Parallel evolution and control method for predicting the effectiveness of non-pharmaceutical interventions in pandemics

Abstract

Aim

Nonpharmaceutical interventions (NPIs) are important strategies to utilize in reducing the negative systemic impact pandemic disasters have on human health. However, early on in the pandemic, the lack of prior knowledge and the rapidly changing nature of pandemics make it challenging to construct effective epidemiological models that can be used for anti-contagion decision-making.

Subject and methods

Based on the parallel control and management theory (PCM) and epidemiological models, we developed a Parallel Evolution and Control Framework for Epidemics (PECFE), which can optimize epidemiological models according to the dynamic information during the evolution of pandemics.

Results

The cross-application between PCM and epidemiological models enabled us to successfully construct an anti-contagion decision-making model for the early stages of COVID-19 in Wuhan, China. Using the model, we estimated the effects of gathering bans, intra-city traffic blockades, emergency hospitals, and disinfection, forecasted pandemic trends under different NPIs strategies, and analyzed specific strategies to prevent pandemic rebounds.

Conclusion

The successful simulation and forecasting of the pandemic showed that the PECFE could be effective in constructing decision models during pandemic outbreaks, which is crucial for emergency management where every second counts.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10389-023-01843-2.

Introduction

Pandemics (1918 Spanish Flu, 2003 SARS, 2009 H1N1, 2019 COVID-19, etc.) are disasters often resulting in systemic health and economic losses around the world. Even after more than a year of rigorous COVID-19 prevention and control, the spread of the virus is still threatening the well-being of many individuals and countries. Governments are trying to reduce the impact of pandemics on population health through nonpharmaceutical interventions (NPIs, such as closing restaurants, restricting travel, etc.). However, there remains a lack of clarity on how to apply these NPIs in the right way, at the right place, at the right time. Effective anti-contagion suggestions require scientific analysis, how to effectively predict epidemic trends, and how to effectively estimate the effectiveness of NPIs in reducing virus transmission are the main research questions facing scholars.

So far, scholars have studied the issue of “the relationship between NPIs and virus transmission.” These research results are divided into empirical estimation (Brauner et al. 2021; Flaxman et al. 2020; Banholzer et al. 2021; Islam et al. 2020; Maier and Brockmann 2020; Chang et al. 2020) and model forecasting (Dehning et al. 2020; Wu et al. 2020; Lin et al. 2020; Pandey et al. 2014). Empirical estimation uses historical data to estimate the impact of NPIs (traffic closures, school closures, factory closures, etc.) on confirmed cases or deaths. Some scholars use Bayesian empirical models, while others use econometric regression. Model forecasting uses transmission dynamics models (Wu et al. 2020; Lin et al. 2020; Pandey et al. 2014) or agent models (Dehning et al. 2020) to capture past epidemic trends and then model analysis to forecast epidemic spread trends. Currently, there is more research on empirical estimation with relatively consistent results. However, the estimation method based on empirical data is only for past NPIs and has some application limitations in the context of a rapidly changing pandemic. Model forecasting research results are less readily available and often suffer from the following problems: (1) The results vary widely between different models; (2) The model variables that represent NPIs are abstract and vague; (3) Only short-term forecasting is possible. These problems are because such studies rely heavily on model accuracy and data comprehensiveness. However, in a pandemic, people often lack prior knowledge about the viruses and the complex mega-systems of social transmission.

Overall, the previous related studies have the following difficulties that need to be explored in depth: (1) The dynamic nature of pandemics: The ever-present interaction between government measures, individual behavior, and the nature of the virus leads to rapid and complex changes in the state of pandemic events. This dynamic nature can reduce the validity of not only empirical findings but also simulation models constructed based on past information. (2) Lack of data and prior knowledge: Lack of data and prior knowledge means that the model may suffer from bias in structure construction and parameter estimation, i.e., not considering or incorrectly considering some cause-effect relationship. In addition, in the absence of data and prior knowledge, the model results are likely to suffer from overfitting problems, i.e., small fitting error for historical data but significant prediction error for new data.

To address the difficulties caused by the dynamic nature of the pandemic and the lack of data and prior knowledge, we developed a Parallel Evolution and Control Framework for Epidemics (PECFE) by integrating the strengths of epidemiological models and parallel control and management theory (PCM). This part will be described in detail in “Theory basis and inspiration” section.

