Threshold conditions for curbing COVID-19 with a dynamic zero-case policy derived from 101 outbreaks in China.

By 31 May 2022, original/Alpha, Delta and Omicron strains induced 101 outbreaks of COVID-19 in mainland China. Most outbreaks were cleared by combining non-pharmaceutical interventions (NPIs) with vaccines, but continuous virus variations challenged the dynamic zero-case policy (DZCP), posing questions of what are the prerequisites and threshold levels for success? And what are the independent effects of vaccination in each outbreak? Using a modified classic infectious disease dynamic model and an iterative relationship for new infections per day, the effectiveness of vaccines and NPIs was deduced, from which the independent effectiveness of vaccines was derived. There was a negative correlation between vaccination coverage rates and virus transmission. For the Delta strain, a 61.8% increase in the vaccination rate (VR) reduced the control reproduction number (CRN) by about 27%. For the Omicron strain, a 20.43% increase in VR, including booster shots, reduced the CRN by 42.16%. The implementation speed of NPIs against the original/Alpha strain was faster than the virus's transmission speed, and vaccines significantly accelerated the DZCP against the Delta strain. The CRN ([Formula: see text]) during the exponential growth phase and the peak time and intensity of NPIs were key factors affecting a comprehensive theoretical threshold condition for DZCP success, illustrated by contour diagrams for the CRN under different conditions. The DZCP maintained the [Formula: see text] of 101 outbreaks below the safe threshold level, but the strength of NPIs was close to saturation especially for Omicron, and there was little room for improvement. Only by curbing the rise in the early stage and shortening the exponential growth period could clearing be achieved quickly. Strengthening China's vaccine immune barrier can improve China's ability to prevent and control epidemics and provide greater scope for the selection and adjustment of NPIs. Otherwise, there will be rapid rises in infection rates and an extremely high peak and huge pressure on the healthcare system, and a potential increase in excess mortality.

Optimal strategies for coordinating infection control and socio-economic activities.

It becomes challenging to identify feasible control strategies for simultaneously relaxing the countermeasures and containing the Covid-19 pandemic, given China's huge population size, high susceptibility, persist vaccination waning, and relatively weak strength of health systems. We propose a novel mathematical model with waning of immunity and solve the optimal control problem, in order to provide an insight on how much detecting and social distancing are required to coordinate socio-economic activities and epidemic control. We obtain the optimal intensity of countermeasures, i.e., the dynamic nucleic acid screening and social distancing, under which the health system is functioning normally and people can engage in a certain level of socio-economic activities. We find that it is the isolation capacity or the restriction of the case fatality rate (CFR) rather than the hospital capacity that mainly determines the optimal strategies. And the solved optimal controls under quarterly CFR restrictions exhibit oscillations. It is worth noticing that, if without considering booster or very low booster rate, the optimal strategy is a "on-off" mode, alternating between lock down and opening with certain social distancing, which reflects the importance and necessity of China's static management on a certain area during Covid-19 outbreak. The findings suggest some feasible paths to smoothly transit from the Covid-19 pandemic to an endemic phase.

The resurgence risk of COVID-19 in China in the presence of immunity waning and ADE: A mathematical modelling study.

The mass vaccination program has been actively promoted since the end of 2020. However, waning immunity, antibody-dependent enhancement (ADE), and increased transmissibility of variants make the herd immunity untenable and the implementation of dynamic zero-COVID policy challenging in China. To explore how long the vaccination program can prevent China at low resurgence risk, and how these factors affect the long-term trajectory of the COVID-19 epidemics, we developed a dynamic transmission model of COVID-19 incorporating vaccination and waning immunity, calibrated using the data of accumulative vaccine doses administered and the COVID-19 epidemic in 2020 in mainland China. The prediction suggests that the vaccination coverage with at least one dose reach 95.87%, and two doses reach 77.92% on 31 August 2021. However, despite the mass vaccination, randomly introducing infected cases in the post-vaccination period causes large outbreaks quickly with waning immunity, particularly for SARS-CoV-2 variants with higher transmissibility. The results showed that with the current vaccination program and 50% of the population wearing masks, mainland China can be protected at low resurgence risk until 8 January 2023. However, ADE and higher transmissibility for variants would significantly shorten the low-risk period by over 1 year. Furthermore, intermittent outbreaks can occur while the peak values of the subsequent outbreaks decrease, indicating that subsequent outbreaks boosted immunity in the population level, further indicating that follow-up vaccination programs can help mitigate or avoid the possible outbreaks. The findings revealed that the integrated effects of multiple factors: waning immunity, ADE, relaxed interventions, and higher variant transmissibility, make controlling COVID-19 challenging. We should prepare for a long struggle with COVID-19, and not entirely rely on the COVID-19 vaccine.

