### Constructing an evaluation system of monthly economic losses for the city

We base on our analysis of the concept of people-oriented to find the balance between epidemic prevention and economic-social development. This paper constructs a comparative evaluation system of monthly economic loss of “Wuhan Lockdown” Policy from both health loss and industrial economic loss.

### Monthly health loss evaluation: SIR model and health burden assessment

As an emerging and highly infectious disease (Xu et al. 2020), COVID-19 is causing losses in both the physical and mental health of the public at large (Huang et al., 2020). Although this study addresses only the 1-month residents’ health losses, including physical health losses (health burden), and the mental health losses during the lockdown (Tang et al. 2020a), the approach can be applied to other situations with a longer period.

According to the Handbook, the diagnosed people are divided into three categories: mild, severe, and death (2020). There is a significant difference between direct and indirect economic losses, including time loss and the treatment of the three types of patients. However, there is no accurate official data on these three categories yet. To obtain the cumulative number of confirmed cases and the number of the three categories of confirmed cases, we established a SIR (Susceptible-Infected-Recovered) model and simulated the transmission of COVID-19 in the city (Harko et al. 2014; Hu et al. 2012; Liu et al. 2016).

Due to the lack of medical resources and sufficient beds in hospitals, designated hospitals only received severe patients. To relieve the massive shortage of doctors and medical resources, Huoshenshan Hospital and Leishenshan Hospital was built and observation wards were put into service on February 5. After that, mild patients were received into observation wards. Therefore, we consider the designated s and observation wards bed ratio over two different stages of the epidemic. The first stage is from the date when the lockdown started on January 23 to the date when the first bed in observation wards opened to quarantine individuals on February 5, and the second stage is from February 5 to February 23. Also, we considered the effect of designated hospitals and mobile cabin hospital beds capacity on the transmission rate, the transfer rate from mild to severe patients, and death rate. Then the general population is divided into susceptible people (*S*), mild patients (*I*), severe patients (*I*_{1}), mild patients in mobile cabin hospitals (*F*), severe patients in designated hospitals (*H*), Dead patients (*D*), and recovered patients (*R*) (Xu et al. 2020; Huang et al. 2020). Here, we assume that only mild patients can infect healthy people, while severe patients, who are quarantined, cannot infect susceptible people. The flow diagram is shown in Fig. 1.

Then the transmission dynamics of COVID-19 is determined by the following equations:

$$frac{{{mathrm{d}}S(t)}}{{{mathrm{d}}t}} = frac{{ – beta (b_1,I)Sleft( t right)Ileft( t right)}}{{Sleft( t right) + Ileft( t right) + Rleft( t right)}},$$

$$frac{{{mathrm{d}}Ileft( t right)}}{{{mathrm{d}}t}} = frac{{beta (b_1,I)Sleft( t right)Ileft( t right)}}{{Sleft( t right) + Ileft( t right) + Rleft( t right)}} – alpha _{11}(b_1,Ileft( t right))Ileft( t right) – alpha _{12}(b_1,Ileft( t right))Ileft( t right) – gamma Ileft( t right),$$

$$frac{{{mathrm{d}}Fleft( t right)}}{{{mathrm{d}}t}} = alpha _{11}left( {b_1,Ileft( t right)} right)Ileft( t right) – alpha _{21}left( {b_2,F(t)} right)Fleft( t right) – gamma _fFleft( t right),$$

$$frac{{{mathrm{d}}I_1(t)}}{{{mathrm{d}}t}} = alpha _{12}left( {b_1,Ileft( t right)} right)Ileft( t right) – alpha _{31}left( {b_2,I_1left( t right)} right)I_1left( t right) – d_1left( {b_2,I_1left( t right)} right)I_1left( t right),$$

$$frac{{{mathrm{d}}H(t)}}{{{mathrm{d}}t}} = alpha _{21}left( {b_2,F(t)} right)F(t) + alpha _{31}left( {b_2,I_1left( t right)} right)I_1left( t right) – d_hleft( {b_2,Hleft( t right)} right)Hleft( t right) – gamma _hHleft( t right),$$