Parallel evolution and control framework for epidemics

Theory basis and inspiration

Epidemiological models

The study of epidemiological models began in 1927 when Kermack and McKendrick (1927) proposed the Susceptible-Infected-Removed (SIR) ordinary differential equations (ODE) model (also known as the compartmental model) to describe the changes between populations with different infection statuses. Since then, many scholars have been inspired by SIR theory and proposed Susceptible-Exposed-Infected-Removed (SEIR), SEIRS, MSIRS (M means maternal derived immunity), and other models. With new dynamics of epidemics at the spatial scale and the development of computer simulation techniques, meta-population models (Li et al. 2020) and agent models (Pei et al. 2018) have also been applied in epidemic models. With the help of computer simulation techniques, these models have simulated the physical virus transmission process more accurately.

In PECFE, the epidemiological model provides the model basis for simulating the transmission process of a pandemic, which describes the transmission mechanisms, influencing factors, and feedback loops of a pandemic. First, the epidemiological model is able to calculate key epidemiological information such as the number of new infections, the number of new deaths and the number of new recoveries, which provides PECFE with the most intuitive information on the real-time status of the pandemic. Second, epidemiological models such as SIR and SEIR can be improved according to the nature of different pandemics and external environmental characteristics, which gives PECFE flexibility in modeling when facing different pandemics. Finally, the ODE model has a good feedback loop that allows the model to evolve autonomously given the initial parameters, which can provide the necessary basis for pandemic trend prediction.

Parallel control and management

Parallel control and management theory (PCM) (Wang 2010) is a modeling method in the fields of engineering management (Wang 2010; Li et al. 2019) and emergency management (Xie et al. 2020). PCM is divided into parallel evolution and parallel control: (1) Parallel evolution uses real-time data to cultivate artificial models. The complex artificial model undergoes multiple iterations based on the parallel evolution optimization method to reduce the prediction error. (2) Parallel control performs experimental analysis of the artificial model, finds the optimal strategies, and executes these strategies in the real world. Figure 1 shows the specific logic process. Through continuous comparison, the model is able to adapt to environmental changes and improve its own predictive capabilities.

Fig. 1.

PCM operation logic

Facing the difficulties of “The dynamic nature of pandemics” and “Lack of data and prior knowledge” in the current research, PCM can provide some solutions. First, PCM is a data-driven modeling approach that can simplify the modeling process by turning a complex system into an input-output black-box problem through black-box models such as machine learning. Second, the method optimizes the model with real-time information generated from real scenarios, which can improve the adaptability of the model in different scenarios. Finally, data-driven models have a set of methods to reduce overfitting, such as cross-validation and regularization, which can improve the generalization ability of the model in case of insufficient data

Framework content and operation mechanism

This paper integrates the advantages of epidemiological model and PCM, and proposed the Parallel Evolution and Control Framework for Epidemics (PECFE) to solve the problems in the process of epidemic modeling and application. PECFE is divided into two parts: the epidemiological model and parallel evolution and control, and the basic logic of the framework is shown in Fig. 2.

Fig. 2.

Parallel evolution and control framework for epidemics

The main goal of the epidemiological model module is to construct an epidemiological model based on the current pandemic to simulate the virus transmission process. In the process of epidemiological model construction, real data are necessary for model construction, and real data include not only epidemiological data but also anti-contagion data. Epidemiological data are used to construct epidemic transmission mechanisms and anti-contagion data are used to estimate the impact of anti-contagion measures on virus transmission. In PECFE, the construction of epidemiological models can be divided into three steps: first, build epidemiological models based on the nature, transmission mechanisms, and characteristics of epidemics in real scenarios.; second, identify variables or parameters with dynamics and complexity in epidemiological models, for example, virus transmission rates β in SIR models are dynamically and complexly influenced by anti-contagion measures; finally, model these complex and dynamic epidemiological variables or parameters separately, for example, decision makers can build regression models for virus transmission rate β to simulate the trend.

