Measurability of the epidemic reproduction number in data-driven contact networks

Investigating and forecasting infectious disease dynamics using epidemiological and molecular surveillance data

The integration of viral genomic data into public health surveillance has revolutionized our ability to track and forecast infectious disease dynamics. This review addresses two critical aspects of infectious disease forecasting and monitoring: the methodological workflow for epidemic forecasting and the transformative role of molecular surveillance. We first present a detailed approach for validating epidemic models, emphasizing an iterative workflow that utilizes ordinary differential equation (ODE)-based models to investigate and forecast disease dynamics. We recommend a more structured approach to model validation, systematically addressing key stages such as model calibration, assessment of structural and practical parameter identifiability, and effective uncertainty propagation in forecasts. Furthermore, we underscore the importance of incorporating multiple data streams by applying both simulated and real epidemiological data from the COVID-19 pandemic to produce more reliable forecasts with quantified uncertainty. Additionally, we emphasize the pivotal role of viral genomic data in tracking transmission dynamics and pathogen evolution. By leveraging advanced computational tools such as Bayesian phylogenetics and phylodynamics, researchers can more accurately estimate transmission clusters and reconstruct outbreak histories, thereby improving data-driven modeling and forecasting and informing targeted public health interventions. Finally, we discuss the transformative potential of integrating molecular epidemiology with mathematical modeling to complement and enhance epidemic forecasting and optimize public health strategies.

Emergence of the reproduction matrix in epidemic forecasting

During the recent COVID-19 pandemic, the instantaneous reproduction number, R(t), has surged as a widely used measure to target public health interventions aiming at curbing the infection rate. In analogy with the basic reproduction number that arises from the linear stability analysis, R(t) is typically interpreted as a threshold parameter that separates exponential growth (R(t) > 1) from exponential decay (R(t) < 1). In real epidemics, however, the finite number of susceptibles, the stratification of the population (e.g. by age or vaccination state), and heterogeneous mixing lead to more complex epidemic courses. In the context of the multidimensional renewal equation, we generalize the scalar R(t) to a reproduction matrix, [Formula: see text], which details the epidemic state of the stratified population, and offers a concise epidemic forecasting scheme. First, the reproduction matrix is computed from the available incidence data (subject to some a priori assumptions), then it is projected into the future by a transfer functional to predict the epidemic course. We demonstrate that this simple scheme allows realistic and accurate epidemic trajectories both in synthetic test cases and with reported incidence data from the COVID-19 pandemic. Accounting for the full heterogeneity and nonlinearity of the infection process, the reproduction matrix improves the prediction of the infection peak. In contrast, the scalar reproduction number overestimates the possibility of sustaining the initial infection rate and leads to an overshoot in the incidence peak. Besides its simplicity, the devised forecasting scheme offers rich flexibility to be generalized to time-dependent mitigation measures, contact rate, infectivity and vaccine protection.

Assessing the impact of interventions on the major Omicron BA.2 outbreak in spring 2022 in Shanghai

Background

Shanghai experienced a significant surge in Omicron BA.2 infections from March to June 2022. In addition to the standard interventions in place at that time, additional interventions were implemented in response to the outbreak. However, the impact of these interventions on BA.2 transmission remains unclear.

Methods

We systematically collected data on the daily number of newly reported infections during this wave and utilized a Bayesian approach to estimate the daily effective reproduction number. Data on public health responses were retrieved from the Oxford COVID-19 Government Response Tracker and served as a proxy for the interventions implemented during this outbreak. Using a log-linear regression model, we assessed the impact of these interventions on the reproduction number. Furthermore, we developed a mathematical model of BA.2 transmission. By combining the estimated effect of the interventions from the regression model and the transmission model, we estimated the number of infections and deaths averted by the implemented interventions.

Results

We found a negative association (-0.0069, 95% CI: 0.0096 to -0.0045) between the level of interventions and the number of infections. If interventions did not ramp up during the outbreak, we estimated that the number of infections and deaths would have increased by 22.6% (95% CI: 22.4-22.8%), leading to a total of 768,576 (95% CI: 768,021-769,107) infections and 722 (95% CI: 722-723) deaths. If no interventions were deployed during the outbreak, we estimated that the number of infections and deaths would have increased by 46.0% (95% CI: 45.8-46.2%), leading to a total of 915,099 (95% CI: 914,639-915,518) infections and 860 (95% CI: 860-861) deaths.

Conclusion

Our findings suggest that the interventions adopted during the Omicron BA.2 outbreak in spring 2022 in Shanghai were effective in reducing SARS-CoV-2 transmission and disease burden. Our findings emphasize the importance of non-pharmacological interventions in controlling quick surges of cases during epidemic outbreaks.

Static graph approximations of dynamic contact networks for epidemic forecasting

Epidemic modeling is essential in understanding the spread of infectious diseases like COVID-19 and devising effective intervention strategies to control them. Recently, network-based disease models have integrated traditional compartment-based modeling with real-world contact graphs and shown promising results. However, in an ongoing epidemic, future contact network patterns are not observed yet. To address this, we use aggregated static networks to approximate future contacts for disease modeling. The standard method in the literature concatenates all edges from a dynamic graph into one collapsed graph, called the full static graph. However, the full static graph often leads to severe overestimation of key epidemic characteristics. Therefore, we propose two novel static network approximation methods, DegMST and EdgeMST, designed to preserve the sparsity of real world contact network while remaining connected. DegMST and EdgeMST use the frequency of temporal edges and the node degrees respectively to preserve sparsity. Our analysis show that our models more closely resemble the network characteristics of the dynamic graph compared to the full static ones. Moreover, our analysis on seven real-world contact networks suggests EdgeMST yield more accurate estimations of disease dynamics for epidemic forecasting when compared to the standard full static method.

Evaluating Seasonal Variations in Human Contact Patterns and Their Impact on the Transmission of Respiratory Infectious Diseases

BACKGROUND

Human contact patterns are a key determinant driving the spread of respiratory infectious diseases. However, the relationship between contact patterns and seasonality as well as their possible association with the seasonality of respiratory diseases is yet to be clarified.

METHODS

We investigated the association between temperature and human contact patterns using data collected through a cross-sectional diary-based contact survey in Shanghai, China, between December 24, 2017, and May 30, 2018. We then developed a compartmental model of influenza transmission informed by the derived seasonal trends in the number of contacts and validated it against A(H1N1)pdm09 influenza data collected in Shanghai during the same period.

RESULTS

We identified a significant inverse relationship between the number of contacts and the seasonal temperature trend defined as a spline interpolation of temperature data (p = 0.003). We estimated an average of 16.4 (95% PrI: 15.1-17.5) contacts per day in December 2017 that increased to an average of 17.6 contacts (95% PrI: 16.5-19.3) in January 2018 and then declined to an average of 10.3 (95% PrI: 9.4-10.8) in May 2018. Estimates of influenza incidence obtained by the compartmental model comply with the observed epidemiological data. The reproduction number was estimated to increase from 1.24 (95% CI: 1.21-1.27) in December to a peak of 1.34 (95% CI: 1.31-1.37) in January. The estimated median infection attack rate at the end of the season was 27.4% (95% CI: 23.7-30.5%).

