack of personnel, which is associated with inadequate patient supervision and no regularly reporting of daily patients medical [16,17,18]. Sometimes, public health workers require additional hands from hospitals and clinics which experience high inpatient and outpatient visits to avoid risk of injury and illness [19]. Having enough people to perform tasks helps prevent long-term illness among workers as well as any immediate hazards or disasters, which in turn may help employers drive productivity and increase revenue [20].

Understaffing may result in accidents
Inadequate staffing can become a liability for employers if it continues over a long period of period. Recent research published in the Journal of Advanced Nursing (JAN) found an increased workload and a decrease in ability to perform among nurses related to accidental organ failure [21]. Reducing the number of employees to the lowest level of facility negative outcome [22]. As example, twenty-six (26) countries affected by SARS-CoV-1 epidemic have experienced undernumbered medical staff. Besides, a small number of cases have occurred as a result of laboratory accidents in Guangdong [23]. SARS-CoV-2 outbreak has caused accidents among health workers during their work time because of lack of physicians in the USA [24]. Additionally, human error is inevitable in medicine, especially in health care crises where understaffing is high remarked and both patients and physicians receive shocks [25,26,27]. Moreover, Worldwide health care disaster costs 20 to -40% of the budget due to understaffing and physician errors on patients [28]. Lack of personnel is the cause of unsafety or nonrespected desire of patients by nurses. Which was reflected by the case of missing nursing care or omission errors in Saudi Arabic public hospitals [29]. Long-term understaffing increases errors, omissions, or damages and has negatively impacted workers health [31,32].
Lapses in following industry regulations or proper safety precautions around machinery are some of the issues that can arise from overworked employees. Many times, in these situations, occupational fatigue leads to disengagement and decreased productivity [33].

Stress leads to turnover
Increased levels of stress associated with insufficient staffing levels can negatively impact employee health and may even cause worker turnover, leading to more issues for employers [34]. And, putting patients at high risk of succumbing to virus transmission or negative tests [35]. Additionally, both SARS-CoV-1 and Middle East Respiratory Syndrome (MERS) outbreaks were experimented under high understaffing as a result of stress burnout among workers [36,37]. Moreover, depression and psychophysiological symptoms among health workers [38].
impact negatively on occupational health and mental states [40,41].
A study from SARS-CoV-2 outbreak found Nurses who reported elevated stress levels faced by infected and infecting other [5]. Thus, infected and other health-related issues can impair worker productivity and can boost the number of sick days. Employers may also see increases in healthcare insurance costs if workers are sick more often. Employees who work excessively may also seek out other job opportunities, leaving employers with the timeconsuming and costly task of hiring and training new staff [42,43]. On the order of words, overstress gives also employees the intention to quit their jobs and seek for alternative work which may better enjoy their standard life [44,45,46,47]. Understaffing associated with stress has a long run repercussion for health care, including poor working conditions or encouraging errors to be overlooked [48]. Therefore, employers may easily make error in disease prevention (HIV/AIDS, influenza, MERS, SARS-CoV), or may require additional workers to assist. Healthy worker is the first condition to prevent disease and reduce staff injury and illness [49], and not having enough workers leads to less productivity and other uncertainty issues in work contract [48,49,50].

Dempster-Shafer And Evidential reasoning theories
The Dempster-Shafer Theory of Evidence (DST) treats imprecise, uncertainty and incomplete information [51,52]. And, to provide its consistency, DST has two functions: "belief" (Bel) and "plausibility" (Pla), both derived from the "mass function" (m). Their roles are to range weights value on behalf of DST in lower (Bel) and upper (Pla) bounds of probability risk.
Mass function(m), also known as a basic probability assignment (BPA) function, is the power set of the frame of discernment Θ. Generally, its formula is written with its two (2) consistency conditions: ''Mass function (m) or basic probability assignment (BPA)'' (Shafer, 1976): -Condition 1 and 2 -Belief function (Bel) is defined as: -And the plausibility function (Pla) is defined as: In case we have multiple risk subsets of Θ, the overall assessment of belief level (βn) on each assessment grade, and its aggregated degree of ignorance formulas are written below.
Additionally, these estimations are also supported by Evidential Reasoning (ER) [53,54]. (ER) is known as a decision-making methodology based on distributed assessments with n grades.
And, its role is to estimate individual risk based on available shreds of evidence from DST.
The formula of ER is ( (ℎ )) = {( , , , ), = 1, . . . } , ∑ , , =1 ≤ 1. Where is the assessment grade n and , , is the degree of belief that the likelihood of occurrence of risk equals the grade . With the overall assessment aggregation : Where k is: And, aggregated degree of ignorance is defined as:

Data sets
Except population resident's data which are from both city statistical yearbooks, EPS (Easy Professional Superior), in China allows us to collect the majority of data sets. And table 1 shows the descriptive statistics. Moreover, the explanation of each variable is detailed as follows: Decrease in capability of potential hazards detection It explains how understaffed may be unaware of disasters in the workplace that doctors have been controlling. Firstly, to know the number of health workers (doctors in disease prevention and control) who take care of population, we divide the yearly population of residents by the number of assistant doctors and doctors. We then estimate the difference in number of (assistant) doctors between 2003 and each year of disease treatment. This difference is considered probability risk when the value is positive. And, there is no probability risk and the values take zero (0) when the difference is negative or zero. Then, we use percentiles to quantify doctor's ability in disease detection and prevention so that we discern a clear knowledge of hazards exposition risk in Wuhan and Shenzhen cities, respectively.
Lack of task performance or increased disease mortality rate Worker's inefficacity may occur when the mortality rate among patients of disease outbreak increases each year. Based on the data used in this study, we observed since the outbreak of SARS-CoV-1 in Shenzhen to SARS-CoV-2 in Wuhan, the department of disease prevention and control has experienced an increase in mortality rate. As documented by scholars [3,4], SARS-CoV-2 symptoms include sneezing, coughing, and/or fever. Which are similar to those of the SARS-CoV-1. Therefore, this factor risk shows how public health workers (doctors in charge of disease prevention and control), which are understaffed, simply got confused at the early stage of SARS-CoV-2. The lack of task performance was estimated by calculating the differences between yearly mortality due to disease and that of the reference year 2003.
Which represents the year of SARS-CoV-1 outbreak. After the pandemic, the mortality rate due to disease may increase or decrease in the following years depending on depends on the performance of both doctors and assistant doctors. Therefore, doctor's tasks are accomplished successfully, there is no risk when the mortality rate decreases in the aftermath of the outbreak, otherwise, the growth rate of mortality is accounted by understaffed doctor's performance.

Work overload (under stress)
High visited patients in the hospital are natural. However, when the hospitals or centers are understaffed, workers become stressed. Stress affects negative workers through "rustout" [55].
The number of both doctors and assistant doctors in charge of disease prevention and control is inadequate in both cities' epicenter (SARS-CoV-2 Outbreak). This leads to error of early disease detection from patients. 55 Therefore, work overload is the main cause of many jobrelated attitudes, i.e., stress, anxiety, resulting in poor performance and job dissatisfaction [55].
In Wuhan and Shenzhen city, the daily number of visits and inpatients per doctor (person) increased continuously from SARS-CoV-1 to SARS-CoV-2, while the number of doctors and assistant doctors in charge of disease prevention and control is decreased. It has already been proved that SARS-CoV-1 outbreak was understaffed [37,38]. Therefore, we weight overload work by estimating the differences between the daily number of visits and inpatients per doctor (person) in 2003 and the following years. The difference is considered a probability risk when the value is positive and otherwise it takes the value zero (0). Then, we use percentiles to quantify the risk probability.  (2).

Long working hours
It is of no surprise to observe that the number of working hours per day increased, as majority