The goal of the parallel evolution and control module is to improve the generalization ability of the model by dynamically optimizing (cultivating) epidemiological variables or parameters using real-time data. In contrast to the static data used in traditional epidemiological models, the real-time data generated by real pandemic scenarios is the driving force for model optimization (cultivation). The process of using real-time data to optimize (cultivate) a model is called parallel evolution. Through parallel evolution, the cultivated epidemiological variables or parameters are combined with the original epidemiological model to form the epidemiological-PCM model. By analyzing the epidemiological-PCM model, decision makers are able to develop theoretically optimal strategies that should be executed in the real world to control the spread of epidemics. To verify the validity of the epidemiology-PCM model, the real results after the execution need to be fed back to the epidemiology-PCM model and compared with the simulation results of the epidemiology-PCM model to determine whether the epidemiology-PCM model remains consistent with the real scenario, and if not, it needs to return to parallel evolution (re-cultivation). The process of model analysis - strategies execution and comparison of real and virtual results is called parallel control. Parallel evolution and parallel control form a closed loop that allows the epidemiology-PCM model to be continuously improved and optimized (cultivated), while providing real-time decision suggestions.

Methodology

To better apply PECFE, the implementation process of the “epidemiological model” and “parallel evolution and control” will be described in detail in Supplementary materials (section 1).

Case study: COVID-19

COVID-19 is a typical pandemic event. The pandemic broke out in Wuhan in 2020 and swept through every country in the world, causing hundreds of millions of infections and millions of deaths; therefore, we use the COVID-19 event in Wuhan in early 2020 as a real case to implement PECFE to further estimate and predict the effectiveness of NPIs and provide guidance for the prevention and control of the current COVID-19 and similar pandemic events in the future.

Methods and materials

According to PECFE, first, we constructed an epidemiological model of COVID-19 based on the SEIR model considering NPIs (SEIR-NPIs). Equations (1–6) are the mathematical formula for the epidemiological model (Li et al. 2020). Since there were many undocumented cases at the beginning of the COVID-19 outbreak, the reporting rate α (the proportion of cases being documented) is imported into the model to separate the cases that were documented (I^r) and those that were not (I^u). In general, the more severe the symptoms, the more likely to go to the hospital and the more likely to be documented. Therefore, there is an underlying assumption (Li et al. 2020) in the model: documented cases have more severe symptoms than undocumented cases, and the stronger the symptoms, the more infectious they are. Based on this assumption, the transmission rate β for documented cases is more significant than for undocumented cases μβ. μ is the weakening factor and takes a value between [0-1]. The modeling process is detailed in supplementary materials (section 2.1).

$$\frac{\mathit{dS}}{\mathit{dt}}=-\frac{\beta S{I}^r}{N}-\frac{\mu \beta S{I}^u}{N}$$ 1

$$\frac{\mathit{dE}}{\mathit{dt}}=\frac{\beta S{I}^r}{N}+\frac{\mu \beta S{I}^u}{N}-\frac{E}{Z}$$ 2

$$\frac{d{I}^r}{\mathit{dt}}=\alpha \frac{E}{Z}-\frac{I^r}{D}$$ 3

$$\frac{d{I}^u}{\mathit{dt}}=\left(1,-,\alpha \right)\frac{E}{Z}-\frac{I^u}{D}$$ 4

$$\frac{d{R}^r}{\mathit{dt}}=\frac{I^r}{D}$$ 5

$$\frac{d{R}^u}{\mathit{dt}}=\frac{I^u}{D}$$ 6

Where S is susceptible, N is the total number of people, E is exposed, Z is the latent period, and D is the infectious period.

Second, we used parallel evolution and control method to cultivate (optimize) the SEIR-NPIs model, and the cultivation process and results are detailed in supplementary materials (section 2.3). Finally, the cultivated SEIR-NPIs are upgraded to the SEIR-NPIs-PCM model, and the running method of the SEIR-NPIs-PCM model is detailed in supplementary materials (section 2.4).

To implement PECFE, COVID-19 case data, initial parameters of the epidemiological model and NPIs data were collected in this paper. The source, content and method of collection of these data are detailed in Supplementary materials (section 2.2). In this paper, a total of 16 categories of NPIs were collected, and their categories and explanations are shown in Table 1.

Table 1.

