Application of the Time Derivative (TD) Method for Early Alert of Influenza Epidemics.

BACKGROUND: In order to minimize the spread of seasonal influenza epidemic to communities worldwide, the Korea Disease Control and Prevention Agency has issued an influenza epidemic alert using the influenza epidemic threshold formula based on the results of the influenza-like illness (ILI) rate. However, unusual changes have occurred in the pattern of respiratory infectious diseases, including seasonal influenza, after the coronavirus disease 2019 (COVID-19) pandemic. As a result, the importance of detecting the onset of an epidemic earlier than the existing epidemic alert system is increasing. Accordingly, in this study, the Time Derivative (TD) method was suggested as a supplementary approach to the existing influenza alert system for the early detection of seasonal influenza epidemics. METHODS: The usefulness of the TD method as an early epidemic alert system was evaluated by applying the ILI rate for each week during past seasons when seasonal influenza epidemics occurred, ranging from the 2013-2014 season to the 2022-2023 season to compare it with the issued time of the actual influenza epidemic alert. RESULTS: As a result of applying the TD method, except for the two seasons (2020-2021 season and 2021-2022 season) that had no influenza epidemic, an influenza early epidemic alert was suggested during the remaining seasons, excluding the 2017-2018 and 2022-2023 seasons. CONCLUSION: The TD method is a time series analysis that enables early epidemic alert in real-time without relying on past epidemic information. It can be considered as an alternative approach when it is challenging to set an epidemic threshold based on past period information. This situation may arise when there has been a change in the typical seasonal epidemic pattern of various respiratory viruses, including influenza, following the COVID-19 pandemic.

Epidemic dynamics on metapopulation networks with node2vec mobility.

Metapopulation models have been a powerful tool for both theorizing and simulating epidemic dynamics. In a metapopulation model, one considers a network composed of subpopulations and their pairwise connections, and individuals are assumed to migrate from one subpopulation to another obeying a given mobility rule. While how different mobility rules affect epidemic dynamics in metapopulation models has been studied, there have been relatively few efforts on comparison of the effects of simple (i.e., unbiased) random walks and more complex mobility rules. Here we study a susceptible-infectious-susceptible (SIS) dynamics in a metapopulation model in which individuals obey a parametric second-order random-walk mobility rule called the node2vec. We map the second-order mobility rule of the node2vec to a first-order random walk in a network whose each node is a directed edge connecting a pair of subpopulations and then derive the epidemic threshold. For various networks, we find that the epidemic threshold is large (therefore, epidemic spreading tends to be suppressed) when the individuals infrequently backtrack or infrequently visit the common neighbors of the currently visited and the last visited subpopulations than when the individuals obey the simple random walk. The amount of change in the epidemic threshold induced by the node2vec mobility is in general not as large as, but is sometimes comparable with, the one induced by the change in the diffusion rate for individuals.

Site-bond percolation model of epidemic spreading with vaccination in complex networks.

To study disease transmission with vaccination based on the network, we map an SIR model to a site-bond percolation model. In the case where the vaccination probability is zero, this model degenerates into a bond percolation model without the immunization. Using the method of generation functions, we obtain exact theoretical results for the epidemic threshold and the average outbreak size. From these exact solutions, we find that the epidemic threshold increases while the average outbreak size decreases with vaccination probability. Numerical simulations show that the size of giant component S increases with transmissibility T but decreases with the probability of vaccination. In addition, we compare the epidemic threshold and the size of the giant component for a Poisson network, an exponential network and a power-law network using numerical simulations. When the probability of vaccination is fixed, the epidemic threshold is the smallest for heterogeneous networks and the size of giant component S in homogeneous networks becomes largest for large transmissibility T(T close to 1).

Population structure, intergroup interaction, and human contact govern infectious disease impacts in mountain gorilla populations.