CONCLUSIONS

Our findings support a relationship between temperature and contact patterns, which can contribute to deepen the understanding of the relationship between social interactions and the epidemiology of respiratory infectious diseases.

Assessing the impact of different contact patterns on disease transmission: Taking COVID-19 as a case

Human-to-human contact plays a leading role in the transmission of infectious diseases, and the contact pattern between individuals has an important influence on the intensity and trend of disease transmission. In this paper, we define regular contacts and random contacts. Then, taking the COVID-19 outbreak in Yangzhou City, China as an example, we consider age heterogeneity, household structure and two contact patterns to establish discrete dynamic models with switching between daytime and nighttime to depict the transmission mechanism of COVID-19 in population. We studied the changes in the reproduction number with different age groups and household sizes at different stages. The effects of the proportion of two contacts patterns on reproduction number were also studied. Furthermore, taking the final size, the peak value of infected individuals in community and the peak value of quarantine infected individuals and nucleic acid test positive individuals as indicators, we evaluate the impact of the number of random contacts, the duration of the free transmission stage and summer vacation on the spread of the disease. The results show that a series of prevention and control measures taken by the Chinese government in response to the epidemic situation are reasonable and effective, and the young and middle-aged adults (aged 18-59) with household size of 6 have the strongest transmission ability. In addition, the results also indicate that increasing the proportion of random contact is beneficial to the control of the infectious disease in the phase with interventions. This work enriches the content of infectious disease modeling and provides theoretical guidance for the prevention and control of follow-up major infectious diseases.

Structural network characteristics affect epidemic severity and prediction in social contact networks

Understanding and mitigating epidemic spread in complex networks requires the measurement of structural network properties associated with epidemic risk. Classic measures of epidemic thresholds like the basic reproduction number (R0) have been adapted to account for the structure of social contact networks but still may be unable to capture epidemic potential relative to more recent measures based on spectral graph properties. Here, we explore the ability of R0 and the spectral radius of the social contact network to estimate epidemic susceptibility. To do so, we simulate epidemics on a series of constructed (small world, scale-free, and random networks) and a collection of over 700 empirical biological social contact networks. Further, we explore how other network properties are related to these two epidemic estimators (R0 and spectral radius) and mean infection prevalence in simulated epidemics. Overall, we find that network properties strongly influence epidemic dynamics and the subsequent utility of R0 and spectral radius as indicators of epidemic risk.

Unveiling invisible farm-to-farm PRRSV-2 transmission links and routes through transmission tree and network analysis

The United States (U.S.) swine industry has struggled to control porcine reproductive and respiratory syndrome (PRRS) for decades, yet the causative virus, PRRSV-2, continues to circulate and rapidly diverges into new variants. In the swine industry, the farm is typically the epidemiological unit for monitoring, prevention, and control; breaking transmission among farms is a critical step in containing disease spread. Despite this, our understanding of farm transmission still is inadequate, precluding the development of tailored control strategies. Therefore, our objective was to infer farm-to-farm transmission links, estimate farm-level transmissibility as defined by reproduction numbers (R), and identify associated risk factors for transmission using PRRSV-2 open reading frame 5 (ORF5) gene sequences, animal movement records, and other data from farms in a swine-dense region of the U.S. from 2014 to 2017. Timed phylogenetic and transmission tree analyses were performed on three sets of sequences (n = 206) from 144 farms that represented the three largest genetic variants of the virus in the study area. The length of inferred pig-to-pig infection chains that corresponded to pairs of farms connected via direct animal movement was used as a threshold value for identifying other feasible transmission links between farms; these links were then transformed into farm-to-farm transmission networks and calculated farm-level R-values. The median farm-level R was one (IQR = 1-2), whereas the R value of 28% of farms was more than one. Exponential random graph models were then used to evaluate the influence of farm attributes and/or farm relationships on the occurrence of farm-to-farm transmission links. These models showed that, even though most transmission events cannot be directly explained by animal movement, movement was strongly associated with transmission. This study demonstrates how integrative techniques may improve disease traceability in a data-rich era by providing a clearer picture of regional disease transmission.

Angular reproduction numbers improve estimates of transmissibility when disease generation times are misspecified or time-varying

We introduce the angular reproduction number Ω, which measures time-varying changes in epidemic transmissibility resulting from variations in both the effective reproduction number R, and generation time distribution w. Predominant approaches for tracking pathogen spread infer either R or the epidemic growth rate r. However, R is biased by mismatches between the assumed and true w, while r is difficult to interpret in terms of the individual-level branching process underpinning transmission. R and r may also disagree on the relative transmissibility of epidemics or variants (i.e. rA > rB does not imply RA > RB for variants A and B). We find that Ω responds meaningfully to mismatches and time-variations in w while mostly maintaining the interpretability of R. We prove that Ω > 1 implies R > 1 and that Ω agrees with r on the relative transmissibility of pathogens. Estimating Ω is no more difficult than inferring R, uses existing software, and requires no generation time measurements. These advantages come at the expense of selecting one free parameter. We propose Ω as complementary statistic to R and r that improves transmissibility estimates when w is misspecified or time-varying and better reflects the impact of interventions, when those interventions concurrently change R and w or alter the relative risk of co-circulating pathogens.

Using spectral characterization to identify healthcare-associated infection (HAI) patients for clinical contact precaution

Healthcare-associated infections (HAIs) are a major problem in hospital infection control. Although HAIs can be suppressed using contact precautions, such precautions are expensive, and we can only apply them to a small fraction of patients (i.e., a limited budget). In this work, we focus on two clinical problems arising from the limited budget: (a) choosing the best patients to be placed under precaution given a limited budget to minimize the spread (the isolation problem), and (b) choosing the best patients to release when limited budget requires some of the patients to be cleared from precaution (the clearance problem). A critical challenge in addressing them is that HAIs have multiple transmission pathways such that locations can also accumulate 'load' and spread the disease. One of the most common practices when placing patients under contact precautions is the regular clearance of pathogen loads. However, standard propagation models like independent cascade (IC)/susceptible-infectious-susceptible (SIS) cannot capture such mechanisms directly. Hence to account for this challenge, using non-linear system theory, we develop a novel spectral characterization of a recently proposed pathogen load based model, 2-MODE-SIS model, on people/location networks to capture spread dynamics of HAIs. We formulate the two clinical problems using this spectral characterization and develop effective and efficient algorithms for them. Our experiments show that our methods outperform several natural structural and clinical approaches on real-world hospital testbeds and pick meaningful solutions.