$$frac{{{mathrm{d}}Rleft( t right)}}{{{mathrm{d}}t}} = gamma Ileft( t right) + gamma _fFleft( t right) + gamma _hHleft( t right),$$

$$frac{{{mathrm{d}}Dleft( t right)}}{{{mathrm{d}}t}} = d_1left( {b_2,I_1left( t right)} right)I_1left( t right) + d_hleft( {b_2,Hleft( t right)} right)Hleft( t right),$$

where (b_1 = left{ {begin{array}{*{20}{l}} {0,t , < ,14} \ {b_{10},t ,ge , 14} end{array}} right.),(b_2 = left{ {begin{array}{*{20}{l}} {b_{21},t , < , 14} \ {b_{22},t , ge , 14} end{array}} right.), ({upgamma}_f = left{ {begin{array}{*{20}{l}} {0,t , < , 14} \ {{upgamma}_{f0},t , ge , 14} end{array}} right.)

$$beta left( {b_1,Ileft( t right)} right) = frac{{beta _0Ileft( t right)}}{{b_1 + Ileft( t right)}},,alpha _{11}left( {b_1,Ileft( t right)} right) = frac{{alpha _{110}Ileft( t right)}}{{b_1 + Ileft( t right)}},\ ,alpha _{12}left( {b_1,Ileft( t right)} right) = frac{{alpha _{120}Ileft( t right)}}{{b_1 + Ileft( t right)}}, ,alpha _{21}left( {b_2,F(t)} right) = frac{{alpha _{210}F(t)}}{{b_2 + F(t)}},$$

$$alpha _{31}left( {b_2,I_1left( t right)} right) = frac{{alpha _{110}I_1left( t right)}}{{b_2 + I_1left( t right)}},,d_1left( {b_2,I_1left( t right)} right) = frac{{d_{10}I_1left( t right)}}{{b_2 + I_1left( t right)}},$$

$$d_hleft( {b_2,H(t)} right) = frac{{d_{h0}Hleft( t right)}}{{b_2 + Hleft( t right)}},,alpha _{110} = left{ {begin{array}{*{20}{l}} {0,,t , < , 14} \ {alpha _{110},,t , ge , 14} end{array}} right.,,alpha _{210} = left{ {begin{array}{*{20}{l}} {0, ,t , < , 14} \ {alpha _{210},,t , ge , 14} end{array}} right.$$

The effects of designated hospitals and mobile cabin hospital beds capacity on the transmission rate, the transfer rate from mild to severe patients, and death rate were considered as the parameters. The effect of mobile cabin hospitals beds capacity on the transmission rate, transfer rate from mild to severe patients and occupancy rate of mild patients in mobile cabin hospitals was denoted by the mobile cabin hospitals beds ratio *b*_{1} corresponding to the mild patients. The effect of designated hospitals beds capacity on the hospitalization rate and death rate of severe patients were denoted by the mobile cabin hospitals ratio *b*_{2} corresponding to severe patients (Shan and Zhu 2014; WHO 2020b).