Controlling Multiple COVID-19 Epidemic Waves: An Insight from a Multi-scale Model Linking the Behaviour Change Dynamics to the Disease Transmission Dynamics.

COVID-19 epidemics exhibited multiple waves regionally and globally since 2020. It is important to understand the insight and underlying mechanisms of the multiple waves of COVID-19 epidemics in order to design more efficient non-pharmaceutical interventions (NPIs) and vaccination strategies to prevent future waves. We propose a multi-scale model by linking the behaviour change dynamics to the disease transmission dynamics to investigate the effect of behaviour dynamics on COVID-19 epidemics using game theory. The proposed multi-scale models are calibrated and key parameters related to disease transmission dynamics and behavioural dynamics with/without vaccination are estimated based on COVID-19 epidemic data (daily reported cases and cumulative deaths) and vaccination data. Our modeling results demonstrate that the feedback loop between behaviour changes and COVID-19 transmission dynamics plays an essential role in inducing multiple epidemic waves. We find that the long period of high-prevalence or persistent deterioration of COVID-19 epidemics could drive almost all of the population to change their behaviours and maintain the altered behaviours. However, the effect of behaviour changes fades out gradually along the progress of epidemics. This suggests that it is essential to have not only persistent, but also effective behaviour changes in order to avoid subsequent epidemic waves. In addition, our model also suggests the importance to maintain the effective altered behaviours during the initial stage of vaccination, and to counteract relaxation of NPIs, it requires quick and massive vaccination to avoid future epidemic waves.

Analysis of a diffusive epidemic system with spatial heterogeneity and lag effect of media impact.

We considered an SIS functional partial differential model cooperated with spatial heterogeneity and lag effect of media impact. The wellposedness including existence and uniqueness of the solution was proved. We defined the basic reproduction number and investigated the threshold dynamics of the model, and discussed the asymptotic behavior and monotonicity of the basic reproduction number associated with the diffusion rate. The local and global Hopf bifurcation at the endemic steady state was investigated theoretically and numerically. There exists numerical cases showing that the larger the number of basic reproduction number, the smaller the final epidemic size. The meaningful conclusion generalizes the previous conclusion of ordinary differential equation.

Complex dynamics of an epidemic model with saturated media coverage and recovery.

During the outbreak of emerging infectious diseases, media coverage and medical resource play important roles in affecting the disease transmission. To investigate the effects of the saturation of media coverage and limited medical resources, we proposed a mathematical model with extra compartment of media coverage and two nonlinear functions. We theoretically and numerically investigate the dynamics of the proposed model. Given great difficulties caused by high nonlinearity in theoretical analysis, we separately considered subsystems with only nonlinear recovery or with only saturated media impact. For the model with only nonlinear recovery, we theoretically showed that backward bifurcation can occur and multiple equilibria may coexist under certain conditions in this case. Numerical simulations reveal the rich dynamic behaviors, including forward-backward bifurcation, Hopf bifurcation, saddle-node bifurcation, homoclinic bifurcation and unstable limit cycle. So the limitation of medical resources induces rich dynamics and causes much difficulties in eliminating the infectious diseases. We then investigated the dynamics of the system with only saturated media impact and concluded that saturated media impact hardly induces the complicated dynamics. Further, we parameterized the proposed model on the basis of the COVID-19 case data in mainland China and data related to news items, and estimated the basic reproduction number to be 2.86. Sensitivity analyses were carried out to quantify the relative importance of parameters in determining the cumulative number of infected individuals at the end of the first month of the outbreak. Combining with numerical analyses, we suggested that providing adequate medical resources and improving media response to infection or individuals' response to mass media may reduce the cumulative number of the infected individuals, which mitigates the transmission dynamics during the early stage of the COVID-19 pandemic.