Assessing individual risk and the latent transmission of COVID-19 in a population with an interaction-driven temporal model

Interaction-driven modeling of diseases over real-world contact data has been shown to promote the understanding of the spread of diseases in communities. This temporal modeling follows the path-preserving order and timing of the contacts, which are essential for accurate modeling. Yet, other important aspects were overlooked. Various airborne pathogens differ in the duration of exposure needed for infection. Also, from the individual perspective, Covid-19 progression differs between individuals, and its severity is statistically correlated with age. Here, we enrich an interaction-driven model of Covid-19 and similar airborne viral diseases with (a) meetings duration and (b) personal disease progression. The enriched model enables predicting outcomes at both the population and the individual levels. It further allows predicting individual risk of engaging in social interactions as a function of the virus characteristics and its prevalence in the population. We further showed that the enigmatic nature of asymptomatic transmission stems from the latent effect of the network density on this transmission and that asymptomatic transmission has a substantial impact only in sparse communities.

Epidemic thresholds and human mobility

A comprehensive view of disease epidemics demands a deep understanding of the complex interplay between human behaviour and infectious diseases. Here, we propose a flexible modelling framework that brings conclusions about the influence of human mobility and disease transmission on early epidemic growth, with applicability in outbreak preparedness. We use random matrix theory to compute an epidemic threshold, equivalent to the basic reproduction number [Formula: see text], for a SIR metapopulation model. The model includes both systematic and random features of human mobility. Variations in disease transmission rates, mobility modes (i.e. commuting and migration), and connectivity strengths determine the threshold value and whether or not a disease may potentially establish in the population, as well as the local incidence distribution.

Network-augmented compartmental models to track asymptomatic disease spread

Summary

A major challenge in understanding the spread of certain newly emerging viruses is the presence of asymptomatic cases. Their prevalence is hard to measure in the absence of testing tools, and yet the information is critical for tracking disease spread and shaping public health policies. Here, we introduce a framework that combines classic compartmental models with travel networks and we use it to estimate asymptomatic rates. Our platform, traSIR ("tracer"), is an augmented susceptible-infectious-recovered (SIR) model that incorporates multiple locations and the flow of people between them; it has a compartment model for each location and estimates of commuting traffic between compartments. TraSIR models both asymptomatic and symptomatic infections, as well as the dampening effect symptomatic infections have on traffic between locations. We derive analytical formulae to express the asymptomatic rate as a function of other key model parameters. Next, we use simulations to show that empirical data fitting yields excellent agreement with actual asymptomatic rates using only information about the number of symptomatic infections over time and compartments. Finally, we apply our model to COVID-19 data consisting of reported daily infections in the New York metropolitan area and estimate asymptomatic rates of COVID-19 to be ∼34%, which is within the 30-40% interval derived from widespread testing. Overall, our work demonstrates that traSIR is a powerful approach to express viral propagation dynamics over geographical networks and estimate key parameters relevant to virus transmission.

Availability and implementation

No public repository.

A model for the SARS-CoV-2 dynamics in a population lacking herd immunity

We introduced the S-HI model, a generalized SEIR model to describe the dynamics of the SARS-CoV-2 virus in a community without herd immunity and performed simulations for six months. The S- HI model consists of eight equations corresponding to susceptible individuals, exposed, asymptomatic infected, asymptomatic recovered, symptomatic infected, quarantined, symptomatic recovered and dead. We study the dynamics of the infected, asymptomatic. Dead classes in 4 different networks: households, workplaces, agglomeration places and the general community, showing that the dynamics of the three compartments have the exact nature in each layer and that the speed of the disease considerably increases in the networks with the highest weight of contacts. The reproduction number, R0, is greater than 1 in all networks conforming to the theory. The variants of the SARS-Cov-2 virus are not taken into account, so the S-HI model would fit a situation similar to the first wave of contagion after the mandatory lockdown. Keywords: SARS-Cov-2, mathematical models, SEIR, data-driven networks, simulations, basic reproduction number, lack of herd immunity.

Bayesian inference in epidemics: linear noise analysis

This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the Bayesian model's convergence with increasing amounts of data under measurement limitations. Depending on how weakly informative the disease measurements are, we offer a kind of 'best case' as well as a 'worst case' analysis where, in the former case, we assume that the prevalence is directly accessible, while in the latter that only a binary signal corresponding to a prevalence detection threshold is available. Both cases are studied under an assumed so-called linear noise approximation as to the true dynamics. Numerical experiments test the sharpness of our results when confronted with more realistic situations for which analytical results are unavailable.

Coupling the Within-Host Process and Between-Host Transmission of COVID-19 Suggests Vaccination and School Closures are Critical

Most models of COVID-19 are implemented at a single micro or macro scale, ignoring the interplay between immune response, viral dynamics, individual infectiousness and epidemiological contact networks. Here we develop a data-driven model linking the within-host viral dynamics to the between-host transmission dynamics on a multilayer contact network to investigate the potential factors driving transmission dynamics and to inform how school closures and antiviral treatment can influence the epidemic. Using multi-source data, we initially determine the viral dynamics and estimate the relationship between viral load and infectiousness. Then, we embed the viral dynamics model into a four-layer contact network and formulate an agent-based model to simulate between-host transmission. The results illustrate that the heterogeneity of immune response between children and adults and between vaccinated and unvaccinated infections can produce different transmission patterns. We find that school closures play a significant effect on mitigating the pandemic as more adults get vaccinated and the virus mutates. If enough infected individuals are diagnosed by testing before symptom onset and then treated quickly, the transmission can be effectively curbed. Our multiscale model reveals the critical role played by younger individuals and antiviral treatment with testing in controlling the epidemic.

Estimation of the incubation period and generation time of SARS-CoV-2 Alpha and Delta variants from contact tracing data

Quantitative information on epidemiological quantities such as the incubation period and generation time of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants is scarce. We analysed a dataset collected during contact tracing activities in the province of Reggio Emilia, Italy, throughout 2021. We determined the distributions of the incubation period for the Alpha and Delta variants using information on negative polymerase chain reaction tests and the date of last exposure from 282 symptomatic cases. We estimated the distributions of the intrinsic generation time using a Bayesian inference approach applied to 9724 SARS-CoV-2 cases clustered in 3545 households where at least one secondary case was recorded. We estimated a mean incubation period of 4.9 days (95% credible intervals, CrI, 4.4-5.4) for Alpha and 4.5 days (95% CrI 4.0-5.0) for Delta. The intrinsic generation time was estimated to have a mean of 7.12 days (95% CrI 6.27-8.44) for Alpha and of 6.52 days (95% CrI 5.54-8.43) for Delta. The household serial interval was 2.43 days (95% CrI 2.29-2.58) for Alpha and 2.74 days (95% CrI 2.62-2.88) for Delta, and the estimated proportion of pre-symptomatic transmission was 48-51% for both variants. These results indicate limited differences in the incubation period and intrinsic generation time of SARS-CoV-2 variants Alpha and Delta compared to ancestral lineages.