Infectious zoonotic diseases are a threat to wildlife conservation and global health. They are especially a concern for wild apes, which are vulnerable to many human infectious diseases. As ecotourism, deforestation, and great ape field research increase, the threat of human-sourced infections to wild populations becomes more substantial and could result in devastating population declines. The endangered mountain gorillas (Gorilla beringei beringei) of the Virunga Massif in east-central Africa suffer periodic disease outbreaks and are exposed to infections from human-sourced pathogens. It is important to understand the possible risks of disease introduction and spread in this population and how human contact may facilitate disease transmission. Here we present and evaluate an individual-based, stochastic, discrete-time disease transmission model to predict epidemic outcomes and better understand health risks to the Virunga mountain gorilla population. To model disease transmission we have derived estimates for gorilla contact, interaction, and migration rates. The model shows that the social structure of gorilla populations plays a profound role in governing disease impacts with subdivided populations experiencing less than 25% of the outbreak levels of a single homogeneous population. It predicts that gorilla group dispersal and limited group interactions are strong factors in preventing widespread population-level outbreaks of infectious disease after such diseases have been introduced into the population. However, even a moderate amount of human contact increases disease spread and can lead to population-level outbreaks.

The coupled dynamics of information dissemination and SEIR-based epidemic spreading in multiplex networks.

The outbreak of coronavirus disease 2019 (COVID-19) threatens the health and safety of all humanity. This disease has a prominent feature: the presymptomatic and asymptomatic viral carriers can spread the disease. It is crucial to estimate the impact of this undetected transmission on epidemic outbreaks. Currently, disease-related information has been widely disseminated by the mass media. To investigate the impact of both individuals and mass media information dissemination on the epidemic spreading, we establish a new UAU-SEIR (Unaware-Aware-Unaware-Susceptible-Exposed-Infected-Recovered) model with mass media on two-layer multiplex networks. In the model, E-state individuals denote asymptomatic infections, and a single node connecting to all individuals denotes the mass media. In this work, we use the Microscopic Markovian Chain Approach (MMCA) to derive the epidemic threshold. Comparing the MMCA theoretical results with Monte Carlo (MC) simulations, we find that the MMCA has a good consistency with MC simulations. In addition, we also analyze the impact of model parameters on epidemic spreading and epidemic threshold. The results show that reducing the proportion of asymptomatic infections, accelerating the dissemination of information between individuals and the dissemination of information via the mass media can effectively inhibit the epidemic spreading and raise the epidemic threshold.

A Low-Dimensional Network Model for an SIS Epidemic: Analysis of the Super Compact Pairwise Model.

Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the complex dynamics induced by the network structure. We analyze one recently introduced model and derive important epidemiological quantities for the system. We derive the epidemic threshold and analyze the bifurcation that occurs, and we use asymptotic techniques to derive an approximation for the endemic equilibrium when it exists. We consider the sensitivity of this approximation to network parameters, and the implications for disease control measures are found to be in line with the results of existing studies.

Epidemic in networked population with recurrent mobility pattern.

The novel Coronavirus (COVID-19) has caused a global crisis and many governments have taken social measures, such as home quarantine and maintaining social distance. Many recent studies show that network structure and human mobility greatly influence the dynamics of epidemic spreading. In this paper, we utilize a discrete-time Markov chain approach and propose an epidemic model to describe virus propagation in the heterogeneous graph, which is used to represent individuals with intra social connections and mobility between individuals and common locations. There are two types of nodes, individuals and public places, and disease can spread by social contacts among individuals and people gathering in common areas. We give theoretical results about epidemic threshold and influence of isolation factor. Several numerical simulations are performed and experimental results further demonstrate the correctness of proposed model. Non-monotonic relationship between mobility possibility and epidemic threshold and differences between Erdös-Rényi and power-law social connections are revealed. In summary, our proposed approach and findings are helpful to analyse and prevent the epidemic spreading in networked population with recurrent mobility pattern.

Interaction between epidemic spread and collective behavior in scale-free networks with community structure.