Determining travel fluxes in epidemic areas.

Infectious diseases attack humans from time to time and threaten the lives and survival of people all around the world. An important strategy to prevent the spatial spread of infectious diseases is to restrict population travel. With the reduction of the epidemic situation, when and where travel restrictions can be lifted, and how to organize orderly movement patterns become critical and fall within the scope of this study. We define a novel diffusion distance derived from the estimated mobility network, based on which we provide a general model to describe the spatiotemporal spread of infectious diseases with a random diffusion process and a deterministic drift process of the population. We consequently develop a multi-source data fusion method to determine the population flow in epidemic areas. In this method, we first select available subregions in epidemic areas, and then provide solutions to initiate new travel flux among these subregions. To verify our model and method, we analyze the multi-source data from mainland China and obtain a new travel flux triggering scheme in the selected 29 cities with the most active population movements in mainland China. The testable predictions in these selected cities show that reopening the borders in accordance with our proposed travel flux will not cause a second outbreak of COVID-19 in these cities. The finding provides a methodology of re-triggering travel flux during the weakening spread stage of the epidemic.

The effectiveness of quarantine and isolation determine the trend of the COVID-19 epidemics in the final phase of the current outbreak in China

Objectives: Since January 23rd 2020, stringent measures for controlling the novel coronavirus epidemics have been gradually enforced and strengthened in mainland China. The detection and diagnosis have been improved as well. However, the daily reported cases staying in a high level make the epidemics trend prediction difficult.

Investigating the relationship between reopening the economy and implementing control measures during the COVID-19 pandemic.

OBJECTIVES: The COVID-19 pandemic has resulted in an enormous burden on population health and the economy around the world. Although most cities in the United States have reopened their economies from previous lockdowns, it was not clear how the magnitude of different control measures-such as face mask use and social distancing-may affect the timing of reopening the economy for a local region. This study aimed to investigate the relationship between reopening dates and control measures and identify the conditions under which a city can be reopened safely. STUDY DESIGN: This was a mathematical modeling study. METHODS: We developed a dynamic compartment model to capture the transmission dynamics of COVID-19 in New York City. We estimated model parameters from local COVID-19 data. We conducted three sets of policy simulations to investigate how different reopening dates and magnitudes of control measures would affect the COVID-19 epidemic. RESULTS: The model estimated that maintaining social contact at 80% of the prepandemic level and a 50% face mask usage would prevent a major surge of COVID-19 after reopening. If social distancing were completely relaxed after reopening, face mask usage would need to be maintained at nearly 80% to prevent a major surge. CONCLUSIONS: Adherence to social distancing and increased face mask usage are keys to prevent a major surge after a city reopens its economy. The findings from our study can help policymakers identify the conditions under which a city can be reopened safely.

Quantifying competitive advantages of mutant strains in a population involving importation and mass vaccination rollout.

The SARS-CoV-2 Delta variant, known as B.1.617.2 and first identified in India, is becoming a dominant strain in many countries due to its extreme infectiousness. Assessing and quantifying the transmissibility and competitive advantage of the Delta variant is of major significance for countries around the world so that appropriate measures to mitigate and even eliminate the epidemic can be introduced. Aiming at such problems, we proposed a method to model the invasion process of a novel strain and estimate the competitive advantage of the invading strain over the local strain. We applied this method to study the invasion and spread of the Delta variant into England. We have estimated the basic reproduction number of the Delta variant as being 49% higher than that of the Alpha variant (CI: 45-52%), assuming a mean generation interval of 5 days with a standard deviation of 3 days. In the period 11 April to 17 May 2021, the effective reproduction number of the Delta variant was 65% higher than that of the Alpha variant in England (CI: 61-70%). Our results show that the Delta variant has a significantly higher transmission capacity than other strains, which explains the rebound of the epidemic in many countries, even in those with relatively high vaccination coverages.

