key: cord-1041233-of0yv40l authors: Hu, Ruimin; Wang, Xiaochen; Ma, Jianhua; Pan, Hao; Xu, Danni; Wu, Junhang title: Urban Hierarchical Open-up Schemes Based on Fine Regional Epidemic Data for the Lockdown in COVID-19 date: 2021-06-15 journal: nan DOI: 10.1016/j.bdr.2021.100243 sha: 89595b391d11af73df51e1ff9432cfcb66582ab6 doc_id: 1041233 cord_uid: of0yv40l During the COVID-19 outbreaking, China's lock-down measures have played an outstanding role in epidemic prevention; many other countries have followed similar practices. The policy of social alienation and community containment was executed to reduce civic activities, which brings up numerous economic losses. It has become an urgent task for these countries to open-up, while the epidemic has almost under control. However, it still lacks sufficient literature to set appropriate open-up schemes that strike a balance between open-up risk and lock-down cost. Big data collection and analysis, which play an increasingly important role in urban governance, provide a useful tool for solving the problem. This paper explores the influence of open-up granularity on both the open-up risk and the lock-down cost. It proposes an SEIR-CAL model considering the effect of asymptomatic patients based on propagation dynamics, and offered a model to calculate the lock-down cost based on the lock-down population. A simulation experiment is then carried out based on the mass actual data of Wuhan City to explore the influence of open-up granularity. Finally, this paper proposed the evaluation score (ES) to comprehensively measure schemes with different costs and risks. The experiments suggest that when released under the non-epidemic situation, the open-up scheme with the granularity refined to the block has the optimal ES. Results indicated that the fine-grained open-up scheme could significantly reduce the lock-down cost with a relatively low open-up risk increase. about by the COVID-19 [24, 25] . Some studies hope to help to put forward some more reasonable lock-down schemes. E.g., Alvarez et al. studied the optimal lock-down policy for a schemer who wants to control the fatalities of a pandemic while minimizing the output costs of the lock-down [25] . However, there are few studies on the impact of open-up schemes. This paper focuses on open-up schemes of different granularity. It explores the effects of granularity on economic cost and risk. Considering that Wuhan is the city with the earliest outbreak of the epidemic, the most rapid implementation of lock-down actions, and the quickest recovery from the epidemic situation, we did a simulation open-up experiment based on Wuhan epidemic data, from which the impact of granularity is detected. Finally, the optimal scheme suggestions is given by comprehensively analyze these open-up schemes. The contribution of this paper includes: 1. We explored the impact of open-up granularity on both risk and economic costs. With higher granularity, the risk increases slightly, and the cost reduces significantly. We verified this rule by a simulation experiment based on the actual data of Wuhan; 2. We introduced the regional epidemic risk calculation model under the isolating state based on the epidemiological model; 3. We proposed the simplified calculation formula of urban lockdown cost; 4. Finally, through the comprehensive analysis of risk and cost, we introduced the scheme evaluation model, based on which to suggest Wuhan's optimal multi-granularity open-up scheme (MGOS); Section 2 describes the basic relative concepts in this paper. The Multi Granularity Open-up Scheme is illustrated in Section 3; the lock-down cost formulation and risk model are presented in Sections 4 and 5. The comprehensive analysis model is presented in Section 6. Section 7 includes the simulation experiment on Wuhan City and results analysis. The paper concludes with a brief conclusion in Section 8. Lock-down. Residents are required to isolate at home, restrict outdoor activities, close public transport, and strictly control urban external traffic. These restrictions are lock-down control. The specific forms include but are not limited to setting up checkpoints at the exit of residential areas, setting up roadblocks at critical intersections, and stopping public transport. Open-up. As the epidemic gradually subsides, the production and life of residents are required restoring. The process of releasing these lock-down measures is called open-up, and the conditions that each region must meet to be allowed opening up are called open-up conditions. Lock-down cost. When a city is in the state of lock-down, many economic activities are stagnant, so the lock-down measures bring significant economic loss, which is lock-down cost. In reality, the calculation of lock-down cost is very complicated. However, there is a highly positive correlation between economic growth and the employment [26] . Therefore, this paper proposes a simplified expression of lock-down cost, which uses a function constructed by the free population. In Section 4, we will present the details of the calculation formula. Open-up risk. Open-up allows residents to have social contact again, which may provide conditions for the epidemic's resurgence. Therefore, open-up brings about risk, which refers to the risk of virus re-spreading in the population. In Section 5, we will study the factors that affect the risk. Open-up