Mathematical models have been used to understand the transmission dynamics of infectious diseases and to assess the impact of intervention strategies. Traditional mathematical models usually assume a homogeneous mixing in the population, which is rarely the case in reality. Here, we construct a new transmission function by using as the probability density function a negative binomial distribution, and we develop a compartmental model using it to model the heterogeneity of contact rates in the population. We explore the transmission dynamics of the developed model using numerical simulations with different parameter settings, which characterize different levels of heterogeneity. The results show that when the reproductive number, R0, is larger than one, a low level of heterogeneity results in dynamics similar to those predicted by the homogeneous mixing model. As the level of heterogeneity increases, the dynamics become more different. As a test case, we calibrated the model with the case incidence data for severe acute respiratory syndrome (SARS) in Beijing in 2003, and the estimated parameters demonstrated the effectiveness of the control measures taken during that period.

Background The coronavirus disease 2019 (COVID-19) epidemic, considered as the worst global public health event in nearly a century, has severely affected more than 200 countries and regions around the world. To effectively prevent and control the epidemic, researchers have widely employed dynamic models to predict and simulate the epidemic’s development, understand the spread rule, evaluate the effects of intervention measures, inform vaccination strategies, and assist in the formulation of prevention and control measures. In this review, we aimed to sort out the compartmental structures used in COVID-19 dynamic models and provide reference for the dynamic modeling for COVID-19 and other infectious diseases in the future. Main text A scoping review on the compartmental structures used in modeling COVID-19 was conducted. In this scoping review, 241 research articles published before May 14, 2021 were analyzed to better understand the model types and compartmental structures used in modeling COVID-19. Three types of dynamics models were analyzed: compartment models expanded based on susceptible-exposed-infected-recovered (SEIR) model, meta-population models, and agent-based models. The expanded compartments based on SEIR model are mainly according to the COVID-19 transmission characteristics, public health interventions, and age structure. The meta-population models and the agent-based models, as a trade-off for more complex model structures, basic susceptible-exposed-infected-recovered or simply expanded compartmental structures were generally adopted. Conclusion There has been a great deal of models to understand the spread of COVID-19, and to help prevention and control strategies. Researchers build compartments according to actual situation, research objectives and complexity of models used. As the COVID-19 epidemic remains uncertain and poses a major challenge to humans, researchers still need dynamic models as the main tool to predict dynamics, evaluate intervention effects, and provide scientific evidence for the development of prevention and control strategies. The compartmental structures reviewed in this study provide guidance for future modeling for COVID-19, and also offer recommendations for the dynamic modeling of other infectious diseases. Graphical Abstract "Image missing"

Dengue fever is one of the most important vector-borne diseases in the world, and modeling its transmission dynamics allows for determining the key influence factors and helps to perform interventions. The heterogeneity of mosquito bites of humans during the spread of dengue virus is an important factor that should be considered when modeling the dynamics. However, traditional models generally assumed homogeneous mixing between humans and vectors, which is inconsistent with reality. In this study, we proposed a compartmental model with negative binomial distribution transmission terms to model this heterogeneity at the population level. By including the aquatic stage of mosquitoes and incorporating the impacts of the environment and climate factors, an extended model was used to simulate the 2014 dengue outbreak in Guangzhou, China, and to simulate the spread of dengue in different scenarios. The results showed that a high level of heterogeneity can result in a small peak size in an outbreak. As the level of heterogeneity decreases, the transmission dynamics approximate the dynamics predicted by the corresponding homogeneous mixing model. The simulation results from different scenarios showed that performing interventions early and decreasing the carrying capacity for mosquitoes are necessary for preventing and controlling dengue epidemics. This study contributes to a better understanding of the impact of heterogeneity during the spread of dengue virus.