Many real-world networks exhibit community structure: the connections within each community are dense, while connections between communities are sparser. Moreover, there is a common but non-negligible phenomenon, collective behaviors, during the outbreak of epidemics, are induced by the emergence of epidemics and in turn influence the process of epidemic spread. In this paper, we explore the interaction between epidemic spread and collective behavior in scale-free networks with community structure, by constructing a mathematical model that embeds community structure, behavioral evolution and epidemic transmission. In view of the differences among individuals' responses in different communities to epidemics, we use nonidentical functions to describe the inherent dynamics of individuals. In practice, with the progress of epidemics, individual behaviors in different communities may tend to cluster synchronization, which is indicated by the analysis of our model. By using comparison principle and Gers˘gorin theorem, we investigate the epidemic threshold of the model. By constructing an appropriate Lyapunov function, we present the stability analysis of behavioral evolution and epidemic dynamics. Some numerical simulations are performed to illustrate and complement our theoretical results. It is expected that our work can deepen the understanding of interaction between cluster synchronization and epidemic dynamics in scale-free community networks.

A maximum curvature method for estimating epidemic onset of seasonal influenza in Japan.

BACKGROUND: Detecting the onset of influenza epidemic is important for epidemiological surveillance and for investigating the factors driving spatiotemporal transmission patterns. Most approaches define the epidemic onset based on thresholds, which use subjective criteria and are specific to individual surveillance systems. METHODS: We applied the empirical threshold method (ETM), together with two non-thresholding methods, including the maximum curvature method (MCM) that we proposed and the segmented regression method (SRM), to determine onsets of influenza epidemics in each prefecture of Japan, using sentinel surveillance data of influenza-like illness (ILI) from 2012/2013 through 2017/2018. Performance of the MCM and SRM was evaluated, in terms of epidemic onset, end, and duration, with those derived from the ETM using the nationwide epidemic onset indicator of 1.0 ILI case per sentinel per week. RESULTS: The MCM and SRM yielded complete estimates for each of Japan's 47 prefectures. In contrast, ETM estimates for Kagoshima during 2012/2013 and for Okinawa during all six influenza seasons, except 2013/2014, were invalid. The MCM showed better agreement in all estimates with the ETM than the SRM (R2 = 0.82, p < 0.001 vs. R2 = 0.34, p < 0.001 for epidemic onset; R2 = 0.18, p < 0.001 vs. R2 = 0.05, p < 0.001 for epidemic end; R2 = 0.28, p < 0.001 vs. R2 < 0.01, p = 0.35 for epidemic duration). Prefecture-specific thresholds for epidemic onset and end were established using the MCM. CONCLUSIONS: The Japanese national epidemic onset threshold is not applicable to all prefectures, particularly Okinawa. The MCM could be used to establish prefecture-specific epidemic thresholds that faithfully characterize influenza activity, serving as useful complements to the influenza surveillance system in Japan.

Effects of asymptomatic infection on the dynamical interplay between behavior and disease transmission in multiplex networks.

Multiplex network theory is widely introduced to deepen the understanding of the dynamical interplay between self-protective behavior and epidemic spreading. Most of the existing studies assumed that all infected individuals can transmit disease- related information or can be perceived by their neighbors. However, owing to lack of distinct symptoms for patients in the initial stage of infection, the disease information cannot be transmitted in the population, which may lead to the wrong perception of infection risk and inappropriate behavior response. In this work, we divide infected individuals into Exposed-state (without obvious clinical symptoms) individuals and Infected-state (with evident clinical symptoms) individuals, both of whom can spread disease, but only Infected-state individuals can diffuse disease information. Then, in this work we establish UAU-SEIS (Unaware-Aware-Unaware-Susceptible-Exposed-Infected-Susceptible) model in multiplex networks and analyze the effect of asymptomatic infection and the isolation of Infected-state individuals on the density of infection and the epidemic threshold. Furthermore, we extend the UAU-SEIS model by taking the individual heterogeneity into consideration. Combined Markov chain approach and Monte-Carlo Simulations, we find that asymptomatic infection has an effect on the density of infected individuals and the epidemic threshold, and the extent of the effect is influenced by whether Infected-state individuals are isolated or treated. In addition, results show that the individual heterogeneity can lower the density of infected individuals, but cannot enhance the epidemic threshold.

Effects of awareness diffusion and self-initiated awareness behavior on epidemic spreading - An approach based on multiplex networks.