scheme. For a city, an open-up scheme includes a specific open-up schedule for every region. Usually, there are many possible open-up schemes at the beginning. The optimal one would be chosen after the evaluation of these schemes' risk and cost. The open-up time of a region has an impact on both its lockdown cost and epidemic risk. Because the epidemic severity is usually different in different parts of a city, a fine-grained open-up scheme can reduce the interaction between regions. It makes the low-risk areas can be open-up as soon as possible without being bounded by high-risk areas, therefore reduce the lock-down cost. It also makes the high-risk areas can maintain the lock-down status to ensure that the urban risk is staying at a low level. Therefore, in this paper, we propose the multi-granularity open-up scheme (MGOS) based on the urban management structure. Within a specific range, the lock-down cost would reduce effectively while the open-up granularity was refining. At the same time, the risk would increase slightly but still maintains at a low level. Therefore, it is an optimal choice to choose a fine-grained open-up scheme. A clear definition of MGOS is as follows. MGOS: Firstly, the object city's management structure is divided into a tree-likestructure with a depth of L (L-tree). MGOS refers to a scheme using some nodes (regions) selected from the L-tree. If only when the respective non-epidemic situation (NES) of a node reaches openup condition (OC) could the people inside move freely in the city. Here NES is defined as the proportion of uninfected people in the total local population; OC is the value of NES, which must be satisfied when an area is open-up. Under the requirements for risk minimization, it is 100%. Notice that the selected nodes are independent of each other, and they cover the whole city. A set of node selection represents an MGOS. The number of selected nodes is defined as granularity. Before filtering, there are usually multiple MGOSs constructed. Section 7 will build MGOSs based on the Wuhan city's actual data and compare their lock-down cost and risk to verify the hypothesis in simulation experiments. Next, we will introduce the model used to calculate the lock-down cost and risk. There are few pieces of researches on economic cost (lock-down cost) under the open-up process. The lock-down cost contains very complex factors, so it is difficult to calculate accurately. Therefore, we can only use a very simplified model to express the lock-down cost. As mentioned in the second Section, the Lock-down cost C is highly correlated with the population under lock-down. Therefore, it is simplified as a linear function of the number of lock-down population U: C=K*U. K is the average economic value a person brings in a day. When the area is under completely lock-down, C=K*N (N is the total population of the region). In Eq. (1), U i,t represents the lock-down population of the i-th area on day t, and n i=1 U i,t represents the total population under control in the city on day t, and TW represents the selected time window. Table 1 The description of each sub-classes in SEIR-CAL model. The same description with S(t) in the basic model E N(t) The infectors who are not self-aware, including the presymptomatic infectors and the asymptomatic infectors The infectious people who are free to move R N(t) The same description with R(t) in the basic model The susceptible people who are isolating at home EC(t) The exposed people who are isolating at home IC H(t) The asymptomatic infectors who are isolated in a particular facility, such as a hotel IC M(t) The Infectious people who are isolating in hospitals and being treated RC(t) The Recovered people who are isolating at home While opening up the city, the risk of the open-up scheme lies in the probability that the virus may spread between the unblocked people. At the beginning of the open-up process, a certain number of infected people existed, which constituted the initial risk of each open-up plans. Transmission from the infected to the healthy will increase the total risk, and isolation and cure of the infected will reduce the total risk. A decrease of or at least no increase in the number of infected people after a city has been open for a while means that the epidemic is under control, which is what the city's open-up process hopes to achieve. There also exists a harsh situation that the infected population keeps growing, leading to the second outbreak. SEIR-CAL, an SEIR model considering activity limitation, was applied to simulate the progress of the virus spreading. Given the open-up scheme, the model could generate a time series of the infected population, as a measurement of risk. The well-known Susceptible-Exposed-Infectious-Removed (SEIR) model was modified to a hierarchical version with consideration of activity limitation to determine the effect of open-up. In a basic SEIR model, the total human population at time t is N(t), which is divided into four sub-classes: Susceptible S(t), Exposed E(t), Infectious I(t), Removed R(t). Further, each sub-class could be divided into two statuses: closed and not-closed. Thus there would be eight sub-classes in total. The descriptions of these sub-classes are given in Table 1 . Assumption 1: the city would only be opened up when the epidemic begins to subside in its later stages. Assumption 1 is fundamental in constructing of SEIR-CAL model. Only in such cases will the medical facility be sufficient to ensure the needs that may occur during the opening process and prevent a run on medical resources. Under this assumption, there are some significant differences between the SEIR-CAL model and the basic SEIR model. 