Classification and explanation of NPIs

Type of NPIs	Abbreviations	Explanations
Stay at home	SH	People are asked to stay at home
Public service suspension and public place closure	PSS&PPC	Closure of public services (e.g., civil services, etc.) and public places (parks, squares, scenic spots, etc.)
Intra-city traffic blockades	IATB	Public transportation in the city is closed and personal travel is restricted
Inter-city traffic blockades	ITB	Prohibited from leaving Wuhan and restricted from entering Wuhan
Extended company holidays	ECH	Extended leave and limited return to work
No gathering activities	NGA	Prohibit people from gathering offline, including parties, chatting, chess and cards
Medical resource support	MRS	Other regions support medical supplies to Wuhan, including masks, medicines, medical equipment, etc.
Emergency support from doctors and nurses	ESDN	Other regions send doctors and nurses to Wuhan
Emergency hospitals	EH	Increase the number of emergency hospitals and beds, such as Huoshenshan Hospital
Search for infected people	SIP	Large-scale detection of residents to search for suspected cases
Administrative and legal support	ALS	Laws and regulations issued to ensure the implementation of measures
Basic living support	BLS	Measures taken to ensure the basic livelihood of residents during their stay at home, such as centralized shopping, online shopping, etc.
Disinfection	DF	Regular public place disinfection
Limit the number of people gathered	LNPG	In the case of epidemic mitigation, gatherings within the limit of numbers are allowed
Individual protection	IP	People are required to wear masks in public places
Popularization of virus knowledge	PVK	Educate people online about virus transmission and prevention

Experimental analysis and results

The simulation results of virus transmission from day0 to day60 are shown in Fig. 3. α is the proportion of confirmed cases being documented and β is the rate of virus transmission, see Supplementary materials (section 2.1) for details of the meaning. In Fig. 3, the simulation results cover almost all the real data, which proves the validity of the SEIR-NPIs-PCM model.

Fig. 3.

Simulation results of the first 60 days of the spread trend of COVID-19 in Wuhan. Note. Horizontal axis: Time0–Time60 means 60 days from 2020/1/11–2020/3/10. The light blue fill (panel label: “Simulation: Range”) indicates the range of values for the 200 random simulations. The blue line (panel label: “Simulation: Mean”) indicates the average of 200 random simulations. The orange line (panel label: “Real Data”) indicates real data for 2020/1/11-2020/3/10. α and β denote the case documented rate and the virus transmission rate, respectively

We split the experimental analysis into two parts: empirical estimation and forecasting. Empirical estimation serves to estimate the impact of different NPIs strategies on the epidemic. The specific estimation strategy is shown in Table 2. The estimation results are shown in Fig. 4. All estimation results showed that NPIs (IATB, EH, NGA, DF) were inversely proportional to virus transmission. Compared to baseline, a 50% increase or decrease in NGA resulted in a 48% decrease or 165% increase in the cumulative number of cases. Figure 4(A3,B3,C3) shows that after Time 35, the range of random estimation of NGA is significantly different from baseline. These results indicate that the effect of NGA on the number of cases is significant. The ranking of the effects of the NPIs in strategies E11–E42 is NGA≥DF≥IATB≥EH. In addition, we add two composite strategies, E51 and E52, to estimate the impact of changes in NPI packages on the epidemic. When all NPIs were down, the cumulative number of cases on Time60 (2020/3/10) reached 991832 [583040, 1400624], an increase of 1833% compared to the baseline indicating that the spread of the virus is no longer under control. Finally, we found an interesting “rowing upstream” phenomenon: the effect of increasing NPIs is much weaker than the effect of decreasing NPIs. This means that stopping the spread of the virus is like rowing upstream, not to advance is to drop back.

Table 2.