Background The continuous mutation of severe acute respiratory syndrome coronavirus 2 has made the coronavirus disease 2019 (COVID-19) pandemic complicated to predict and posed a severe challenge to the Beijing 2022 Winter Olympics and Winter Paralympics held in February and March 2022. Methods During the preparations for the Beijing 2022 Winter Olympics, we established a dynamic model with pulse detection and isolation effect to evaluate the effect of epidemic prevention and control measures such as entry policies, contact reduction, nucleic acid testing, tracking, isolation, and health monitoring in a closed-loop management environment, by simulating the transmission dynamics in assumed scenarios. We also compared the importance of each parameter in the combination of intervention measures through sensitivity analysis. Results At the assumed baseline levels, the peak of the epidemic reached on the 57th day. During the simulation period (100 days), 13,382 people infected COVID-19. The mean and peak values of hospitalized cases were 2650 and 6746, respectively. The simulation and sensitivity analysis showed that: (1) the most important measures to stop COVID-19 transmission during the event were daily nucleic acid testing, reducing contact among people, and daily health monitoring, with cumulative infections at 0.04%, 0.14%, and 14.92% of baseline levels, respectively (2) strictly implementing the entry policy and reducing the number of cases entering the closed-loop system could delay the peak of the epidemic by 9 days and provide time for medical resources to be mobilized; (3) the risk of environmental transmission was low. Conclusions Comprehensive measures under certain scenarios such as reducing contact, nucleic acid testing, health monitoring, and timely tracking and isolation could effectively prevent virus transmission. Our research results provided an important reference for formulating prevention and control measures during the Winter Olympics, and no epidemic spread in the closed-loop during the games indirectly proved the rationality of our research results. Graphical Abstract

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Dengue fever (DF) has been a growing public-health concern in China since its emergence in Guangdong Province in 1978. Of all the regions that have experienced dengue outbreaks in mainland China, the city of Guangzhou is the most affected. This study aims to investigate the potential risk factors for dengue virus (DENV) transmission in Guangzhou, China, from 2006 to 2014. The impact of risk factors on DENV transmission was qualified by the q-values calculated using a novel spatial-temporal method, the GeoDetector model. Both climatic and socioeconomic factors were considered. The impacts on DF incidence of each single factor and the interaction of two factors were analysed. The results show that the number of days with rainfall of the month before last has the highest determinant power, with a q-value of 0.898 (P < 0.01); the q-values of the other factors related to temperature and precipitation were around 0.38–0.50. Integrating a Pearson correlation analysis, nonlinear associations were found between the DF incidence in Guangzhou and the climatic factors considered. The coupled impact of the different variables considered was enhanced compared with their individual effects. In addition, an increased number of tourists in the city were associated with a high incidence of DF. This study demonstrates that the number of rain days in a month has great influence on the DF incidence of the month after next; the temperature and precipitation have nonlinear impacts on the DF incidence in Guangzhou; both the domestic and overseas tourists coming to the city increase the risk of DENV transmission. These findings are useful in the risk assessment of DENV transmission, to predict DF outbreaks and to implement preventive DF reduction strategies.

Understanding the intercity poultry trading network is crucial for assessing the risk of avian influenza prevalence. Unfortunately, the poultry trading network in China has rarely been described. Here, with a modified radiation model, we obtain values for a proxy variable for poultry trade flows among 318 prefecture-level cities in China in 2015 utilizing the product capacity and demand quantity of poultry of the cities. The results are validated by comparing the proxy variable values with the trade volumes investigated in the literature, and it is found that the modified radiation model can accurately predict the main poultry trade flows among cities. This is the first dataset on China’s poultry trade pattern, and it can be used to analyze the production and consumption structure of poultry in prefecture-level cities within China. The dataset can be a tool for avian influenza epidemic risk assessment as well as a basis to develop prevention and control measures during an epidemic.

Background Prior to Wuhan lock-down in 2020, chunyun, the largest population mobility on this planet, had begun. We quantified impact of Wuhan lock-down on COVID-19 spread during chunyun across the nation. Methods During the period of January 1 to February 9, 2020, a total of 40,278 confirmed COVID-19 cases from 319 municipalities in mainland China were considered in this study. The cross-coupled meta-population methods were employed using between-city Baidu migration index. We modelled four scenarios of geographic spread of COVID-19 including the presence of both chunyun and lock-down (baseline); lock-down without chunyun (scenario 1); chunyun without lock-down (scenario 2); and the absence of both chunyun and lock-down (scenario 3). Results Compared with the baseline, scenario 1 resulted in 3.84% less cases by February 9 while scenario 2 and 3 resulted in 20.22 and 32.46% more cases by February 9. The geographic distribution of cases revealed that chunyun facilitated the COVID-19 spread in the majority but not all cities, and the effectiveness of Wuhan lock-down was offset by chunyun. Impacts of Wuhan lock-down during chunyun on the COVID-19 spread demonstrated heterogenetic geographic patterns. Conclusion Our results strongly supported the travel restriction as one of the effective responses and highlighted the importance of developing area-specific rather than universal countermeasures.