Linking the disease transmission to information dissemination dynamics: An insight from a multi-scale model study.

During the outbreak of emerging infectious diseases, information dissemination dynamics significantly affects the individuals' psychological and behavioral changes, and consequently influences on the disease transmission. To investigate the interaction of disease transmission and information dissemination dynamics, we proposed a multi-scale model which explicitly models both the disease transmission with saturated recovery rate and information transmission to evaluate the effect of information transmission on dynamic behaviors. Considering time variation between information dissemination, epidemiological and demographic processes, we obtained a slow-fast system by reasonably introducing a sufficiently small quantity. We carefully examined the dynamics of proposed system, including existence and stability of possible equilibria and existence of backward bifurcation, by using the fast-slow theory and directly investigating the full system. We then compared the dynamics of the proposed system and the essential thresholds based on two methods, and obtained the similarity between the basic dynamical behaviors of the slow system and that of the full system. Finally, we parameterized the proposed model on the basis of the COVID-19 case data in mainland China and data related to news items, and estimated the basic reproduction number to be 3.25. Numerical analysis suggested that information transmission about COVID-19 pandemic caused by media coverage can reduce the peak size, which mitigates the transmission dynamics during the early stage of the COVID-19 pandemic.

Effects of medical resource capacities and intensities of public mitigation measures on outcomes of COVID-19 outbreaks.

BACKGROUND: The COVID-19 pandemic is complex and is developing in different ways according to the country involved. METHODS: To identify the key parameters or processes that have the greatest effects on the pandemic and reveal the different progressions of epidemics in different countries, we quantified enhanced control measures and the dynamics of the production and provision of medical resources. We then nested these within a COVID-19 epidemic transmission model, which is parameterized by multi-source data. We obtained rate functions related to the intensity of mitigation measures, the effective reproduction numbers and the timings and durations of runs on medical resources, given differing control measures implemented in various countries. RESULTS: Increased detection rates may induce runs on medical resources and prolong their durations, depending on resource availability. Nevertheless, improving the detection rate can effectively and rapidly reduce the mortality rate, even after runs on medical resources. Combinations of multiple prevention and control strategies and timely improvement of abilities to supplement medical resources are key to effective control of the COVID-19 epidemic. A 50% reduction in comprehensive control measures would have led to the cumulative numbers of confirmed cases and deaths exceeding 590,000 and 60,000, respectively, by 27 March 2020 in mainland China. CONCLUSIONS: Multiple data sources and cross validation of a COVID-19 epidemic model, coupled with a medical resource logistic model, revealed the key factors that affect epidemic progressions and their outbreak patterns in different countries. These key factors are the type of emergency medical response to avoid runs on medical resources, especially improved detection rates, the ability to promote public health measures, and the synergistic effects of combinations of multiple prevention and control strategies. The proposed model can assist health authorities to predict when they will be most in need of hospital beds and equipment such as ventilators, personal protection equipment, drugs, and staff.

Effects of New York's Executive Order on Face Mask Use on COVID-19 Infections and Mortality: A Modeling Study.

There is growing evidence on the effect of face mask use in controlling the spread of COVID-19. However, few studies have examined the effect of local face mask policies on the pandemic. In this study, we developed a dynamic compartmental model of COVID-19 transmission in New York City (NYC), which was the epicenter of the COVID-19 pandemic in the USA. We used data on daily and cumulative COVID-19 infections and deaths from the NYC Department of Health and Mental Hygiene to calibrate and validate our model. We then used the model to assess the effect of the executive order on face mask use on infections and deaths due to COVID-19 in NYC. Our results showed that the executive order on face mask use was estimated to avert 99,517 (95% CIs 72,723-126,312) COVID-19 infections and 7978 (5692-10,265) deaths in NYC. If the executive order was implemented 1 week earlier (on April 10), the averted infections and deaths would be 111,475 (81,593-141,356) and 9017 (6446-11,589), respectively. If the executive order was implemented 2 weeks earlier (on April 3 when the Centers for Disease Control and Prevention recommended face mask use), the averted infections and deaths would be 128,598 (94,373-162,824) and 10,515 (7540-13,489), respectively. Our study provides public health practitioners and policymakers with evidence on the importance of implementing face mask policies in local areas as early as possible to control the spread of COVID-19 and reduce mortality.