Machine learning based regional epidemic transmission risks precaution in digital society

The contact and interaction of human is considered to be one of the important factors affecting the epidemic transmission, and it is critical to model the heterogeneity of individual activities in epidemiological risk assessment. In digital society, massive data makes it possible to implement this idea on large scale. Here, we use the mobile phone signaling to track the users' trajectories and construct contact network to describe the topology of daily contact between individuals dynamically. We show the spatiotemporal contact features of about 7.5 million mobile phone users during the outbreak of COVID-19 in Shanghai, China. Furthermore, the individual feature matrix extracted from contact network enables us to carry out the extreme event learning and predict the regional transmission risk, which can be further decomposed into the risk due to the inflow of people from epidemic hot zones and the risk due to people close contacts within the observing area. This method is much more flexible and adaptive, and can be taken as one of the epidemic precautions before the large-scale outbreak with high efficiency and low cost.

Age-specific transmission dynamic of mumps: A long-term large-scale modeling study in Jilin Province, China

Objectives

Despite the adoption of a new childhood immunization program in China, the incidence of mumps remains high. This study aimed to describe the epidemiological characteristics of mumps in Jilin Province from 2005 to 2019 and to assess the transmissibility of mumps virus among the whole population and different subgroups by regions and age groups.

Methods

The Non-age-specific and age-specific Susceptible-Exposed-Pre-symptomatic-Infectious-Asymptomatic-Recovered (SEPIAR) models were fitted to actual mumps incidence data. The time-varying reproduction number (R _t ) was used to evaluate and compare the transmissibility.

Results

From 2005 to 2019, a total of 57,424 cases of mumps were reported in Jilin Province. The incidence of mumps was the highest in people aged 5 to 9 years (77.37 per 100,000). The two SEPIAR models fitted the reported data well (P < 0.01). The median transmissibility (R _t ) calculated by the two SEPIAR models were 1.096 (range: 1.911 × 10^-5-2.192) and 1.074 (range: 0.033-2.114) respectively. The age-specific SEPIAR model was more representative of the actual epidemic of mumps in Jilin Province from 2005-2019.

Conclusions

For mumps control, it is recommended that mumps-containing vaccines (MuCV) coverage be increased nationwide in the 5-9 years age group, either by a mumps vaccine alone or by a combination of vaccines such as measles-mumps-rubella (MMR) vaccine. The coverage of vaccines in Jilin Province should be continuously expanded to establish solid immunity in the population. China needs to redefine the optimal time interval for MuCV immunization.

Epidemic spreading under mutually independent intra- and inter-host pathogen evolution

The dynamics of epidemic spreading is often reduced to the single control parameter R0 (reproduction-rate), whose value, above or below unity, determines the state of the contagion. If, however, the pathogen evolves as it spreads, R0 may change over time, potentially leading to a mutation-driven spread, in which an initially sub-pandemic pathogen undergoes a breakthrough mutation. To predict the boundaries of this pandemic phase, we introduce here a modeling framework to couple the inter-host network spreading patterns with the intra-host evolutionary dynamics. We find that even in the extreme case when these two process are driven by mutually independent selection forces, mutations can still fundamentally alter the pandemic phase-diagram. The pandemic transitions, we show, are now shaped, not just by R0, but also by the balance between the epidemic and the evolutionary timescales. If mutations are too slow, the pathogen prevalence decays prior to the appearance of a critical mutation. On the other hand, if mutations are too rapid, the pathogen evolution becomes volatile and, once again, it fails to spread. Between these two extremes, however, we identify a broad range of conditions in which an initially sub-pandemic pathogen can breakthrough to gain widespread prevalence.

SOPHIE: Viral outbreak investigation and transmission history reconstruction in a joint phylogenetic and network theory framework

Genomic epidemiology is now widely used for viral outbreak investigations. Still, this methodology faces many challenges. First, few methods account for intra-host viral diversity. Second, maximum parsimony principle continues to be employed for phylogenetic inference of transmission histories, even though maximum likelihood or Bayesian models are usually more consistent. Third, many methods utilize case-specific data, such as sampling times or infection exposure intervals. This impedes study of persistent infections in vulnerable groups, where such information has a limited use. Finally, most methods implicitly assume that transmission events are independent, although common source outbreaks violate this assumption. We propose a maximum likelihood framework, SOPHIE, based on the integration of phylogenetic and random graph models. It infers transmission networks from viral phylogenies and expected properties of inter-host social networks modeled as random graphs with given expected degree distributions. SOPHIE is scalable, accounts for intra-host diversity, and accurately infers transmissions without case-specific epidemiological data.

Susceptibility to Resurgent COVID-19 Outbreaks Following Vaccine Rollouts: A Modeling Study

Using the recently proposed Susceptible–Asymptomatic–Infected–Vaccinated–Removed (SAIVR) model, we study the impact of key factors affecting COVID-19 vaccine rollout effectiveness and the susceptibility to resurgent epidemics. The SAIVR model expands the widely used Susceptible–Infectious–Removed (SIR) model for describing epidemics by adding compartments to include the asymptomatic infected (A) and the vaccinated (V) populations. We solve the model numerically to make predictions on the susceptibility to resurgent COVID-19 epidemics depending on initial vaccination coverage, importation loads, continuing vaccination, and more contagious SARS-CoV-2 variants, under persistent immunity and immunity waning conditions. The parameters of the model represent reported epidemiological characteristics of the SARS-CoV-2 virus such as the disease spread in countries with high levels of vaccination coverage. Our findings help explain how the combined effects of different vaccination coverage levels and waning immunity lead to distinct patterns of resurgent COVID-19 epidemics (either surges or endemic), which are observed in countries that implemented different COVID-19 health policies and achieved different vaccinated population plateaus after the vaccine rollouts in the first half of 2021.

Risk assessment of imported COVID-19 in China: A modelling study in Sichuan Province

The importation of COVID-19 cases in China is due to the returning of Chinese citizens abroad, where the majority of cases stand. This study aimed to evaluate the risk of importing COVID-19 into the Sichuan Province of China and conduct a short-term risk prediction assessment and analysis. Data on COVID-19 cases in each country and Sichuan were collected, as well as visitors to Sichuan, population, area, and medical resources in each city in Sichuan province. According to different control strategies of entry aviation and quarantine control, we built models of epidemic transmission to estimate the risk for imported COVID-19 cases in 21 cities of Sichuan. Within 140 days of the policy change's implementation, the number of susceptible, infected, and recovered people in all cities followed the same pattern over time: (1) the number of susceptible people declined slowly at first, then accelerated to reach a stable value; (2) the number of infections gradually increased to a peak, then decreased; and (3) the number of recovered patients gradually increased to a stable value. Under the four different scenarios, there were no significant differences between the risk peaks because the social distance did not change. However, the peak time would be delayed due to the implementation of flight control and nucleic acid detection measures. The improvement of foreign epidemics (reduction of attenuation factors) all delayed the arrival of the peak risk value in Chengdu by about 20 days; however, the size of the peak value did not change significantly. The improvement of nucleic acid detection accuracy delayed the arrival of the peak risk value in Chengdu, but the size of the peak value did not change significantly. Therefore, flight control and the improvement of nucleic acid detection accuracy and overseas epidemic situations have positively affected the prevention and control of the epidemic in Sichuan.

