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Abstract

After successfully preventing the spread of five waves of COVID-19 epidemics in Shanghai, the Omicron and Delta variants have been causing a surge of COVID-19 infections in this city recently. Summaries, analyses, and simulations for this wave of the epidemic are important issues. Using differential equations and real-world data, this study models and simulates the recent COVID-19epidemic in Shanghai (March 1 Í  June 14, 2022), estimates transmission rates, recovery rates, and blocking rates to symptomatic and asymptomatic infections, and symptomatic (infected) individuals’ death rates. Visual simulations predict the outcomes of this Shanghai epidemic wave. It compares with the recent mainland China COVID-19 epidemics(RMCE). The simulation results were in good agreement with the real-world data at the end points of 13 investigated time intervals (day 0 to day 75). The visual simulations imply that in the last month (day 76 to day 105), the blocking rates of the symptomatic and asymptomatic infections almost reach 100%, the recovery rates of symptomatic and asymptomatic infections increase significantly, and the death rate of the infected individuals decreases significantly. The transmission rate of the symptomatic infections caused by the symptomatic individuals was much lower than the corresponding average transmission rate of the RMCE. The transmission rate of the asymptomatic infections caused by the symptomatic individuals was much higher than the first 75 days’s average transmission rate of RMCE. The transmission rate of the symptomatic infections caused by the asymptomatic individuals was much lower than the first 75 days’s average transmission rate and the last 30 days’ average transmission rate of RMCE. The transmission rate to the asymptomatic infections caused by the asymptomatic individuals was much higher than the corresponding average transmission rate of RMCE. The average recovery rate of the symptomatic individuals was much lower than the corresponding average recovery rate of the symptomatic individuals of RMCE. The first 30 days’ average recovery rate of the asymptomatic individuals was much lower than the first 30 days’ average recovery rate of RMCE. The last 30 days’ average recovery rate of the symptomatic individuals was higher than the last 30 days’ average recovery rate of RMCE. The average low blocking rates to the symptomatic infections, the first 30 days’s low blocking rates to the symptomatic infections, the low recovery rates of the symptomatic individuals, and the high transmission rate of the asymptomatic infections may be the reasons forthe rapid spread of the recent Shanghai epidemic. The last month’s strict prevention and control strategies, the high recovery rates of symptomatic and asymptomatic infections, and the low death rates have prevented the rapid spread of the sixth wave of the COVID-19 epidemic in Shanghai.

Introduction

The Omicron and Delta variants have been causing a surge in COVID-19 worldwide. Many countries have experienced multiple outbreaks of the COVID-19 epidemic caused by the variants. As of 15 May 2022, over 518 million confirmed cases of COVID-19 and over six million deaths have been reported globally [1]. After successfully preventing the spread of five waves of COVID-19 epidemics in Shanghai, Omicron variants have broken through the COVID-19 prevention of this city recently. Analysis and simulations for this epidemic wave are important issues. Since the outbreak of COVID-19 in Wuhan, China, a large number of articles on modeling and predictions of COVID-19 epidemics have been published (for examples, see [2–10]). Recently, the author has used several simple differential equation models to successfully describe the dynamics of the spreads of the COVID-19 epidemics in mainland China [11–14]. Using the differential equation model and real-world data, this study models and simulates the recent sixth wave of the COVID-19 epidemic (March 1 to April 30, 2022) in Shanghai, estimates transmission rates, recovery rates, and blockingrates to symptomatic and asymptomatic infections, and symptomatic individuals’ death rate. Visual simulations predict the outcomes of this Shanghai epidemic wave. It compares in parallel with the recent mainland China COVID-19 epidemics (RMCE).