Estimation strategies and estimation results

Codes	NPIs strategies	Cumulative cases (Percentage change compared to baseline) [95% confidence interval]	Results: Fig 4
Baseline	No change	51321 (0) [36545, 65751]	–
E11	IATB 50% increase	37682 (–27%) [27151, 48213]	A1,B1,C1
E12	IATB 50% decrease	75951 (+48%) [52536, 99366]
E21	EH 50% increase	44186 (–14%) [33185, 55188]	A2,B2,C2
E22	EH 50% decrease	62518 (+22%) [42880, 82157]
E31	NGA 50% increase	26802 (–48%) [19603, 34001]	A3,B3,C3
E32	NGA 50% decrease	136180 (+165%) [91257, 181102]
E41	DF50% increase	37801 (–26%) [27477, 48125]	A4,B4,C4
E42	DF 50% decrease	93592 (+82%) [61976, 125208]
E51	IATB,EH,NGA,DF 50% increase	20013 (–61%) [15423, 24604]	A5,B5,C5
E52	IATB,EH,NGA,DF 50% decrease	991832 (+1833%) [583040, 1400624]

1: Duration of strategies implementation: 2020/1/11–2020/3/10 (60 Days)

Fig 4.

Estimation of the impact of NPIs strategies. Note. Horizontal axis: Time0–Time 60 means 60 days from 2020/1/11–2020/3/10. The light fill (panel labels: light blue, light orange and light green) indicates the range of values for 200 random simulations with different NPIs strategies. The solid lines (panel labels: blue, orange and green) represent the average of 200 random simulations under different NPIs strategies. The description of specific NPIs strategies is detailed in Table 2. α and β denote the case documented rate and the virus transmission rate, respectively

The purpose of forecasting is to provide theoretical guidance for future decision-making. We designed the NPIs strategies for the future period Time61–Time120 (2020/3/11–2020/5/9) to forecast the epidemic trend for these 60 days. NPIs strategies are given in Table 3. As shown in Fig. 3, in 2020/3/10, both new cases and β in Wuhan have been controlled at a low level. The main task at hand is how to mitigate restrictions while avoiding the rebound of the epidemic. The removal of restrictions necessarily involves the opening of transportation, the relaxation of the gathering ban, and the restoration of normal medical care. Therefore, IATB, NGA, and EH are our main forecasting analysis variables. To make NPIs strategies highly executable, we set NPIs to decrease by 1%, 2.5%, 5%, and 10% per day to simulate a decrease in NPIs by about 75%, 50%, 25%, and 0% after 30 days. The forecasting results under different strategies are shown in Fig. 5. As seen in Fig. 5(A1,A2,A3), whether the traffic is fully open after 30 days (2020/4/9) or half-open, the R_e (Time91-Time120) of IATB remains around 1 (or less than 1). R_e ≤ 1 keeps the number of new cases at low levels and does not lead to a rebound of the epidemic. Figure 5(A3,B3,C3) shows a decreasing trend in the number of new cases (R_e<1) even if hospitals all return to normal medical care. The results of F21 and F22 suggest that relaxing the gathering ban by half within 30 days can keep the R_e around 1. However, a complete lifting of the gathering ban can increase the R_e to 1.59 [0.76, 2.31], which leads to a significant upward trend in the number of new cases after Time100. Finally, we also forecasted the epidemic trend under the simultaneous change of IATB, EH, and NGA (F41 and F42). The results of F41 suggest that the NPIs decrease at a rate of 1% per day and stop after Time91, which can keep R_e around 1. Once the rate of decrease of NPIs is higher than 1%, e.g., 5% (F42), it leads to an upward trend in the number of new cases.

Table 3.

Forecasting strategies and results

Codes	NPIs strategies	2020/4/9 Re [95% Confidence interval]	Results: Fig 5
Baseline	No change	0.32 [0.01, 0.67]	–
F11	IATB 2.5% decrease per day	0.74 [0.01, 1.42]	A1,B1,C1
F12	IATB 10% decrease per day	1.07 [0.37, 1.76]
F21	NGA 2.5% decrease per day	1.02 [0.25, 1.67]	A2,B2,C2
F22	NGA 10% decrease per day	1.59 [0.76, 2.31]
F31	EH 2.5% decrease per day	0.54 [0.09, 0.95]	A3,B3,C3
F32	EH 10% decrease per day	0.74 [0.13, 1.36]
F41	IATB,EH,NGA 1% decrease per day	1.01 [0.2, 1.81]	A4-F4
F42	IATB,EH,NGA 5% decrease per day	2.13 [1.38, 2.88]

1: Duration of strategies implementation: 2020/3/11-2020/4/9 (30 days). R_e = αβD + (1 − α)μβD

Fig. 5.