COVID-19 in Africa: Underreporting, demographic effect, chaotic dynamics, and mitigation strategy impact

The epidemic of COVID-19 has shown different developments in Africa compared to the other continents. Three different approaches were used in this study to analyze this situation. In the first part, basic statistics were performed to estimate the contribution of the elderly people to the total numbers of cases and deaths in comparison to the other continents; Similarly, the health systems capacities were analysed to assess the level of underreporting. In the second part, differential equations were reconstructed from the epidemiological time series of cases and deaths (from the John Hopkins University) to analyse the dynamics of COVID-19 in seventeen countries. In the third part, the time evolution of the contact number was reconstructed since the beginning of the outbreak to investigate the effectiveness of the mitigation strategies. Results were compared to the Oxford stringency index and to the mobility indices of the Google Community Mobility Reports.

Compared to Europe, the analyses show that the lower proportion of elderly people in Africa enables to explain the lower total numbers of cases and deaths by a factor of 5.1 on average (from 1.9 to 7.8). It corresponds to a genuine effect. Nevertheless, COVID-19 numbers are effectively largely underestimated in Africa by a factor of 8.5 on average (from 1.7 to 20. and more) due to the weakness of the health systems at country level. Geographically, the models obtained for the dynamics of cases and deaths reveal very diversified dynamics. The dynamics is chaotic in many contexts, including a situation of bistability rarely observed in dynamical systems. Finally, the contact number directly deduced from the epidemiological observations reveals an effective role of the mitigation strategies on the short term. On the long term, control measures have contributed to maintain the epidemic at a low level although the progressive release of the stringency did not produce a clear increase of the contact number. The arrival of the omicron variant is clearly detected and characterised by a quick increase of interpeople contact, for most of the African countries considered in the analysis.

Data-driven contact network models of COVID-19 reveal trade-offs between costs and infections for optimal local containment policies

While several non-pharmacological measures have been implemented for a few months in an effort to slow the coronavirus disease (COVID-19) pandemic in the United States, the disease remains a danger in a number of counties as restrictions are lifted to revive the economy. Making a trade-off between economic recovery and infection control is a major challenge confronting many hard-hit counties. Understanding the transmission process and quantifying the costs of local policies are essential to the task of tackling this challenge. Here, we investigate the dynamic contact patterns of the populations from anonymized, geo-localized mobility data and census and demographic data to create data-driven, agent-based contact networks. We then simulate the epidemic spread with a time-varying contagion model in ten large metropolitan counties in the United States and evaluate a combination of mobility reduction, mask use, and reopening policies. We find that our model captures the spatial-temporal and heterogeneous case trajectory within various counties based on dynamic population behaviors. Our results show that a decision-making tool that considers both economic cost and infection outcomes of policies can be informative in making decisions of local containment strategies for optimal balancing of economic slowdown and virus spread.

Quantifying the information in noisy epidemic curves

Reliably estimating the dynamics of transmissible diseases from noisy surveillance data is an enduring problem in modern epidemiology. Key parameters are often inferred from incident time series, with the aim of informing policy-makers on the growth rate of outbreaks or testing hypotheses about the effectiveness of public health interventions. However, the reliability of these inferences depends critically on reporting errors and latencies innate to the time series. Here, we develop an analytical framework to quantify the uncertainty induced by under-reporting and delays in reporting infections, as well as a metric for ranking surveillance data informativeness. We apply this metric to two primary data sources for inferring the instantaneous reproduction number: epidemic case and death curves. We find that the assumption of death curves as more reliable, commonly made for acute infectious diseases such as COVID-19 and influenza, is not obvious and possibly untrue in many settings. Our framework clarifies and quantifies how actionable information about pathogen transmissibility is lost due to surveillance limitations.

Commentary on the use of the reproduction number R during the COVID-19 pandemic

Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text]. The magnitude of [Formula: see text] indicates by how much transmission needs to be reduced to control the epidemic. Using [Formula: see text] in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of [Formula: see text] but many, and the precise definition of [Formula: see text] affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined [Formula: see text], there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate [Formula: see text] vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when [Formula: see text] is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of [Formula: see text], and the data and methods used to estimate it, can make [Formula: see text] a more useful metric for future management of the epidemic.

Intrinsic generation time of the SARS-CoV-2 Omicron variant: An observational study of household transmission

Background

Starting from the final months of 2021, the SARS-CoV-2 Omicron variant expanded globally, swiftly replacing Delta, the variant that was dominant at the time. Many uncertainties remain about the epidemiology of Omicron; here, we aim to estimate its generation time.

Methods

We used a Bayesian approach to analyze 23,122 SARS-CoV-2 infected individuals clustered in 8903 households as determined from contact tracing operations in Reggio Emilia, Italy, throughout January 2022. We estimated the distribution of the intrinsic generation time (the time between the infection dates of an infector and its secondary cases in a fully susceptible population), realized household generation time, realized serial interval (time between symptom onset of an infector and its secondary cases), and contribution of pre-symptomatic transmission.

Findings

We estimated a mean intrinsic generation time of 6.84 days (95% credible intervals, CrI, 5.72-8.60), and a mean realized household generation time of 3.59 days (95%CrI: 3.55-3.60). The household serial interval was 2.38 days (95%CrI 2.30-2.47) with about 51% (95%CrI 45-56%) of infections caused by symptomatic individuals being generated before symptom onset.

Interpretation

These results indicate that the intrinsic generation time of the SARS-CoV-2 Omicron variant might not have shortened as compared to previous estimates on ancestral lineages, Alpha and Delta, in the same geographic setting. Like for previous lineages, pre-symptomatic transmission appears to play a key role for Omicron transmission. Estimates in this study may be useful to design quarantine, isolation and contact tracing protocols and to support surveillance (e.g., for the accurate computation of reproduction numbers).

Funding

The study was partially funded by EU grant 874850 MOOD.

Temporal evolution of the Covid19 pandemic reproduction number: Estimations from proximal optimization to Monte Carlo sampling

Monitoring the evolution of the Covid19 pandemic constitutes a critical step in sanitary policy design. Yet, the assessment of the pandemic intensity within the pandemic period remains a challenging task because of the limited quality of data made available by public health authorities (missing data, outliers and pseudoseasonalities, notably), that calls for cumbersome and ad-hoc preprocessing (denoising) prior to estimation. Recently, the estimation of the reproduction number, a measure of the pandemic intensity, was formulated as an inverse problem, combining data-model fidelity and space-time regularity constraints, solved by nonsmooth convex proximal minimizations. Though promising, that formulation lacks robustness against the limited quality of the Covid19 data and confidence assessment. The present work aims to address both limitations: First, it discusses solutions to produce a robust assessment of the pandemic intensity by accounting for the low quality of the data directly within the inverse problem formulation. Second, exploiting a Bayesian interpretation of the inverse problem formulation, it devises a Monte Carlo sampling strategy, tailored to a nonsmooth log-concave a posteriori distribution, to produce relevant credibility interval-based estimates for the Covid19 reproduction number. Clinical relevance Applied to daily counts of new infections made publicly available by the Health Authorities for around 200 countries, the proposed procedures permit robust assessments of the time evolution of the Covid19 pandemic intensity, updated automatically and on a daily basis.