1. SEIR-CAL model assumes that all infected people with obvious symptoms would be sent to the hospital for treatment, which is described as I N −→ IC M in the model. 2. SEIR-CAL model also assumed that continuous nucleic acid testing would be performed on the population. Those asymptomatic patients detected would be forwarded for isolation, which is described as E N −→ IC H. 3 . In addition to the typical infected ones, asymptomatic infected ones are considered contagious [27] and may even be a valuable infection source in practical situations. Similar to those in the incubation period, the asymptomatic infected ones are infected persons with no self-awareness, who should be classified as exposed ones or E in the basic SEIR model. Therefore, the exposed ones are contagious as a group. EN is contagious in an SEIR-CAL model, but EC is not infectious because it is isolated from the susceptible ones. For the same reason, IN is infectious, but ICH and ICM are not. Assumption 3: neither new births nor death citizens affect the total urban population significantly. Assumption 2 and 3 are two minor assumptions which help to simplify the model without loss of generality. With assumption 2, the transfer path from EC to EN is irreversible, as Fig. 1 illustrated, which insulated the possibility that those infectors in the opened up population may infect those still closed. With assumption 3, the effects of newborns and dead people are not reflected in the model. The total population in the model remains constant. A schematic diagram of the full system is given in Fig. 1 . Let the number of districts that are opened up at date t is A t , and the population in these districts are N t When an area of the city is opened up, its population was added to the disease transmission dynamics, SC t i turns The total free population at date t is represented as below. The schedule of open-up determines its value. Relative transmissibility from an exposed human to a susceptible human [28, 29] Assuming that those infected persons with typical symptoms would be taken to hospital for treatment (I N −→ IC M) within D days of the onset of symptoms: In Eq. (9), D ≥ 1. When D ≥ (t + 1), then I N(t + 1 − D) = 0. Finally, with treatment rate γ , ICM, and RN could be represented as: Eq. (6)-(11) constitute the main framework of the SEIR-CAL model. In the actual calculation, we set the initial state of the model as follows: There is no exact analytic solution of an SEIR model has yet been found. Once the initial status of the model is given as input, and the parameters are determined, results in numerical form could be output. In other words, the output of the model is highly dependent on the value of parameters, which may vary with the specific application scenario. We will discuss the valuation of the settings in Section 5.2 and then validate the model with simple simulation data in Section 5.3. All parameters in the model are listed in Table 2 . Some parameters reflect several inherent characteristics of the COVID-19, which can be verified by other epidemiological studies; the other parameters may vary with different locations or the epidemic stage, and we estimate these parameters based on the epidemic actual data in Wuhan. In Table 2 , R 0 and θ are obtained from fitting the nucleic acid test data of Wuhan from April 1st to May 13th; β 1 and β 2 are derived from R 0 ; σ , d and γ are derived from official statistics, public news reports or other references; the value of D and K are assumed. The estimation of was widely discussed, with values ranging from 1.4 to 5.7 [32] [33] [34] [35] , which reflected the rapid spread of the disease in the early stage of the epidemic and could not simply fit the scenario of city open-up. On the other hand, there are not many pieces of research focused on the asymptomatic infectors, thus the value of θ (equals the multiplicative inverse of the average recovery period of the asymptomatic patients) lacks strong reference support. The above two reasons suggest the necessity of data fitting. Article [12] investigated the Epidemiological case data at Ningbo, Zhejiang Province from January to March in 2020, and concluded that the transmissibility of an asymptomatic case equals about 0.65 times of a general infector. Considering that Ningbo has abundant medical resources, which is not significantly different from the case in Wuhan on the process of open-up, thus we can set β 1 = 0.65β 2 in our case; Our method to compute β 2 or the transmission rates of general infectors is the same with β 2 = R 0 /d [29] :, where d = pip + D. Here d represents the length of the time window in which a virus carrier has a chance to infect susceptible people, and pip represents the average asymptomatic infectious period, which equals 4.5 days [29] . We assume D = 1, therefore, d = 4.5 + 1 = 5.5. Assuming that k represents the transmission rate from EN to IN and k = w ÷ ip, where w represents the proportion of the latent infectors in the total exposed human (EN), and ip represents the length of the incubation period. Throughout the