Projected COVID-19 epidemic in the United States in the context of the effectiveness of a potential vaccine and implications for social distancing and face mask use.

BACKGROUND: Multiple candidates of COVID-19 vaccines have entered Phase III clinical trials in the United States (US). There is growing optimism that social distancing restrictions and face mask requirements could be eased with widespread vaccine adoption soon. METHODS: We developed a dynamic compartmental model of COVID-19 transmission for the four most severely affected states (New York, Texas, Florida, and California). We evaluated the vaccine effectiveness and coverage required to suppress the COVID-19 epidemic in scenarios when social contact was to return to pre-pandemic levels and face mask use was reduced. Daily and cumulative COVID-19 infection and death cases from 26th January to 15th September 2020 were obtained from the Johns Hopkins University Coronavirus resource center and used for model calibration. RESULTS: Without a vaccine (scenario 1), the spread of COVID-19 could be suppressed in these states by maintaining strict social distancing measures and face mask use levels. But relaxing social distancing restrictions to the pre-pandemic level without changing the current face mask use would lead to a new COVID-19 outbreak, resulting in 0.8-4 million infections and 15,000-240,000 deaths across these four states over the next 12 months. Under this circumstance, introducing a vaccine (scenario 2) would partially offset this negative impact even if the vaccine effectiveness and coverage are relatively low. However, if face mask use is reduced by 50% (scenario 3), a vaccine that is only 50% effective (weak vaccine) would require coverage of 55-94% to suppress the epidemic in these states. A vaccine that is 80% effective (moderate vaccine) would only require 32-57% coverage to suppress the epidemic. In contrast, if face mask usage stops completely (scenario 4), a weak vaccine would not suppress the epidemic, and further major outbreaks would occur. A moderate vaccine with coverage of 48-78% or a strong vaccine (100% effective) with coverage of 33-58% would be required to suppress the epidemic. Delaying vaccination rollout for 1-2 months would not substantially alter the epidemic trend if the current non-pharmaceutical interventions are maintained. CONCLUSIONS: The degree to which the US population can relax social distancing restrictions and face mask use will depend greatly on the effectiveness and coverage of a potential COVID-19 vaccine if future epidemics are to be prevented. Only a highly effective vaccine will enable the US population to return to life as it was before the pandemic.

Estimating the time interval between transmission generations and the presymptomatic period by contact tracing surveillance data from 31 provinces in the mainland of China

The global pandemic of 2019 coronavirus disease (COVID-19) is a great assault to public health. Presymptomatic transmission cannot be controlled with measures designed for symptomatic persons, such as isolation. This study aimed to estimate the interval of the transmission generation (TG) and the presymptomatic period of COVID-19, and compare the fitting effects of TG and serial interval (SI) based on the SEIHR model incorporating the surveillance data of 3453 cases in 31 provinces. These data were allocated into three distributions and the value of AIC presented that the Weibull distribution fitted well. The mean of TG was 5.2 days (95% CI: 4.6-5.8). The mean of the presymptomatic period was 2.4 days (95% CI: 1.5-3.2). The dynamic model using TG as the generation time performed well. Eight provinces exhibited a basic reproduction number from 2.16 to 3.14. Measures should be taken to control presymptomatic transmission in the COVID-19 pandemic.