Epidemic management and control through risk-dependent individual contact interventions

Testing, contact tracing, and isolation (TTI) is an epidemic management and control approach that is difficult to implement at scale because it relies on manual tracing of contacts. Exposure notification apps have been developed to digitally scale up TTI by harnessing contact data obtained from mobile devices; however, exposure notification apps provide users only with limited binary information when they have been directly exposed to a known infection source. Here we demonstrate a scalable improvement to TTI and exposure notification apps that uses data assimilation (DA) on a contact network. Network DA exploits diverse sources of health data together with the proximity data from mobile devices that exposure notification apps rely upon. It provides users with continuously assessed individual risks of exposure and infection, which can form the basis for targeting individual contact interventions. Simulations of the early COVID-19 epidemic in New York City are used to establish proof-of-concept. In the simulations, network DA identifies up to a factor 2 more infections than contact tracing when both harness the same contact data and diagnostic test data. This remains true even when only a relatively small fraction of the population uses network DA. When a sufficiently large fraction of the population (≳ 75%) uses network DA and complies with individual contact interventions, targeting contact interventions with network DA reduces deaths by up to a factor 4 relative to TTI. Network DA can be implemented by expanding the computational backend of existing exposure notification apps, thus greatly enhancing their capabilities. Implemented at scale, it has the potential to precisely and effectively control future epidemics while minimizing economic disruption.

During the ongoing COVID-19 pandemic, exposure notification apps have been developed to scale up manual contact tracing. The apps use proximity data from mobile devices to automate notifying direct contacts of an infection source. The information they provide is limited because users receive only rare and binary alerts. Here we present network data assimilation (DA) as a new digital approach to epidemic management and control. Network DA uses the same data as exposure notification apps but uses it more effectively to provide frequently updated individual risk assessments to users.

Network DA is based on automated learning about individuals’ risk of exposure and infection from crowd-sourced health data and proximity data. The data are aggregated with models of disease transmission to produce statistical assessments of users’ risks. In an extensive simulation study of the COVID-19 epidemic in New York City (NYC), we show that network DA with diagnostic testing achieves epidemic control with fewer than half the deaths that occurred during NYC’s lockdown, while isolating a far smaller fraction of the population (typically only 5–10% of the population at any given time).

Implemented at scale, then, network DA has the potential to effectively control epidemics while minimizing economic and social disruption.

Disease spreading modeling and analysis: a survey

MOTIVATION

The control of the diffusion of diseases is a critical subject of a broad research area, which involves both clinical and political aspects. It makes wide use of computational tools, such as ordinary differential equations, stochastic simulation frameworks and graph theory, and interaction data, from molecular to social granularity levels, to model the ways diseases arise and spread. The coronavirus disease 2019 (COVID-19) is a perfect testbench example to show how these models may help avoid severe lockdown by suggesting, for instance, the best strategies of vaccine prioritization.

RESULTS

Here, we focus on and discuss some graph-based epidemiological models and show how their use may significantly improve the disease spreading control. We offer some examples related to the recent COVID-19 pandemic and discuss how to generalize them to other diseases.

Analysis of the competition among viral strains using a temporal interaction-driven contagion model

The temporal dynamics of social interactions were shown to influence the spread of disease. Here, we model the conditions of progression and competition for several viral strains, exploring various levels of cross-immunity over temporal networks. We use our interaction-driven contagion model and characterize, using it, several viral variants. Our results, obtained on temporal random networks and on real-world interaction data, demonstrate that temporal dynamics are crucial to determining the competition results. We consider two and three competing pathogens and show the conditions under which a slower pathogen will remain active and create a second wave infecting most of the population. We then show that when the duration of the encounters is considered, the spreading dynamics change significantly. Our results indicate that when considering airborne diseases, it might be crucial to consider the duration of temporal meetings to model the spread of pathogens in a population.

Analytical estimation of maximum fraction of infected individuals with one-shot non-pharmaceutical intervention in a hybrid epidemic model

BACKGROUND

Facing a global epidemic of new infectious diseases such as COVID-19, non-pharmaceutical interventions (NPIs), which reduce transmission rates without medical actions, are being implemented around the world to mitigate spreads. One of the problems in assessing the effects of NPIs is that different NPIs have been implemented at different times based on the situation of each country; therefore, few assumptions can be shared about how the introduction of policies affects the patient population. Mathematical models can contribute to further understanding these phenomena by obtaining analytical solutions as well as numerical simulations.

METHODS AND RESULTS

In this study, an NPI was introduced into the SIR model for a conceptual study of infectious diseases under the condition that the transmission rate was reduced to a fixed value only once within a finite time duration, and its effect was analyzed numerically and theoretically. It was analytically shown that the maximum fraction of infected individuals and the final size could be larger if the intervention starts too early. The analytical results also suggested that more individuals may be infected at the peak of the second wave with a stronger intervention.

CONCLUSIONS

This study provides quantitative relationship between the strength of a one-shot intervention and the reduction in the number of patients with no approximation. This suggests the importance of the strength and time of NPIs, although detailed studies are necessary for the implementation of NPIs in complicated real-world environments as the model used in this study is based on various simplifications.

Are epidemic growth rates more informative than reproduction numbers?

statistics, often derived from simplified models of epidemic spread, inform public health policy in real time. The instantaneous reproduction number,R t , is predominant among these statistics, measuring the average ability of an infection to multiply. However,R t encodes no temporal information and is sensitive to modelling assumptions. Consequently, some have proposed the epidemic growth rate,r t , that is, the rate of change of the log-transformed case incidence, as a more temporally meaningful and model-agnostic policy guide. We examine this assertion, identifying if and when estimates ofr t are more informative than those ofR t . We assess their relative strengths both for learning about pathogen transmission mechanisms and for guiding public health interventions in real time.

Quantifying human mixing patterns in Chinese provinces outside Hubei after the 2020 lockdown was lifted

Background

Contact patterns play a key role in the spread of respiratory infectious diseases in human populations. During the COVID-19 pandemic, the regular contact patterns of the population have been disrupted due to social distancing both imposed by the authorities and individual choices. Many studies have focused on age-mixing patterns before the COVID-19 pandemic, but they provide very little information about the mixing patterns in the COVID-19 era. In this study, we aim at quantifying human heterogeneous mixing patterns immediately after lockdowns implemented to contain COVID-19 spread in China were lifted. We also provide an illustrative example of how the collected mixing patterns can be used in a simulation study of SARS-CoV-2 transmission.

Methods and results

In this work, a contact survey was conducted in Chinese provinces outside Hubei in March 2020, right after lockdowns were lifted. We then leveraged the estimated mixing patterns to calibrate a mathematical model of SARS-CoV-2 transmission. Study participants reported 2.3 contacts per day (IQR: 1.0–3.0) and the mean per-contact duration was 7.0 h (IQR: 1.0–10.0). No significant differences in average contact number and contact duration were observed between provinces, the number of recorded contacts did not show a clear trend by age, and most of the recorded contacts occurred with family members (about 78%). The simulation study highlights the importance of considering age-specific contact patterns to estimate the COVID-19 burden.