In this paper, we study the interplay between the epidemic spreading and the diffusion of awareness in multiplex networks. In the model, an infectious disease can spread in one network representing the paths of epidemic spreading (contact network), leading to the diffusion of awareness in the other network (information network), and then the diffusion of awareness will cause individuals to take social distances, which in turn affects the epidemic spreading. As for the diffusion of awareness, we assume that, on the one hand, individuals can be informed by other aware neighbors in information network, on the other hand, the susceptible individuals can be self-awareness induced by the infected neighbors in the contact networks (local information) or mass media (global information). Through Markov chain approach and numerical computations, we find that the density of infected individuals and the epidemic threshold can be affected by the structures of the two networks and the effective transmission rate of the awareness. However, we prove that though the introduction of the self-awareness can lower the density of infection, which cannot increase the epidemic threshold no matter of the local information or global information. Our finding is remarkably different to many previous results on single-layer network: local information based behavioral response can alter the epidemic threshold. Furthermore, our results indicate that the nodes with more neighbors (hub nodes) in information networks are easier to be informed, as a result, their risk of infection in contact networks can be effectively reduced.

A theoretical framework to identify invariant thresholds in infectious disease epidemiology.

Setting global strategies and targets for disease prevention and control often involves mathematical models. Model structure is typically subject to intense scrutiny, such as confrontation with empirical data and alternative formulations, while a less frequently challenged aspect is the widely adopted reduction of parameters to their average values. Focusing on endemic diseases, we use a general transmission model to explain how mean field approximations decrease the estimated R0 from prevalence data, while threshold phenomena - such as the epidemic and reinfection thresholds - remain invariant. This results in an underestimation of the effort required to control disease, which may be particularly severe when the approximation inappropriately places transmission estimates below important thresholds. These concepts are widely applicable across endemic pathogen systems.

Epidemics in markets with trade friction and imperfect transactions.

Market trade-routes can support infectious-disease transmission, impacting biological populations and even disrupting trade that conduces the disease. Epidemiological models increasingly account for reductions in infectious contact, such as risk-aversion behaviour in response to pathogen outbreaks. However, responses in market dynamics clearly differ from simple risk aversion, as are driven by other motivation and conditioned by "friction" constraints (a term we borrow from labour economics). Consequently, the propagation of epidemics in markets of, for example livestock, is frictional due to time and cost limitations in the production and exchange of potentially infectious goods. Here we develop a coupled economic-epidemiological model where transient and long-term market dynamics are determined by trade friction and agent adaptation, and can influence disease transmission. The market model is parameterised from datasets on French cattle and pig exchange networks. We show that, when trade is the dominant route of transmission, market friction can be a significantly stronger determinant of epidemics than risk-aversion behaviour. In particular, there is a critical level of friction above which epidemics do not occur, which suggests some epidemics may not be sustained in highly frictional markets. In addition, friction may allow for greater delay in removal of infected agents that still mitigates the epidemic and its impacts. We suggest that policy for minimising contagion in markets could be adjusted to the level of market friction, by adjusting the urgency of intervention or by increasing friction through incentivisation of larger-volume less-frequent transactions that would have limited effect on overall trade flow. Our results are robust to model specificities and can hold in the presence of non-trade disease-transmission routes.

Estimating the Baseline and Threshold for the Incidence of Diseases with Seasonal and Long-Term Trends.

In epidemiology, it is very important to estimate the baseline incidence of infectious diseases. From this baseline, the epidemic threshold can be derived as a clue to recognize an excess incidence, i.e. to detect an epidemic by mathematical methods. Nevertheless, a problem is posed by the fact that the incidence may vary during the year, as a rule, in a season dependent manner. To model the incidence of a disease, some authors use seasonal trend models. For instance, Serfling applies the sine function with a phase shift and amplitude. A similar model based on the analysis of variance with kernel smoothing and Serfling's higher order models, i.e. models composed of multiple sine-cosine function pairs with a variably long period, will be presented below. Serfling's model uses a long-term linear trend, but the linearity may not be always acceptable. Therefore, a more complex, long-term trend estimation will also be addressed, using different smoothing methods. In addition, the issue of the time unit (mostly a week) used in describing the incidence is discussed.