The challenges of the coming mass vaccination and exit strategy in prevention and control of COVID-19, a modelling study (preprint)

With success in the development of COVID-19 vaccines, it is urgent and challenging to analyse how the coming large-scale vaccination in the population and the growing public desire of relaxation of non-pharmaceutical interventions (NPIs) interact to impact the prevention and control of the COVID-19 pandemic. Using mathematical models, we focus on two aspects: 1) how the vaccination program should be designed to balance the dynamic exit of NPIs; 2) how much the vaccination coverage is needed to avoid a second wave of the epidemics when the NPIs exit in stages. We address this issue globally, and take six countries--China, Brazil, Indonesia, Russia, UK, and US—in our case study. We showed that a dynamic vaccination program in three stages can be an effective approach to balance the dynamic exit of the NPIs in terms of mitigating the epidemics. The vaccination rates and the accumulative vaccination coverage in these countries are estimated by fitting the model to the real data. We observed that the required effective vaccination coverages are greatly different to balance the dynamic exit of NPIs in these countries, providing a quantitative criterion for the requirement of an integrative package of NPIs. We predicted the epidemics under different vaccination rates for these countries, and showed that the vaccination can significantly decrease the peak value of a future wave. Furthermore, we found that a lower vaccination coverage can result in a subsequent wave once the NPIs exit. Therefore, there is a critical (minimum) vaccination coverage, depending on effectiveness of NPIs to avoid a subsequent wave. We estimated the critical vaccination coverages for China, Brazil, and Indonesia under different scenarios. In conclusion, we quantitatively showed that the dynamic vaccination program can be the effective approach to supplement or even eventually replace NPIs in mitigating the epidemics and avoiding future waves, and we suggest that country level-based exit strategies of the NPIs should be considered, according to the possible quarantine rate and testing ability, and the accessibility, affordability and efficiency of the vaccines.

Impact of Hospital Bed Shortages on the Containment of COVID-19 in Wuhan.

The global outbreak of COVID-19 has caused worrying concern amongst the public and health authorities. The first and foremost problem that many countries face during the outbreak is a shortage of medical resources. In order to investigate the impact of a shortage of hospital beds on the COVID-19 outbreak, we formulated a piecewise smooth model for describing the limitation of hospital beds. We parameterized the model while using data on the cumulative numbers of confirmed cases, recovered cases, and deaths in Wuhan city from 10 January to 12 April 2020. The results showed that, even with strong prevention and control measures in Wuhan, slowing down the supply rate, reducing the maximum capacity, and delaying the supply time of hospital beds all aggravated the outbreak severity by magnifying the cumulative numbers of confirmed cases and deaths, lengthening the end time of the pandemic, enlarging the value of the effective reproduction number during the outbreak, and postponing the time when the threshold value was reduced to 1. Our results demonstrated that establishment of the Huoshenshan, Leishenshan, and Fangcang shelter hospitals avoided 22,786 people from being infected and saved 6524 lives. Furthermore, the intervention of supplying hospital beds avoided infections in 362,360 people and saved the lives of 274,591 persons. This confirmed that the quick establishment of the Huoshenshan, Leishenshan Hospitals, and Fangcang shelter hospitals, and the designation of other hospitals for COVID-19 patients played important roles in containing the outbreak in Wuhan.

Differences in how interventions coupled with effective reproduction numbers account for marked variations in COVID-19 epidemic outcomes.

The COVID-19 outbreak, designated a "pandemic" by the World Health Organization (WHO) on 11 March 2020, has spread worldwide rapidly. Each country implemented prevention and control strategies, mainly classified as SARS LCS (SARS-like containment strategy) or PAIN LMS (pandemic influenza-like mitigation strategy). The reasons for variation in each strategy's efficacy in controlling COVID-19 epidemics were unclear and are investigated in this paper. On the basis of the daily number of confirmed local (imported) cases and onset-to-confirmation distributions for local cases, we initially estimated the daily number of local (imported) illness onsets by a deconvolution method for mainland China, South Korea, Japan and Spain, and then estimated the effective reproduction numbers Rt by using a Bayesian method for each of the four countries. China and South Korea adopted a strict SARS LCS, to completely block the spread via lockdown, strict travel restrictions and by detection and isolation of patients, which led to persistent declines in effective reproduction numbers. In contrast, Japan and Spain adopted a typical PAIN LMS to mitigate the spread via maintaining social distance, self-quarantine and isolation etc., which reduced the Rt values but with oscillations around 1. The finding suggests that governments may need to consider multiple factors such as quantities of medical resources, the likely extent of the public's compliance to different intensities of intervention measures, and the economic situation to design the most appropriate policies to fight COVID-19 epidemics.