Forecasting results under NPIs strategies. Note. Horizontal axis: Time0–Time60 means 60 days from 2020/1/11-2020/3/10, where Time 61–Time90 is the duration of NPIs strategies implementation and Time 61–Time120 is the forecast interval.R_e is the reproduction number over time, and R_e ≤ 1 indicates that virus transmission has been contained. The red solid line is to assist in determining whether R_e ≤ 1. Subplots C1, C2, C3, D4, E4, and F4 indicate the variation in the strength of the measures for different NPIs. The light fill (panel labels: light blue, light orange, and light green) indicates the range of values for 200 random simulations with different NPIs strategies. The solid lines (panel labels: blue, orange, and green) represent the average of 200 random simulations under different NPIs strategies. The description of specific NPIs strategies is detailed in Table 3

Discussions

Under PECFE, we constructed an SEIR-NPIs-PCM model. With continuous model testing, validation and optimization, we estimated and predicted the effects of NPIs on the epidemic. These effects are robust in similar settings.

Intra-regional traffic blockade and gathering ban both seem to have been effective at reducing COVID-19 transmission. This is consistent with the empirical studies of Brauner et al. (2021) and Flaxman et al. (2020). The results of the Bayesian hierarchical model from Brauner et al. (2021) showed that the anti-contagion effect of limiting the number of people in the gathering to less than 10 was significant in 41 countries. Our model results suggest that gathering bans are the most effective in reducing COVID-19 transmission compared to other NPIs. The gathering ban stops the spread of the virus caused by the close contact among people. It greatly reduces the risk of viral infections associated with Spring Festival activities such as New Year’s Eve dinners and New Year visits. In China, many cases come from large family gatherings. The impact of intra-regional traffic blockade (shutting down public transport, blocking roads, etc.) on the virus transmission differs in the available studies. Several research results (Lai et al. 2020; Liu et al. 2021; Banholzer et al. 2021; Islam et al. 2020) have shown that restricting traffic has less impact on virus transmission when other NPIs measures are in place. In contrast, the Bayesian empirical estimates of Flaxman et al. (2020) show the opposite. Our estimates suggest that traffic closures can influence virus transmission, but with limited effect. Essentially, the existing findings do not deny the impact of traffic closures but only differ in the effect scope and hypothetical conditions. Observing our forecasting results, IATB does not lead to a rebound of the epidemic even if the entire lifting is within one month when other NPIs are unchanged. This again validates previous observations (Lai et al. 2020; Liu et al. 2021; Banholzer et al. 2021; Islam et al. 2020).

Most existing studies have focused on the effects of NPIs that limit inter-individual contact such as traffic bans, gathering bans, etc. However, studies on the effect of NPIs on limiting the virus itself, such as emergency hospitals and disinfection, are very rare, and our findings extend this field. The results of the experimental analysis show that the construction of emergency hospitals and disinfection seems to reduce the spread of COVID-19. The forecasting results of EH show that emergency hospitals have very limited effectiveness after the outbreak is controlled. The possible reason for this is that the decrease in cases has led to redundancies in beds and emergency hospitals. Wuhan has been closing many mobile and emergency hospitals since early March, which indirectly proves the results of our experimental analysis. The effectiveness of disinfection in reducing COVID-19 transmission is significant. According to the World Health Organization (World Health Organization 2020), the transmission routes of the SARS-CoV-2 virus include droplet and contact transmission. SARS-CoV-2 virus remaining in the external environment has a lipid envelope, which is efficiently disrupted by most disinfectants (Abramowicz and Basseal 2020). For example, 62–75% alcohol, 0.5% hydrogen peroxide, or 0.1% sodium hypochlorite can quickly inactivate the virus. Therefore, regular disinfection of hospitals, elevators, and poorly ventilated places (Zhang et al. 2020; Jin et al. 2020) can significantly reduce virus survivability.