month of April, the Wuhan government had reported 741 new cases of asymptomatic infection, but only 1 new confirmed case [30] . It could be assumed that after excluding the influence of imported cases, the vast majority of the virus carriers in Wuhan would be the asymptomatic infectors, it would be possible that the value of is much smaller than 1/741, we choose w = 1 ÷ 10000 and ip = 5.6 [29] , and k = 1/56000. The estimation of is based on the daily number of nucleic acid tests reported in Wuhan, from April 1st, 2020 to May 13th, 2020, an average of 41,740 cases of nucleic acid were tested and which was equivalent to 0.327% of the total population of Wuhan, so we choose σ = 0.00327. At last, we choose γ = 1/24.7 [31] . An SEIR-CAL model was verified on MATLAB (version: R2019b). Assuming that the total population is 10 million and 20,000 exposed cases at the initial time of opening, we listed ten opening schemes. We ran the model to observe the trends of the critical variables EN, IN, and IC. As Table 3 demonstrates, we assumed that the same number of people are opened at a time under each scheme. By adjusting the batches (1 to 4) and the length of the opening operation period (7 days, 11 days, and 14 days), we can obtain ten different schemes. Fig. 4 demonstrates the trend of the critical variables EN, IN, ICH and ICM. These four key variables represent four groups of potentially at-risk people. It can be seen that the blue line was describing the most radical opening scheme, which opened all the population on the first date, is on the top in each of the figures. The black line with the cross representing the most conservative opening scheme is on the bottom, which shows that these two correspond to the highest risk and the lowest risk. Take Fig. 4a for an example: the variable EN under each scheme almost shows a monotonous downward trend (which reflects that the epidemic is subsiding under our parameter setting). At the day 30, there would be 4,681 exposed cases remain under the most radical scheme (open all, scheme 1), the number of remaining exposed cases at day 30 was only 3,380 under the second most radical opening scheme (2batches+7days, scheme 2), and 2,423 under the most conservative scheme (4batches+14days, scheme 10). In scheme 1, the number of exposed cases would be reduced to below 2,000 on day 47, compared with 34 days for scheme 10. Fig. 4b shows the change in the number of confirmed cases, Fig. 4c for the asymptomatic infectors being observed in isolation and Fig. 4d for hospitalized patients. Table 3 Given an opening-up scheme, its cost value and risk value can be drawn according to the methods proposed in Sections 4 and 5. Reducing cost or risk is both the improvement to the scheme; however, these two goals often conflict, which is a typical multiobjective optimization problem. We establish an evaluation score to measure the risk and cost comprehensively and transform the multi-objective optimization problem into a single-objective problem. Since risk and cost have different physical meanings and cannot be added together, they need to be normalized 2 . We denote the scheme as P i (i = 1, 2, · · · , n), then denote its normalized cost value as C p i , and its normalized risk value as R p i . The evaluation score of a scheme P i can be represented as: In Eq. (15), w 1 and w 2 are the weights of risk and cost, respectively. w 2 = 1 is set to simplify the model: According to Eq. (16), the evaluation score for an open-up scheme, comprehensively measures the cost and the risk, and it was chosen as the reference index we used to evaluate and select the schemes. The lower ES, the better the scheme. The output of the cost model in Section 4 is a scalar. However, the risk model in Section 5 generates a time series of the population of those asymptomatic infectors (and the confirmed cases). Both the average value and the peak value in the series should be taken into consideration. Given an observing time window T, the average risk R = T 1 R t /T measured the overall risk of scheme P i , and R p i is the normalization of R . The peak of the risk sequence measures the severity of the scheme, which is related to w 1 . The capacity of medical resources in a city has an upper limit. The closer the peak risk is to the ceiling, the higher w 1 will be. In extreme cases, the risk may exceed the city's medical resources' capacity, and then w 1 would rise sharply. However, since we assume that the city would only open on the late stage of the epidemic, this extreme scenario should be avoided while formulating an opening-up scheme. We choose the total number of hospital beds Z as the indicator of the total amount of medical resources in the city, and we assume that one patient corresponds to one bed. Based on Wuhan's practice, our model pays attention to the risk of asymptomatic patients. The government department of Wuhan would actively carry out nucleic acid testing on the public, then put the detected asymptomatic patients into medical quarantine, which is taking up medical resources. Generally, an asymptomatic patient consumes fewer medical resources than a "normal" patient. The consumption will even be lower if some regions do not actively test and treat asymptomatic infected patients like Wuhan. We assume that the average amount of medical resources consumed by an asymptomatic patient is k times of a confirmed patient, 0