Where *β* is the contact transmission rate, *α*_{11} is the occupancy rate of mild patients in mobile cabin hospitals, *α*_{12} is the transfer probability from mild to severe.*α*_{21} is the transfer probability from mild to severe in mobile cabin hospitals, *α*_{31} is the hospitalization rate of severe patients.And *γ* is the recovery rate of mild patients,*γ*_{1} is the recovery rate of severe patients, *γ*_{h} is the recovery rate of severe patients in the hospital, *d*_{1} is the mortality rate of severe patients, and *d*_{h} is the mortality rate of severe patients in the hospital. Here, the time unit t in the equation is defined as “day” of the event. Based on relevant epidemic data in Wuhan (2020), and the initial values on January 23, 2020 are chosen as follows: *S*(0) = 55439, *I*(0) = 269, *F*(0) = 1000, *I*_{1}(0) = 129, *H*(0) = 494, *D*(0) = 23, and *R*(0) = 31. From the available literature on COVID-19 (Tang et al. 2020b; Zhou et al. 2020; Guan et al. 2020) we assume that *β* = 0.813, (b_{21} = 800,b_{10} = 1500,b_{22} = 1000,alpha _{110}) = 0.7, *α*_{210} = 0.01, *α*_{120} = 0.04, *α*_{310} = 0.6. Since the average incubation period is 7 days and the treatment time for mild patients is 10 days, so *γ* = 1/17 and *γ*_{f0} = 1/17. The average treatment time for severe patients is 20 days, hence *γ*_{h} = 1/20 (Lu et al. 2020). The mortality rates of severe patients are *d*_{10} = 0.016 and *d*_{h0} = 0.016, respectively (Newall et al. 2010).

We then estimate the health burden attributable to patients’ infection with the virus. The precondition of health burden assessment determines suitable health endpoints and gaining the number of infections in different health endpoints. The health endpoint is the final level of health risk caused by hazardous substances, and the final level can be classified based on the severity of diseases (Yao et al. 2020). A large number of domestic and foreign literature applied the health burden assessment to estimate the economic loss of health attributable to exposure to multiple air pollutants where the health endpoints were defined by the exposure-response function (Yao et al. 2020; Zhang et al. 2017; Maji et al. 2018). This method is used to estimate the economic v44 vloss of health due to this pandemic. Since the pathogenic mechanism of this pandemic is different from that of exposure to pollution and the SIR model built above would simulate to give the estimation of the numbers of the three categories of confirmed cases, the health endpoints in this paper are defined as the different levels of pulmonary infection caused by the COVID-19 and are divided into mild, severe, and death based on the computational results from the SIR model simulation. Thus,

$$L_{{mathrm{p}}_i} = C_{{mathrm{p}}_i} + {mathrm{GDP}}_P times T_{L_i},$$

$$L_i = P_i times L_{{mathrm{p}}_i},$$

$$L ={sum limits_{i = 1}^n} L_i,$$

where *i* is the health endpoints, *L*_{i} is the total cost of COVID-19 at health endpoint *i*, (C_{{mathrm{p}}_i}) is the unit cost of treatment cost at health endpoint *i*, ({mathrm{GDP}}_P) is the daily average GDP per capita in Wuhan Unit: Yuan/(person**d*), (T_{{mathrm{L}}_i}) is the cost of lost time due to disease at health endpoint *i*, *P*_{i} is the number of people diagnosed at health endpoint *i*, and the sum of the economic losses at each health endpoint (*L*_{i}) is the total attributable economic losses of the population (*L*) under the outbreak (Lu et al. 2016). Then, we calculate the total economic loss of health (*L*), which is the health burden in a month of lockdown against COVID-19 in Wuhan.

To match the data of different health endpoints of COVID-19 with the data during the lockdown, we computed the cumulative cases using the SIR model, which would give the numbers of cumulative cases. Then, the monthly health burden can be estimated using the average treatment cost and the cost of lost time of different health endpoints.

Apart from physical health loss, the loss caused and associated with mental health due to that strict social distancing and home quarantine policy for combating COVID-19 prevented their public entertainment and cultural activities. Since the utility of consumption is hard to quantify, the revenues of cultural services were used to approximate and to evaluate the loss of mental health. Furthermore, the strict social distancing policy objectively restricted the personal freedom, mental loss caused by lockdown was evaluated based on the new state compensation standard for violating personal freedom unveiled by the Supreme People’s Procuratorate of the People’s Republic of China. Meanwhile, patients with acute or severe chronic diseases are unable to receive timely treatment, which leads to health loss by clinical exacerbation and increased mortality due to the lockdown policy. The lockdown also brought restrictions to transportation, social activities, and various constructions and could reduce mortality caused by traffic accidents, excessive drinking, cardiovascular diseases, industrial injury, etc. As these two aspects show opposite effects on the health of people and data availability limitation, these two indirect effects were ignored in our current studies.