COVID-19 surveillance report for Sudan, 2020 to 2021.

Background: Following the World Health Organization declaration, COVID-19 was first appearance in Sudan was in March 2020. Cases were reported to the Sudan Federal Ministry of Heath through the surveillance system from different sources. This study used surveillance data from 2020 to 2021 to describe the epidemiologic patterns of COVID-19 occurrence in Sudan and provide insight for better preparedness and response. Methods: Through a retrospective descriptive study, COVID19 cases records obtained from the national surveillance line-list in Surveillance and Information Directorate in Federal Ministry of Health. The analysis of data was done with SPSS version 21. Descriptive analysis done by frequencies and percentages, and further analysis through performing multivariate logistic regression. Results: Out of 48,545 suspected cases tested for COVID-19 using RT-PCR, 27,453 (56.5%) tested positive with case fatality ratio of 6.5%. Higher death rate among elderly (78% > 60-year-old) and males (70.1%). From the reported cases, 53.8% showed no symptoms, while the common symptoms among symptomatic patients were; fever (26.4%), cough (19.1%), shortness of breath (16.8%) with small proportion (4.5%) reported loss of smell and taste. Specific states, Khartoum, Gezira and Red Sea showed highest prevalence. The disease peaked four times during 2020-2021, with a proposed alert threshold of 200-250 cases per week acting as an explosion point nationwide. Conclusions: The high case fatality rate in the country requires further analysis, as well as the high proportion of asymptomatic infection. This will be ensured by improving the quality and completeness of surveillance data. A proposed threshold of 200-250 cases per week should be an alert to augment the measures of controlling the pandemic over the country, including providing enough supplies to decrease mortality.

Exploring the threshold for the start of respiratory syncytial virus infection epidemic season using sentinel surveillance data in Japan.

Introduction: An unusual seasonality of respiratory syncytial virus (RSV) infection in Japan is observed in recent years after 2017, becoming challenging to prepare for: a seasonal shift from autumn-winter to summer-autumn in 2017-2019, no major epidemic in 2020, and an unusually high number of cases reported in 2021. Methods: To early detect the start-timing of epidemic season, we explored the reference threshold for the start-timing of the epidemic period based on the number of cases per sentinel (CPS, a widely used indicator in Japanese surveillance system), using a relative operating characteristic curve analysis (with the epidemic period defined by effective reproduction number). Results: The reference values of Tokyo, Kanagawa, Osaka, and Aichi Prefectures were 0.41, 0.39, 0.42, and 0.24, respectively. Discussion: The reference CPS value could be a valuable indicator for detecting the RSV epidemic and may contribute to the planned introduction of monoclonal antibody against RSV to prevent severe outcomes.

Scalable Estimation of Epidemic Thresholds via Node Sampling.

Infectious or contagious diseases can be transmitted from one person to another through social contact networks. In today's interconnected global society, such contagion processes can cause global public health hazards, as exemplified by the ongoing Covid-19 pandemic. It is therefore of great practical relevance to investigate the network transmission of contagious diseases from the perspective of statistical inference. An important and widely studied boundary condition for contagion processes over networks is the so-called epidemic threshold. The epidemic threshold plays a key role in determining whether a pathogen introduced into a social contact network will cause an epidemic or die out. In this paper, we investigate epidemic thresholds from the perspective of statistical network inference. We identify two major challenges that are caused by high computational and sampling complexity of the epidemic threshold. We develop two statistically accurate and computationally efficient approximation techniques to address these issues under the Chung-Lu modeling framework. The second approximation, which is based on random walk sampling, further enjoys the advantage of requiring data on a vanishingly small fraction of nodes. We establish theoretical guarantees for both methods and demonstrate their empirical superiority.

Applying the moving epidemic method to determine influenza epidemic and intensity thresholds using influenza-like illness surveillance data 2009-2018 in Tunisia.

