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A delayed reaction-diffusion system with free boundaries is investigated in this paper to understand how the bacteria spread spatially to larger area from the initial infected habitat. Under the assumptions that the nonlinearities are of monostable type and the initial values satisfy some compatible condition, we show that the free boundary problem is well-posed and discuss the long-time behaviour of solution (including spreading and vanishing) in terms of the spatial-temporal risk index. Furthermore, to determine the spreading speed of free boundaries when spreading occurs, we first study the distribution of roots of a transcendental equation containing a polynomial of degree four and then establish the existence and uniqueness of monotone solution to a delay-induced nonlocal semi-wave problem by employing the approximation method, lower-upper solutions technique and Schauder fixed point theorem. It is shown that time delays slow down the spreading of bacteria. [ABSTRACT FROM AUTHOR]

An outbreak of dengue fever in Guangdong province in 2014 was the most serious outbreak ever recorded in China. Given the known positive correlation between the abundance of mosquitoes and the number of dengue fever cases, a stage structured mosquito model was developed to investigate the cause of the large abundance of mosquitoes in 2014 and its implications for outbreaks of the disease. Data on the Breteau index (number of containers positive for larvae per 100 premises investigated), temperature and precipitation were used for model fitting. The egg laying rate, the development rate and the mortality rates of immatures and adults were obtained from the estimated parameters. Moreover, effects of daily fluctuations of temperature on these parameters were obtained and the effects of temperature and precipitation were analyzed by simulations. Our results indicated that the abundance of mosquitoes depended not only on the total annual precipitation but also on the distribution of the precipitation. The daily mean temperature had a nonlinear relationship with the abundance of mosquitoes, and large diurnal temperature differences can reduce the abundance of mosquitoes. In addition, effects of increasing precipitation and temperature were interdependent. Our findings suggest that the large abundance of mosquitoes in 2014 was mainly caused by the distribution of the precipitation. In the perspective of mosquito control, our results reveal that it is better to clear water early and spray insecticide between April and August in case of limited resources. [ABSTRACT FROM AUTHOR]

News reporting has the potential to modify a community׳s knowledge of emerging infectious diseases and affect peoples’ attitudes and behavior. Here we developed a quantitative approach to evaluate the effects of media on such behavior. Statistically significant correlations between the number of new hospital notifications, during the 2009 A/H1N1 influenza epidemic in the Shaanxi province of China, and the number of daily news items added to eight major websites were found from Pearson correlation and cross-correlation analyses. We also proposed a novel model to examine the implication for transmission dynamics of these correlations. The model incorporated the media impact function into the intensity of infection, and enhanced the traditional epidemic SEIR model with the addition of media dynamics. We used a nonlinear least squares estimation to identify the best-fit parameter values in the model from the observed data. We also carried out the uncertainty and sensitivity analyses to determine key parameters during early phase of the disease outbreak for the final outcome of the outbreak with media impact. The findings confirm the importance of responses by individuals to the media reports, with behavior changes having important consequence for the emerging infectious disease control. Therefore, for mitigating emerging infectious diseases, media reports should be focused on how to guide people׳s behavioral changes, which are critical for limiting the spread of disease. [ABSTRACT FROM AUTHOR]