### Meso-economic loss evaluation: constructing the Input-Output (IO) model

Owing to the rapid spread of COVID-19, Wuhan city has been put under lockdown since January 23, 2020, and public transportation has been closed. The transportation industry is closely related to various industries, such as warehousing and retail, vacation tourism, accommodation and catering, cultural and entertainment industries, etc. Non-related upstream and downstream industries, such as the real estate industry, the financial industry, the construction industry, and other industries, seemed to be spared from COVID-19, but these industries also suffered direct or indirect losses. The effect of the lockdown in Wuhan on meso-economic industries is not limited to one industry. Therefore, we estimated the losses of directly affected industries, and then evaluated the indirect losses of other industries using the IO model (Li et al. 2018).

Based on the IO table, we established the IO model incorporating the linkage of production and consumption to assess the economy of Wuhan. Since the 1970s, the IO model has been used to assess the effect of disasters, such as earthquakes and hurricanes on the economy. The results show that the IO model effectively solves the impact of a disaster on certain departments of the economic system and the assessment of related losses (Crowther et al. 2007; Tan et al. 2019). In this paper, the static IO model is used to evaluate the indirect economic losses among the industries (Crowther et al. 2007; Tan et al. 2019).

The correlations among the industries in the IO table can be expressed as:

That is, ({sum nolimits_{j = 1}^n} a_{ij}X_j + Y_i = X_i)*(i, j* = *1, 2, …, n)*, where *a*_{ij} is the direct consumption coefficient, *X*_{i} is the total output of sector *i*, and *Y*_{i} is the final demand for sector *i*. Then the above formula can be transformed as:

$$X = left( {I – A} right)^{ – 1}Y$$

where *I* is the identity matrix and (left( {I – A} right)^{ – 1}) is the inverse matrix of Leontief.

Taking the sectional direct economic losses as losses in final products, ({Delta}Y = left( {{Delta}Y_1,{Delta}Y_2,…,{Delta}Y_n} right)^{mathrm{T}}). Then the total product loss is:

$${Delta}X = left( {I – A} right)^{ – 1}{Delta}Y.$$

The loss of indirect input is expressed by the reduction of intermediate input as ({Delta}X – {Delta}Y).

To improve the accuracy of the indirect loss assessment of various departments, this paper uses the complete consumption coefficient for analysis. Let *B* be a complete consumption coefficient matrix obtained by transforming the direct consumption coefficient matrix A, then *B* = (*I**−**A*)^{−1 }− *I*. Therefore, the total loss of the product can be further expressed as:

$${Delta}X = left( {B + I} right){Delta}Y.$$

Assume that Δ*Y*_{i} is the economic loss in the sector *I* caused by COVID-19 and the final use of other sectors has no change. Then the total output of the entire economic system becomes

$$left( {begin{array}{*{20}{l}} {{Delta}X_1} hfill \ {{Delta}X_2} hfill \ . hfill \ . hfill \ . hfill \ {{Delta}dot Xn} hfill end{array}} right) = left( {begin{array}{*{20}{c}} {b_{1i}{Delta}Y_i} \ {b_{2i}{Delta}Y_i} \ . \ . \ . \ {b_{ni}{Delta}Y_i} end{array}} right) + left( {begin{array}{*{20}{c}} 0 \ 0 \ . \ {{Delta}Y_i} \ . \ 0 end{array}} right)$$

where (b_{ij}left( {i,j = 1,2, ldots ,n} right)) are the complete consumption coefficients. Then the total output loss of sector *i* is:

$${Delta}X_i = b_{ii}{Delta}Y_i + {Delta}Y_i,$$

where ({Delta}Y_i) is the direct economic loss of sector *i* and (b_{ii}{Delta}Y_i) is the indirect economic loss of sector *i*. The total product losses of other sectors are:

$${Delta}X_n = b_{ni}{Delta}Y_i,n , ne , i.$$