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• A novel Filippov epidemic system involving three containment strategies is constructed. • Rich local and global sliding bifurcations indicate multi-stability dynamics. • Well data fitting results for epidemics A/H1N1 and COVID-19 reveal the applicability of the proposed model. • The final infected population can be maintained in a desired level through the proposed Filippov control measures. A non-smooth SIR Filippov system is proposed to investigate the impacts of three control strategies (media coverage, vaccination and treatment) on the spread of an infectious disease. We synthetically consider both the number of infected population and its changing rate as the switching condition to implement the curing measures. By using the properties of the Lambert W function, we convert the proposed switching condition to a threshold value related to the susceptible population. The classical epidemic model involving media coverage, linear functions describing injecting vaccine and treatment strategies is examined when the susceptible population exceeds the threshold value. In addition, we consider another SIR model accompanied with the vaccination and treatment strategies represented by saturation functions when the susceptible population is smaller than the threshold value. The dynamics of these two subsystems and the sliding domain are discussed in detail. Four types of local sliding bifurcation are investigated, including boundary focus, boundary node, boundary saddle and boundary saddle-node bifurcations. In the meantime, the global bifurcation involving the appearance of limit cycles is examined, including touching bifurcation, homoclinic bifurcation to the pseudo-saddle and crossing bifurcation. Furthermore, the influence of some key parameters related to the three treatment strategies is explored. We also validate our model by the epidemic data sets of A/H1N1 and COVID-19, which can be employed to reveal the effects of media report and existing strategy related to the control of emerging infectious diseases on the variations of confirmed cases. [ABSTRACT FROM AUTHOR]

• Since January 23 2020, stringent measures for controlling novel coronavirus epidemics have been enforced and strengthened in mainland China. • Most infected cases have been quarantined or put in suspected class, which had been ignored in existing models. • Results of our model show that the trend of the epidemics mainly depends on quarantined and suspected cases. • It is important to continue enhancing the quarantine and isolation strategy and improving the detection rate in mainland China. Since January 23, 2020, stringent measures for controlling the novel coronavirus epidemic have been gradually enforced and strengthened in mainland China. The detection and diagnosis have been improved, as well. However, the daily reported cases remaining at a high level make the epidemic trend prediction difficult. Since the traditional SEIR model does not evaluate the effectiveness of control strategies, a novel model in line with the current epidemic's process and control measures was proposed, utilizing multisource datasets including the cumulative number of reported, deceased, quarantined and suspected cases. Results show that the trend of the epidemic mainly depends on quarantined and suspected cases. The predicted cumulative numbers of quarantined and suspected cases nearly reached static states, and their inflection points have already been achieved, with the epidemic's peak coming soon. The estimated effective reproduction numbers using model-free and model-based methods are decreasing, as well as new infections, while newly reported cases are increasing. Most infected cases have been quarantined or put in the suspected class, which has been ignored in existing models. The uncertainty analyses reveal that the epidemic is still uncertain, and it is important to continue enhancing the quarantine and isolation strategy and improving the detection rate in mainland China. [ABSTRACT FROM AUTHOR]

• Since January 23rd 2020, stringent measures for controlling the novel coronavirus epidemics have been enforced and strengthened in mainland China. • Most infected cases have been quarantined or put in suspected class, which has been ignored in existing models. • Results of our model show that the trend of the epidemics mainly depends on quarantined and suspected cases. • It is important to continue enhancing the quarantine and isolation strategy and improving the detection rate in mainland China. 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. Since the traditional SEIR model does not evaluate the effectiveness of control strategies, a novel model in line with the current epidemics process and control measures was proposed, utilizing multisource datasets including cumulative number of reported, death, quarantined and suspected cases. Results show that the trend of the epidemics mainly depends on quarantined and suspected cases. The predicted cumulative numbers of quarantined and suspected cases nearly reached static states and their inflection points have already been achieved, with the epidemics peak coming soon. The estimated effective reproduction numbers using model-free and model-based methods are decreasing, as well as new infections, while new reported cases are increasing. Most infected cases have been quarantined or put in suspected class, which has been ignored in existing models. The uncertainty analyses reveal that the epidemics is still uncertain and it is important to continue enhancing the quarantine and isolation strategy and improving the detection rate in mainland China. [ABSTRACT FROM AUTHOR]