Background: Epidemic zoning is an important option in a series of measures for the prevention and control of infectious diseases. We aim to accurately assess the disease transmission process by considering the epidemic zoning, and we take two epidemics with distinct outbreak sizes as an example, i.e., the Xi'an epidemic in late 2021 and the Shanghai epidemic in early 2022. Methods: For the two epidemics, the total cases were clearly distinguished by their reporting zone and the Bernoulli counting process was used to describe whether one infected case in society would be reported in control zones or not. Assuming the imperfect or perfect isolation policy in control zones, the transmission processes are respectively simulated by the adjusted renewal equation with case importation, which can be derived on the basis of the Bellman-Harris branching theory. The likelihood function containing unknown parameters is then constructed by assuming the daily number of new cases reported in control zones follows a Poisson distribution. All the unknown parameters were obtained by the maximum likelihood estimation. Results: For both epidemics, the internal infections characterized by subcritical transmission within the control zones were verified, and the median control reproduction numbers were estimated as 0.403 (95% confidence interval (CI): 0.352, 0.459) in Xi'an epidemic and 0.727 (95% CI: 0.724, 0.730) in Shanghai epidemic, respectively. In addition, although the detection rate of social cases quickly increased to 100% during the decline period of daily new cases until the end of the epidemic, the detection rate in Xi'an was significantly higher than that in Shanghai in the previous period. Conclusions: The comparative analysis of the two epidemics with different consequences highlights the role of the higher detection rate of social cases since the beginning of the epidemic and the reduced transmission risk in control zones throughout the outbreak. Strengthening the detection of social infection and strictly implementing the isolation policy are of great significance to avoid a larger-scale epidemic. [ABSTRACT FROM AUTHOR]

Past seasonal influenza epidemics and vaccination experience may affect individuals' decisions on whether to be vaccinated or not, decisions that may be constantly reassessed in relation to recent influenza related experience. To understand the potentially complex interaction between experience and decisions and whether the vaccination rate is likely to reach a critical coverage level or not, we construct an adaptive‐decision model. This model is then coupled with an influenza vaccination dynamics (SIRV) model to explore the interaction between individuals' decision‐making and an influenza epidemic. Nonlinear least squares estimation is used to obtain the best‐fit parameter values in the SIRV model based on data on new influenza‐like illness (ILI) cases in Texas. Uncertainty and sensitivity analyses are then carried out to determine the impact of key parameters of the adaptive decision‐making model on the ILI epidemic. The results showed that the necessary critical coverage rate of ILI vaccination could not be reached by voluntary vaccination. However, it could be reached in the fourth year if mass media reports improved individuals' memory of past vaccination experience. Individuals' memory of past vaccination experience, the proportion with histories of past vaccinations and the perceived cost of vaccination are important factors determining whether an ILI epidemic can be effectively controlled or not. Therefore, health authorities should guide people to improve their memory of past vaccination experience through media reports, publish timely data on annual vaccination proportions and adjust relevant measures to appropriately reduce vaccination perceived cost, in order to effectively control an ILI epidemic. [ABSTRACT FROM AUTHOR]

Abstract: HIV has spread widely in mainland China, but there is significant geographic variation in the severity of the epidemic. We aimed to assess the HIV/AIDS epidemic in mainland China accurately, and address the effect of population mobility on it. Markov-Chain Monte-Carlo simulations and Latin Hypercube Sampling were used to estimate the basic reproductive ratio and its sensitivity to parameter variations. We estimated a mean reproduction number of 1.708 (95% CI 1.440–1.977). Our analysis using national surveillance data indicates that HIV-positive individuals most likely move from economically developed regions to regions with more numerous HIV cases, while mobility of AIDS patients likely flows in the opposite direction, due to the current policy that AIDS patients must return to their registered residence to receive free antiretroviral therapy. Our results based on a spatially stratified population dynamical model show increasing mobility rates of HIV/AIDS cases can have a significant effect on the number of HIV/AIDS cases per province and has the potential to decrease the overall number of HIV/AIDS cases in the country. We recommend that the community-based HIV/AIDS support and care program should be implemented by some local governments (especially in epidemically severe areas) to mitigate HIV infections in China. [Copyright &y& Elsevier]

• 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]

A network model at both the population and individual levels, which simulates both between-patch and within-patch dynamics, is proposed. We investigated the effects of dispersal networks and distribution of local dynamics on the outcome of an epidemic at the population level. Numerical studies show that disease control on random networks may be easier than on small-world networks, depending on the initial distribution of the local dynamics. Spatially separating instead of gathering patches where disease locally persists is beneficial to global disease control if dispersal networks are a type of small-world networks. Dispersal networks with higher degree lead to a higher mean value of R0. Furthermore, irregularity of network and randomization are beneficial to disease stabilization and greatly affect the resulting global dynamics. [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]