Conclusions

Our findings suggest that, despite lockdowns were no longer in place at the time of the survey, people were still heavily limiting their contacts as compared to the pre-pandemic situation.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12879-022-07455-7.

Generation time of the alpha and delta SARS-CoV-2 variants: an epidemiological analysis

Background

In May, 2021, the delta (B.1.617.2) SARS-CoV-2 variant became dominant in the UK, superseded by the omicron (B.1.1.529) variant in December, 2021. The delta variant is associated with increased transmissibility compared with the alpha variant, which was the dominant variant in the UK between December, 2020, and May, 2021. To understand transmission and the effectiveness of interventions, we aimed to investigate whether the delta variant generation time (the interval between infections in infector–infectee pairs) is shorter—ie, transmissions are happening more quickly—than that of the alpha variant.

Methods

In this epidemiological analysis, we analysed transmission data from an ongoing UK Health Security Agency (UKHSA) prospective household study. Households were recruited to the study after an index case had a positive PCR test and genomic sequencing was used to determine the variant responsible. By fitting a mathematical transmission model to the data, we estimated the intrinsic generation time (which assumes a constant supply of susceptible individuals throughout infection) and the household generation time (which reflects realised transmission in the study households, accounting for susceptible depletion) for the alpha and delta variants.

Findings

Between February and August, 2021, 227 households consisting of 559 participants were recruited to the UKHSA study. The alpha variant was detected or assumed to be responsible for infections in 131 households (243 infections in 334 participants) recruited in February–May, and the delta variant in 96 households (174 infections in 225 participants) in May–August. The mean intrinsic generation time was shorter for the delta variant (4·7 days, 95% credible interval [CI] 4·1–5·6) than the alpha variant (5·5 days, 4·7–6·5), with 92% posterior probability. The mean household generation time was 28% (95% CI 0–48%) shorter for the delta variant (3·2 days, 95% CI 2·5–4·2) than the alpha variant (4·5 days, 3·7–5·4), with 97·5% posterior probability.

Interpretation

The delta variant transmits more quickly in households than the alpha variant, which can be attributed to faster depletion of susceptible individuals in households and a possible decrease in the intrinsic generation time. Interventions such as contact tracing, testing, and isolation might be less effective if transmission of the virus occurs quickly.

Funding

National Institute for Health Research, UK Health Security Agency, Engineering and Physical Sciences Research Council, and UK Research and Innovation.

Fundamental limits on inferring epidemic resurgence in real time using effective reproduction numbers

We find that epidemic resurgence, defined as an upswing in the effective reproduction number (R) of the contagion from subcritical to supercritical values, is fundamentally difficult to detect in real time. Inherent latencies in pathogen transmission, coupled with smaller and intrinsically noisier case incidence across periods of subcritical spread, mean that resurgence cannot be reliably detected without significant delays of the order of the generation time of the disease, even when case reporting is perfect. In contrast, epidemic suppression (where R falls from supercritical to subcritical values) may be ascertained 5-10 times faster due to the naturally larger incidence at which control actions are generally applied. We prove that these innate limits on detecting resurgence only worsen when spatial or demographic heterogeneities are incorporated. Consequently, we argue that resurgence is more effectively handled proactively, potentially at the expense of false alarms. Timely responses to recrudescent infections or emerging variants of concern are more likely to be possible when policy is informed by a greater quality and diversity of surveillance data than by further optimisation of the statistical models used to process routine outbreak data.

Modeling COVID-19 Incidence by the Renewal Equation after Removal of Administrative Bias and Noise

Simple Summary

In the past two years, the COVID-19 incidence curves and reproduction number Rt have been the main metrics used by policy makers and journalists to monitor the spread of this global pandemic. However, these metrics are not always reliable in the short term, because of a combination of delay in detection, administrative delays and random noise. In this article, we present a complete model of COVID-19 incidence, faithfully reconstructing the incidence curve and reproduction number from the renewal equation of the disease and precisely estimating the biases associated with periodic weekly bias, festive day bias and residual noise.

Abstract

The sanitary crisis of the past two years has focused the public’s attention on quantitative indicators of the spread of the COVID-19 pandemic. The daily reproduction number Rt, defined by the average number of new infections caused by a single infected individual at time t, is one of the best metrics for estimating the epidemic trend. In this paper, we provide a complete observation model for sampled epidemiological incidence signals obtained through periodic administrative measurements. The model is governed by the classic renewal equation using an empirical reproduction kernel, and subject to two perturbations: a time-varying gain with a weekly period and a white observation noise. We estimate this noise model and its parameters by extending a variational inversion of the model recovering its main driving variable Rt. Using Rt, a restored incidence curve, corrected of the weekly and festive day bias, can be deduced through the renewal equation. We verify experimentally on many countries that, once the weekly and festive days bias have been corrected, the difference between the incidence curve and its expected value is well approximated by an exponential distributed white noise multiplied by a power of the magnitude of the restored incidence curve.

Estimating the generation interval from the incidence rate, the optimal quarantine duration and the efficiency of fast switching periodic protocols for COVID-19

The transmissibility of an infectious disease is usually quantified in terms of the reproduction number [Formula: see text] representing, at a given time, the average number of secondary cases caused by an infected individual. Recent studies have enlightened the central role played by w(z), the distribution of generation times z, namely the time between successive infections in a transmission chain. In standard approaches this quantity is usually substituted by the distribution of serial intervals, which is obtained by contact tracing after measuring the time between onset of symptoms in successive cases. Unfortunately, this substitution can cause important biases in the estimate of [Formula: see text]. Here we present a novel method which allows us to simultaneously obtain the optimal functional form of w(z) together with the daily evolution of [Formula: see text], over the course of an epidemic. The method uses, as unique information, the daily series of incidence rate and thus overcomes biases present in standard approaches. We apply our method to one year of data from COVID-19 officially reported cases in the 21 Italian regions, since the first confirmed case on February 2020. We find that w(z) has mean value [Formula: see text] days with a standard deviation [Formula: see text] day, for all Italian regions, and these values are stable even if one considers only the first 10 days of data recording. This indicates that an estimate of the most relevant transmission parameters can be already available in the early stage of a pandemic. We use this information to obtain the optimal quarantine duration and to demonstrate that, in the case of COVID-19, post-lockdown mitigation policies, such as fast periodic switching and/or alternating quarantine, can be very efficient.

Agent-based modelling of reactive vaccination of workplaces and schools against COVID-19

With vaccination against COVID-19 stalled in some countries, increasing vaccine accessibility and distribution could help keep transmission under control. Here, we study the impact of reactive vaccination targeting schools and workplaces where cases are detected, with an agent-based model accounting for COVID-19 natural history, vaccine characteristics, demographics, behavioural changes and social distancing. In most scenarios, reactive vaccination leads to a higher reduction in cases compared with non-reactive strategies using the same number of doses. The reactive strategy could however be less effective than a moderate/high pace mass vaccination program if initial vaccination coverage is high or disease incidence is low, because few people would be vaccinated around each case. In case of flare-ups, reactive vaccination could better mitigate spread if it is implemented quickly, is supported by enhanced test-trace-isolate and triggers an increased vaccine uptake. These results provide key information to plan an adaptive vaccination rollout.