• Periods of epidemics induced by different strains in Asian countries were classified by k-shape and hierarchical clustering methods. • Using correlation and regression analysis to explore the results of clustering Asian countries. • Revealing the reasons behind the development pattern of the epidemic in Asian countries. • Peak value of confirmed cases per capita in the Omicron phase are much higher, while mortality rate is significantly lower than in the earlier phases. • Vaccination rates were associated with lower mortality given the nature of the analysis. The COVID-19 epidemic has lasted for more than two years since the outbreak in late 2019. An urgent and challenging question is how to systematically evaluate epidemic developments in different countries, during different periods, and to determine which measures that could be implemented are key for successful epidemic prevention. In this study, SBD distance-based K-shape clustering and hierarchical clustering methods were used to analyse epidemics in Asian countries. For the hierarchical clustering, epidemic time series were divided into three periods (epidemics induced by the Original/Alpha, Delta and Omicron variants separately). Standard deviations, the Hurst index, mortality rates, peak value of confirmed cases per capita, average growth rates, and the control efficiency of each period were used to characterize the epidemics. In addition, the total numbers of cases in the different countries were analysed by correlation and regression in relation to 15 variables that could have impacts on COVID-19. Finally, some suggestions on prevention and control measures for each category of country are given. We found that the total numbers of cases per million of a population, total deaths per million and mortality rates were highly correlated with the proportion of people aged over 65 years, the prevalence of multiple diseases, and the national GDP. We also found significant associations between case numbers and vaccination rates, health expenditures, and stringency of control measures. Vaccinations have played a positive role in COVID-19, with a gradual decline in mortality rates in later periods, and are still playing protective roles against the Delta and Omicron strains. The stringency of control measures taken by a government is not an indicator of the appropriateness of a country's response to the outbreak, and a higher index does not necessarily mean more effective measures; a combination of factors such as national vaccination rates, the country's economic foundation and the availability of medical equipment is also needed. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics". [ABSTRACT FROM AUTHOR]

• A novel mathematical model is proposed to describe the heterogeneity of control interventions. • Xi'an presents a lower transmission probability but a higher reproduction number. • Enhancing closed-off management, tracing and testing intensities, are effective. • Citywide lockdown is not essential when the closed-off management is strictly implemented. • Enhancing tracing strategy is more effective than enhancing testing strategy in the early stage. Several local outbreaks have occurred and been suppressed with the dynamic zero-COVID policy and widely promoted vaccination program implemented in China. The epidemic duration and final size vary significantly in different cities, which may be attributed to different implementation patterns and intensities of non-pharmaceutical interventions (NPIs). It's important to capture the underlying mechanism to explore more efficient implementation patterns of NPIs in order to prevent the future resurgence. In this study, outbreaks caused by Delta variant in Xi'an, Yangzhou and Guangzhou in 2021 are chosen as the examples. A novel model dividing the population into three groups is proposed to describe the heterogeneity of control interventions. The model is calibrated and key parameters related to NPIs are estimated by using multi-source epidemic data. The estimation results show a lower transmission probability but a higher initial reproduction number in Xi'an. Sensitivity analysis are conducted to investigate the impact of various control measures in different epidemic phases. The results identify the vital role of enhancing closed-off management, strengthening tracing and testing intensities, on shortening the epidemic durations and reducing the final size. Further, we find that sufficiently implemented closed-off management would prevent the city from lockdown. Strengthening the tracing other than the testing strategy in the initial stage is more effective on containing the epidemic in a shorter duration with less infections. [ABSTRACT FROM AUTHOR]

• Countries pursuing 'zero COVID' rely on strong restrictions or even city lockdown. • Optimally balancing restrictions's length and confidence that the outbreak is ending is important. • The proportion of cases who miss the intervention restrictions and thus are capable of causing secondary transmission is estimated. • An iterative method is designed to quantify the daily end-of-outbreak confidence since the last reported case. • The projection of the end-of-outbreak day relies on the size of reproduction number and the acceptable risk threshold assuming the invariant distribution of serial interval. The end-of-outbreak declaration is an important part of epidemic control, marking the relaxation or cancellation of prevention and control measures. We propose a probability model to retrospectively quantify the confidence of giving the end-of-outbreak declaration during the COVID-19 epidemic in early 2020 in Wuhan. By using the linear spline, we firstly estimates the time-varying proportion of cases who miss the nonpharmaceutical interventions (NPIs) among all reported cases. Assuming the reproduction numbers being 1.5, 2.0, 3.0, 4.0, 5.0 and 6.0, the respective probability of the end of the COVID-19 outbreak with time after the last reported case can be iteratively computed. Consequently, the varying reproduction numbers produce slightly different increasing patterns of NPI effectiveness, and the end-of-outbreak declarations with 95% confidence are projected consistently earlier than the day when the lockdown was actually lifted. The reason for the timing discrepancy is discussed as well. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]