BACKGROUND: Defining the start and assessing the intensity of influenza seasons are essential to ensure timely preventive and control measures and to contribute to the pandemic preparedness. The present study aimed to determine the epidemic and intensity thresholds of influenza season in Tunisia using the moving epidemic method. METHODS: We applied the moving epidemic method (MEM) using the R Language implementation (package "mem"). We have calculated the epidemic and the different intensity thresholds from historical data of the past nine influenza seasons (2009-2010 to 2017-2018) and assessed the impact of the 2009-2010 pandemic year. Data used were the weekly influenza-like illness (ILI) proportions compared with all outpatient acute consultations. The goodness of the model was assessed using a cross validation procedure. RESULTS: The average duration of influenza epidemic during a typical season was 20 weeks and ranged from 11 weeks (2009-2010 season) to 23 weeks (2015-2016 season). The epidemic threshold with the exclusion of the pandemic season was 6.25%. It had a very high sensitivity of 85% and a high specificity of 69%. The different levels of intensity were established as follows: low, if ILI proportion is below 9.74%, medium below 12.05%; high below 13.27%; and very high above this last rate. CONCLUSIONS: This is the first mathematically based study of seasonal threshold of influenza in Tunisia. As in other studies in different countries, the model has shown both good specificity and sensitivity, which allows timely and accurate detection of the start of influenza seasons. The findings will contribute to the development of more efficient measures for influenza prevention and control.

Hospital and Population-Based Evidence for COVID-19 Early Circulation in the East of France.

BACKGROUND: Understanding SARS-CoV-2 dynamics and transmission is a serious issue. Its propagation needs to be modeled and controlled. The Alsace region in the East of France has been among the first French COVID-19 clusters in 2020. METHODS: We confront evidence from three independent and retrospective sources: a population-based survey through internet, an analysis of the medical records from hospital emergency care services, and a review of medical biology laboratory data. We also check the role played in virus propagation by a large religious meeting that gathered over 2000 participants from all over France mid-February in Mulhouse. RESULTS: Our results suggest that SARS-CoV-2 was circulating several weeks before the first officially recognized case in Alsace on 26 February 2020 and the sanitary alert on 3 March 2020. The religious gathering seems to have played a role for secondary dissemination of the epidemic in France, but not in creating the local outbreak. CONCLUSIONS: Our results illustrate how the integration of data coming from multiple sources could help trigger an early alarm in the context of an emerging disease. Good information data systems, able to produce earlier alerts, could have avoided a general lockdown in France.

[Application of moving epidemic method in establishing epidemic intensity threshold of hand, foot, and mouth disease in southern China].

Objective: To evaluate the incidence intensity of hand, foot, and mouth disease (HFMD) in 2018/2019 season in southern China by Moving Epidemic Method (MEM), and compare the intensity among provinces, so as to provide basis for optimizing the allocation of public health resources. Methods: The weekly incidence data of HFMD of children under 5 years old in 15 provinces of southern China from March 1, 2012 to February 28, 2019 were collected from Disease Surveillance Reporting System of Chinese Center for Disease Control and Prevention, and the epidemic intensity threshold of each province in southern China during this period was calculated and evaluated by MEM. Results: In the first incidence peak of 2018/2019 HFMD season, in 15 provinces in the south China, 6 provinces (Jiangsu, Zhejiang, Jiangxi, Chongqing, Sichuan and Yunnan) reported very high incidence rates in children under 5 years old while Guangdong, Guangxi and Hainan provinces had low incidence level. In the second incidence peak, the incidences in 6 provinces (Shanghai, Jiangsu, Zhejiang, Chongqing, Sichuan and Yunnan) reached very high levels. The incidences in remaining provinces also reached medium or high levels. In most provinces, the thresholds in the first incidence peak were higher than those in the second incidence peak, but Chongqing and Sichuan were different. The results of model validation showed that the sensitivity and specificity of MEM were higher than 70% except for Hainan, Chongqing and Yunnan. Conclusions: For southern provinces with two incidence peaks in HFMD season, MEM can be used to determine the epidemic intensity thresholds of different incidence peaks by dividing the disease season to analyze the incidence intensity of HFMD in different stages. The epidemic intensity threshold established by MEM integrates the historical data, and the province (city) with extremely high epidemic level identified represents that the province (city) has an abnormal increase compared with the historical incidence level, which requires more attention from all areas and timely implementation of prevention and control measures.