Results
One may argue that dealing with public health care employment assessment as a DST-ER problem is a risk mitigation and improving the ways in which understaffed risk is understood, assessed, and responded to in hospitals or clinics. Such an approach is very convenient especially in the case of analyzing employment, strategic and policies where authorities have different interests (poverty reduction and economic development) and objectives (health care system efficiency, and population well-being). DST-ER approaches for employment evaluation can assess risk in complicated situations such as pandemic period. Thus, the DST and the ER algorithm are innovatively employed to provide a successful risk assessment process. We model risk as the likelihood of occurrence and probability of impact materialization with the degrees of belief in the distributed assessments of understaffed risk impact on the disease prevention. Therefore, the distributed assessment of the impact of understaffing risk " " on disease prevention "ℎ " is obtained in the following form: ( (ℎ )) = {( , , , ), = 1, . . . } , with , , = * * .
Where L equals to likelihood of occurrence; I an impact risk and P is the probability of impact materialization. Which implies that: The tables 2 and 3 recapitulate the risk assessments in distributed forms of ( (ℎ )) disease prevention and control. Based on data sets, we found and affirm that, from the period during SARS-CoV-1 to SARS-CoV-2 outbreaks, the number of annual doctors in charge of disease control was on a decrease while the mortality rate kept increasing. Moreover, doctors were exposed to high work pressure due to the need for disease treatment, which also leads to a constant increase in working hours year by year. To sum up, each of these (6) factors used has 0.1666 of their likelihood of occurrence on disease prevention and we have the sum of mass equals to 1 according to DST rules. Additionally, we choose 4% of magnitude grades to assess these factor risks. To be more explicit, understaffed risk level is assessed on disease prevention using assessment grade, 4% of year to year understaffed. This means that understaffed risk has a maximum magnitude impact of 100% on disease prevention and control and their probability of impact materialization in each year direct equal to 1 of disease control and prevention [51,59]. The probability of impact materialization represents the probability that the actual risk impact equalizes the expected disaster (I) and its value is between 0 and 1. However, we choose the value one (1) for each year of risk impact effected as the data set is based on reality rather than experience. Therefore, we calculate the risk level by multiplying likelihoods of occurrence with risk impact and probability of impact materialization with the degree of belief. The findings are descripted in table 2 and 3. In each table, after estimating the distribution of risks from 2003-2018, we aggregate the individual risk assessment. Aggregating individual risk assessments allows to get different risk levels at differents years of disease prevention [59]. Moreover, it allows to get overall assessment of risk on disease prevention. Therefore, the aggregated degrees of ignorance are evaluated, and they allow to assess risk in minimum and maximum boundaries [59]. Thus, individual risk assessment aggregated, the minimum, maximum, and average risks assessment in both cities can be seen in tables 2 and 3, respectively. Moreover, the estimation details could also be seen. We express risk as percentage according to DST Theory role. Moreover, the assessment grade in 2003 is used to measure the belief in the expected risk of effects not materializing and materializing. The results are also shown in tables 2 and 3 and figure 1 shows the lower, upper, and average risk assessment in this study.
From these results, what we learn is that Wuhan SARS-CoV-2 outbreak was understaffed at 0.014% of magnitude, while Shenzhen city registered a higher level of understaffed with about 0.027% of magnitude.

Conclusion and recommendation
This article studies the understaffed consequences on SARS-CoV-2 outbreak in Wuhan and Shenzhen, which causes population and economic loss. Applying a framework of DST-ER approach, we draw the following main conclusions: first, we show how public health workers, especially workers in disease prevention and control, are under work pressure. Under-work pressure in both cities is mainly due to understaffed workers, which has six (6) factor risks in this study. It includes decrease in ability of potential hazards detection, lack of task performance or increased mortality rate, daily work overload and excessive workload, long working hours and; delay or reduction of multicomponent interventions. Thus, the approximative risks due to understaffed in Wuhan and Shenzhen at the end of 2019 are 0.14 % and 0.27%, respectively. These risk levels contribute to delays in disease prevention or treatment of confirmed SARS-CoV-2 cases in both cities. Moreover, from SARS-CoV-1 to SARS-CoV-2 outbreaks, the results show that Shenzhen city, the epicenter of SARS-CoV-1, is still highly understaffed than Wuhan city, the epicenter of SARS-CoV-2. Meaning that understaffed maximum risk in Shenzhen trails; Wuhan city; by 0.019 % in magnitude. We generally conclude that public health care systems in China, especially in both cities, are at risk and; the Wuhan city SARS-CoV-2 is just the beginning of pandemic of twenty-one century if employment policy in public is not reviewed. Therefore, the SARS CoV-2 outbreak may lead China authorities to rethink public health care employment policy to safeguard workers, patients and prevent future pandemics, respectively. Additionally, this policy may also promote new manufacturing enterprises to strengthen the existence of disease prevention and control machines so that workers can have resort to the technologies of machines to mitigate understaffed effects.