Materials and Methods

The dataset of the Shanghai COVID-19 epidemic from March 1, 2022, to May 15, 2022, was collected and edited from the Health Commission of Shanghai's official website [15]. Using the differential equation model stimulates the outcomes of the numbers of the current symptomatic individuals, the current asymptomatic individuals charged in medical observations, the cumulative recovered symptomatic individuals, the cumulative asymptomatic individuals discharged from medical observations, and the number of the cumulative dead symptomatic (infected) individuals. The equation parameters were determined by the so-called minimization error square criterion described in references [11- 14]. Using virtual simulations estimates the outcomes of the spread of the recent COVID-19 epidemic in Shanghai. Simulations and figure drawings were implemented via MATLAB programs. Summaries, Analysis, and Simulations of Recent Shanghai Epidemic

Summaries

On March 1 (denoted by day 0), one new symptomatic individual was reported, there were ten cumulative asymptomaticindividuals charged in medical observations, and there was one asymptomatic individual discharged from the medical observations. On March 9 (day 8), one new asymptomatic individual was discharged from medical observations, there were 306 asymptomatic individuals charged in medical observations, and there were 23 current symptomatic individuals. The first symptomatic individual’s recovery day was on March 19 (day 18); 10 symptomatic individuals and 72 asymptomaticindividuals recovered on that day. There were 175 current symptomatic (hospitalized) individuals and 2099 asymptomatic individuals charged in the medical observations. The asymptomatic infection turning point appeared on day 44 (April 14); there were 245812 asymptomatic individuals charged in medical observations, and there were 12684 symptomatic individuals in hospitals. There were 2215 cumulative recovered symptomatic individuals and 43768 cumulative asymptomatic individuals discharged from the medical observations. The symptomatic infection turning point appeared on day 52 (April 22), there were 25010 symptomatic individuals in hospitals and 223682 asymptomatic individuals charged in medical observations. There were 11,965 cumulative recovered symptomatic individuals. There were 207012 cumulative asymptomatic individuals discharged from the medical observations. There were 48 cumulative symptomatic individuals who died. The first 3 symptomatic individuals appeared on day 47. On the investigated end day 75 (May 15), there were 4086 symptomatic individuals in hospitals and 39043 asymptomatic individuals charged in medical observations. There were 52137 cumulative recovered symptomatic individuals and 523859 cumulative asymptomatic individuals discharged from medical observations. There were 69 daily increased symptomatic individuals and 869 daily increased asymptomaticindividuals. There were 575 cumulatively dead symptomaticindividuals.

Simulations

In order to describe and understand the spread of an infectious disease, we need to set up a differential equation model to estimate the transmission rates and the blocking rates to symptomatic and asymptomatic infections. Assume that the process of the spread of an infectious disease are divided into m time intervals, representing different prevention control measures and treatment efficacy, respectively. Over the lth time interval, the model has the form (also see [11-13-14])

where 1(l)=(1-1(l)) and 2(l)=(1-2(l)) (l= 1, 2, m) represent the blocking rates to symptomatic and asymptomatic infections, respectively. I and Ia represent the numbers of current symptomatic individuals and current asymptomatic individualscharged in medical observations, respectively. Ir and Ira represent the numbers of current cumulative recovered symptomatic individuals and current cumulative asymptomaticindividuals discharged from medical observations, respectively. D represents the number of current cumulative dead symptomatic individuals. β12 and β22 represent the transmission rates of the symptomatic infections caused by symptomatic individuals and asymptomatic individuals, respectively. β12 and β22 represent the transmission rates of the asymptomatic infections caused by symptomatic individuals and the asymptomatic individuals, respectively. S represents the susceptible population (can assume S = 1, see [11]). κ(l) and κa(l) represent the recovery rates of the symptomaticindividuals and the asymptomatic individuals, respectively. α(l) represents the death rate of the symptomatic individuals. For Shanghai's sixth COVID-19 epidemic, it can be assumed that the transmissions are divided into 13 time intervals (see solid points in Figs. 1 and 2). We need to determine the parameters of equation (1) for i = 1, 2, ..., 13. Denote t1 = 6, t2 = 10, t3 = 15, t4 = 20, t5 = 27, t6 = 30, t7 = 37, t8 = 40, t9 = 47, t10 = 52, t11 = 60, t12 = 67, and t13 = 75. [tl−1, tl] is the lth time interval. Denote Ic (tl) to be the number of the reported current symptomatic individuals, and Ica (tl) to be the number of the reported current asymptomatic individuals charged in medical observations. Denote Icr (tl) to be the number of the reported current cumulative recovered symptomatic individuals, and Icra (tl) to be the number of the reported current cumulative asymptomatic individuals discharged from medical observations. Dc(tl) is the number of the reported current cumulative dead individuals. Using the minimization error square criterion:

θ2(l)’s and α(l)’s. The calculated parameters are shown in Table 1. The corresponding simulation results of equation (1) are shown in Figure-1 and Figure-2. Observe that the simulation results of equation (1) were in good agreement with the data of the COVID-19epidemics. At the end points (see solid dots in Figs. 1 and 2) of the 13 investigated time intervals[tl−1, tl] ′s, the simulated numbers and the actual reported numbers were approximately the same (errors were less than one, respectively). See the solid blue lines, the red lines, and the black line in Fig. 1 and Fig. 2.

Results and Discussions

The equation parameters of the recent mainland COVID-19 epidemics (RMCE) are shown in Table 2 (see reference [16], an amended version of reference [13]). From Table 1, Table 2, Figure- 1, and Figure 2, it follows The transmission rate β11 of the symptomatic infections caused by the symptomatic individuals was much lower than the first 75 days’s (December 31, 2021–March 16, 2022) average transmission rate β11 of RMCE (0.0350:0.1072) and was much lower than the last 75 days’s (March 1–May 15, 2022) average transmission rate β11 of RMCE (0.0350:0.2602). The transmission rate β12 of the asymptomatic infections caused by the symptomatic individuals was much higher than the first 75 days average transmission rate of RMCE (0.4890:0.0417) and was similar to the last 30 days’s (April 16–May 15) average transmission rate of RMCE (0.4890:0.5000). The transmission rate β21 of the symptomatic infections caused by the asymptomatic individuals was much lower than the first 75 days’s average transmission rate of the RMCE (0.0413:0.0637) and was still much lower than the last 30 days’s average transmission rate of the RMCE (0.0413:0.1). The transmission rate β22 of the asymptomatic infections caused by the asymptomatic individuals was much higher than the first 75 days’s corresponding average transmission rate of RMCE (0.4269:0.0128) and was much higher than the last 30 days’s corresponding average transmission rate of RMCE (0.4269:0.1000). The last 30 days’ average blocking rate of Θ1(l)′s to the symptomatic infections was lower than the last 30 days’ average blocking rate of RMCE (82.77%:93.83%). The last 30 days’ average blocking rate of Θ2(l)′s to the asymptomatic infections was much higher than the last 30 days’ average blocking rate of RMCE (87.61%:65.83%). However, the first 30 days’ average blocking rate to the asymptomatic infections was much lower than the first 30 days’ average blocking rate of RMCE (41.86%:53.88%). The average recovery rate (κ(l)′s) of the symptomatic individuals was much lower than the corresponding averagerecovery rate of the symptomatic individuals of RMCE (0.0512:0.0636). The last two weeks’ (May 1–May 15) average recovery rate (κ(l)′s) of the symptomatic individuals was similar to the one of the corresponding RMCE (0.1412:0.1323). The first 30 days’ average recovery rate (κa (l)′s) of the asymptomatic individuals was much lower than the first 30 days’ average recovery rate (κa (l)′s) of RMCE (0.01026:0.01996). The last 30 days’ average recovery rate (κa(l)′s) of the asymptomatic individuals was higher than the last 30 days’ average recovery rate of RMCE (0.10066:0.09149).