Studies have shown (Hsiang et al. 2020; Dehning et al. 2020) that a package of NPIs measures can rapidly reduce virus transmission. Dehning et al. (2020) estimated the effect of a package of NPIs strategies at different stages in Germany and showed that an increasing package of strategies curbed the increase in new cases. The estimated and predicted results of our combination strategies are consistent with these studies. The results of E52 and F42 show that the relaxation of the package of NPIs strategies leads to an out-of-control epidemic (the accelerated increase in cases), but the relaxation of the NPI alone does not. These suggest that the effectiveness of a single NPI is limited and that a package of NPIs strategies needs to be applied to quickly control the outbreak. Based on the above discussion, we offer the following recommendations: (1) A package of NPIs strategies is the most effective way to control the outbreak in a short time. (2) Focus on enforcement of gathering bans, disinfection, and other measures. Intra-regional traffic blockade can be used as a follow-up reinforcement measure. (3) When the epidemic is under control, transportation can be gradually opened to ensure necessary city operations. At the same time, medical resources should be reasonably arranged according to the number of cases to prevent waste of resources. (4) because of the “rowing upstream” phenomenon in epidemic prevention and control, the NPIs strategies need to be implemented in strict accordance with the standards, and any negligence may lead to the loss of success.

Conclusion

This paper investigates epidemiological modeling, analysis and decision execution methods under the difficulties of lack of prior knowledge and rapid changes in pandemic trends. By combining the advantages of epidemiological models and PCM, we propose the Parallel Evolution and Control Framework for Epidemics (PECFE) as a specific framework for solving the above difficulties. Finally, we validated the validity of PECFE using a real example of COVID-19 and estimated and predicted the effect of various NPIs on virus transmission.

Summary points:

1. In this paper, a new epidemiological modeling and decision-making framework is proposed to overcome the problems of difficult modeling, poor adaptability, and weak analysis, and to provide a reference for modeling and analysis of current and future similar pandemics.

2. We give details of the PECFE implementation that will help scholars and public health practitioners to replicate the framework in the event of a similar pandemic in the future.

3. We analyze and discuss the effectiveness of various NPIs to validate and refine existing research findings. In addition, we make specific anti-contagion suggestions that can help relevant institutions to develop scientific public health policies.

In this paper, PECFE only considers an epidemiological model based on an ordinary differential model; other epidemiological models, such as agent models, machine learning models, etc., are not included. These models have different structures and characteristics, and their incorporation into PECFE may yield new highlights. Due to the objective, realistic, easily available and quantitative analysis of announcement data, we used NPIs announcement data to measure the strength of NPIs. Although fluctuations in announcement data are highly correlated with NPIs intensity, there are still unpredictable measurement errors that lead to model estimation bias. How to measure the strength of NPIs realistically, objectively, credibly, and effectively is the direction of further research. In addition, the modeling of COVID-19 considered only the scenario at the beginning of the outbreak and did not take into account factors such as secondary and multiple rebounds of the outbreak and vaccination. These issues need to be further investigated and improved.

Authors’ contributions

All authors contributed to the study conception and design. T.X., H.H., W.C., and Y.W. were involved in conceptualization and developed the specific modelling approach. T.X., and H.H. wrote the model code and undertook the modelling analysis. T.X., H.H., and Y.W. curated the underlying data for the model. H.H., and W.C. produced the visualization for the paper. T.X., and H.H. wrote the original draft. All authors reviewed and edited the manuscript, and all approved the final version.

Funding

This study was funded by National Natural Science Foundation of China (No. 71974090); Natural Science Foundation of Hunan Province of China (No. 2018JJ2336); Postgraduate Scientific Research Innovation Project of Hunan Province (QL20210217); Philosophy and Social Science Foundation of Hunan Province of China (18YBQ105); Youth talents support program of Hunan Province of China (2018HXQ03); Key scientific research project of Education Department(No. 20A443); Social Science Key Breeding Project of USC (2018XZX16); Doctoral scientific research foundation of USC (No. 2013XQD27); Philosophy and Social Science Foundation Youth Project of Hunan Province of China (19YBQ093); Scientific research project of Education Department (No. 20C1625); State Scholarship Fund (202108430098) from CSC; Mr. XIE TIAN (File No. 202208430061); Double Tops Discipline of Management Science and Engineering of USC.

Data availability

The data underlying this article are available in the article and in its online supplementary material.

Code availability

Code for the model and model fitting is available at: https://github.com/MSOROMEGA/AnticontagionStrategies.git.

Declarations

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Conflict of interest

The authors declare they have no conflict of interest.