Virtual Simulations

Assume that after day 75 (May 15, 2022), it still keeps the blocking rates Θ1(13) and Θ2(13), the recovery rates κ (13) and ka (13), and the death rate α (13) until day 105 (June 14, 2022). The simulation results of equation (1) are shown in Fig. 1 and Figure. 2 by cyan lines, magenta lines, and dotted blue lines, respectively. Calculated results show that on day 105, the numbers of the current symptomatic and asymptomatic individuals reach about 409 individuals (see cyan solid dot in Figure-1) and 2460 individuals (see magenta dot in Figure-1), respectively. The numbers of the cumulative recovered symptomatic individuals and cumulative asymptomatic individuals discharged in medical observations reach about 57152 individuals (see cyan solid dot in Figure 2) and 572084 individuals (see magenta dot in Figure 2), respectively. The number of deaths of symptomatic individuals reaches about 619 individuals (see blue dot in Figure 2). Furthermore, assume that after day 75, it still keeps the recovery rates κ (11), κa (11), and the death rate α (11) but increases the blocking rates (Θ1(l), Θ2(l)) ≡ (100%, 100%) until day 105. The simulation results of equation (1) are shown in Figure-1 and Figure-2 by green lines, yellow lines, and dotted red lines, respectively. Calculated results show that on day 105, the numbers of the current symptomatic and the asymptomatic individuals reduce by about 187 (see green solid dot in Figure 1) and 1005 (see yellow solid dot in Figure 1), respectively. The numbers of the cumulative recovered symptomatic individuals and cumulative asymptomatic individuals discharged from medical observations reach about 56002 (see green solid dot in Figure 2) and 561897 (see yellow solid dot in Figure 2), respectively. The number of symptomatic individuals reduced to about 609. Practically on day 105, the numbers of the current symptomatic and asymptomatic individuals, the cumulative recovered symptomatic and asymptomatic individuals, and the dead symptomatic individuals reach 137, 57009, 57729, and 588, respectively. It implies that during days 76–105, the average blocking rates of the symptomatic and the asymptomatic infections reached 100%, and the average recovery rates of the current symptomatic individuals and the current asymptomatic individuals (even though data are not available) increased significantly, and the average death rate of the dead individuals decreased significantly.

Figure 1: Blue circles: outcome of the number of the current symptomatic individuals (CSI); blue line: outcome of the corresponding simulation of equation (1). Red circles: outcome of the number of the current asymptomatic individuals (CAI) charged in medical observations; red line: outcome of the corresponding simulation of equation (1). The lines colored by cyan, magenta, green, and yellow correspond to the virtual simulation results of equation (1). See Section 4, visual simulations, for details

Table 1: Equation parameters of the COVID-19 epidemic in Shanghai during 2022. 3.1-2022. 5.15. β11 = 0.035, β12 = 0.489, β21 = 0.0413, β22 = 0.4269.

Figure 2: Blue circles: outcome of the number of the current cumulative recovered symptomatic individuals (CCSI); blue line: outcome of the corresponding simulations of equation (1). Red circles: outcome of the number of the current cumulative asymptomatic individuals (CCAI) discharged in medical observations; red line: outcome of the corresponding simulations of equation (1). Black circles: the outcome of the number of the current cumulative deceased individuals (CCAI). Black line: outcome of the corresponding simulations of equation (1). The lines colored by cyan, magenta, green, and yellow correspond to the virtual simulation results of equation (1). The dotted lines colored by blue and red correspond to virtual simulation results for the cumulative dead individuals. See Section 4, visual simulations, for details.

Table 2: Equation parameters of the COVID-19 epidemics in mainland China during 2021. 12.31.2022. 5.15 [16]

Conclusion

The main contributions of this paper are summarized as follows: • It is the first time to summarize and analyze the sixth Shanghai COVID-19 epidemic and compare it with the recent mainland China COVID-19 epidemics (RMCE). • It uses model (1) to simulate the dynamics of the sixth Shanghai COVID-19 epidemic. The simulation results were approximately the same as the reported practical data at the end points of the investigated time intervals. • The first 30 days’s low blocking rates to the symptomatic infections, the low recovery rates of the symptomatic individuals, and the high transmission rate of the asymptomatic infections may be the reasons forthe rapid spread of the Shanghai epidemic in the first two months. • It is not a wise strategy to withdraw all prevention and control measures before no new COVID-19-infected cases are reported. A 100% blocking rate to COVID-19 infection spread is a key strategy for early clearance or reduction of epidemic spread [11–14]. • The administration should at least maintain the prevention and control measures implemented 7 days after reaching the infection turning point of the numbers of the current hospitalized symptomatic individuals and the current asymptomatic

Funding

The author has not declared a specific grant for this research from any funding agency in the public, commercial, or nonprofit sectors.

Conflict of Interest

The author declares no potential conflict of interest.

Data Availability Statement

Data are available on reasonable request. Please email the author (13501029489@163.com).

Ethical Statement

Not applicable/No human participants included

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