Applying the Spatial Transmission Network to the Forecast of Infectious Diseases Across Multiple Regions

Objective

Timely and accurate forecast of infectious diseases is essential for achieving precise prevention and control. A good forecasting method of infectious diseases should have the advantages of interpretability, feasibility, and forecasting performance. Since previous research had illustrated that the spatial transmission network (STN) showed good interpretability and feasibility, this study further explored its forecasting performance for infectious diseases across multiple regions. Meanwhile, this study also showed whether the STN could overcome the challenges of model rationality and practical needs.

Methods

The construction of the STN framework involved three major steps: the spatial kluster analysis by tree edge removal (SKATER) algorithm, structure learning by dynamic Bayesian network (DBN), and parameter learning by the vector autoregressive moving average (VARMA) model. Then, we evaluated the forecasting performance of STN by comparing its accuracy with that of the mechanism models like susceptible-exposed-infectious-recovered-susceptible (SEIRS) and machine-learning algorithm like long-short-term memory (LSTM). At the same time, we assessed the robustness of forecasting performance of STN in high and low incidence seasons. The influenza-like illness (ILI) data in the Sichuan Province of China from 2010 to 2017 were used as an example for illustration.

Results

The STN model revealed that ILI was likely to spread among multiple cities in Sichuan during the study period. During the whole study period, the forecasting accuracy of the STN (mean absolute percentage error [MAPE] = 31.134) was significantly better than that of the LSTM (MAPE = 41.657) and the SEIRS (MAPE = 62.039). In addition, the forecasting performance of STN was also superior to those of the other two methods in either the high incidence season (MAPE = 24.742) or the low incidence season (MAPE = 26.209), and the superiority was more obvious in the high incidence season.

Conclusion

This study applied the STN to the forecast of infectious diseases across multiple regions. The results illustrated that the STN not only had good accuracy in forecasting performance but also indicated the spreading directions of infectious diseases among multiple regions to a certain extent. Therefore, the STN is a promising candidate to improve the surveillance work.

Model Integration in Computational Biology: The Role of Reproducibility, Credibility and Utility

During the COVID-19 pandemic, mathematical modeling of disease transmission has become a cornerstone of key state decisions. To advance the state-of-the-art host viral modeling to handle future pandemics, many scientists working on related issues assembled to discuss the topics. These discussions exposed the reproducibility crisis that leads to inability to reuse and integrate models. This document summarizes these discussions, presents difficulties, and mentions existing efforts towards future solutions that will allow future model utility and integration. We argue that without addressing these challenges, scientists will have diminished ability to build, disseminate, and implement high-impact multi-scale modeling that is needed to understand the health crises we face.

Quantifying agent impacts on contact sequences in social interactions

Human social behavior plays a crucial role in how pathogens like SARS-CoV-2 or fake news spread in a population. Social interactions determine the contact network among individuals, while spreading, requiring individual-to-individual transmission, takes place on top of the network. Studying the topological aspects of a contact network, therefore, not only has the potential of leading to valuable insights into how the behavior of individuals impacts spreading phenomena, but it may also open up possibilities for devising effective behavioral interventions. Because of the temporal nature of interactions—since the topology of the network, containing who is in contact with whom, when, for how long, and in which precise sequence, varies (rapidly) in time—analyzing them requires developing network methods and metrics that respect temporal variability, in contrast to those developed for static (i.e., time-invariant) networks. Here, by means of event mapping, we propose a method to quantify how quickly agents mingle by transforming temporal network data of agent contacts. We define a novel measure called contact sequence centrality, which quantifies the impact of an individual on the contact sequences, reflecting the individual’s behavioral potential for spreading. Comparing contact sequence centrality across agents allows for ranking the impact of agents and identifying potential ‘behavioral super-spreaders’. The method is applied to social interaction data collected at an art fair in Amsterdam. We relate the measure to the existing network metrics, both temporal and static, and find that (mostly at longer time scales) traditional metrics lose their resemblance to contact sequence centrality. Our work highlights the importance of accounting for the sequential nature of contacts when analyzing social interactions.

Large deviations of a susceptible-infected-recovered model around the epidemic threshold

We numerically study the dynamics of the SIR disease model on small-world networks by using a large-deviation approach. This allows us to obtain the probability density function of the total fraction of infected nodes and of the maximum fraction of simultaneously infected nodes down to very small probability densities like 10^{-2500}. We analyze the structure of the disease dynamics and observed three regimes in all probability density functions, which correspond to quick mild, quick extremely severe, and sustained severe dynamical evolutions, respectively. Furthermore, the mathematical rate functions of the densities are investigated. The results indicate that the so-called large-deviation property holds for the SIR model. Finally, we measured correlations with other quantities like the duration of an outbreak or the peak position of the fraction of infections, also in the rare regions which are not accessible by standard simulation techniques.

Model-based evaluation of alternative reactive class closure strategies against COVID-19

There are contrasting results concerning the effect of reactive school closure on SARS-CoV-2 transmission. To shed light on this controversy, we developed a data-driven computational model of SARS-CoV-2 transmission. We found that by reactively closing classes based on syndromic surveillance, SARS-CoV-2 infections are reduced by no more than 17.3% (95%CI: 8.0-26.8%), due to the low probability of timely identification of infections in the young population. We thus investigated an alternative triggering mechanism based on repeated screening of students using antigen tests. Depending on the contribution of schools to transmission, this strategy can greatly reduce COVID-19 burden even when school contribution to transmission and immunity in the population is low. Moving forward, the adoption of antigen-based screenings in schools could be instrumental to limit COVID-19 burden while vaccines continue to be rolled out.

Modeling the effect of the vaccination campaign on the COVID-19 pandemic

Population-wide vaccination is critical for containing the SARS-CoV-2 (COVID-19) pandemic when combined with restrictive and prevention measures. In this study we introduce SAIVR, a mathematical model able to forecast the COVID-19 epidemic evolution during the vaccination campaign. SAIVR extends the widely used Susceptible-Infectious-Removed (SIR) model by considering the Asymptomatic (A) and Vaccinated (V) compartments. The model contains several parameters and initial conditions that are estimated by employing a semi-supervised machine learning procedure. After training an unsupervised neural network to solve the SAIVR differential equations, a supervised framework then estimates the optimal conditions and parameters that best fit recent infectious curves of 27 countries. Instructed by these results, we performed an extensive study on the temporal evolution of the pandemic under varying values of roll-out daily rates, vaccine efficacy, and a broad range of societal vaccine hesitancy/denial levels. The concept of herd immunity is questioned by studying future scenarios which involve different vaccination efforts and more infectious COVID-19 variants.

Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique

The COVID-19 pandemic has undergone frequent and rapid changes in its local and global infection rates, driven by governmental measures or the emergence of new viral variants. The reproduction number Rt indicates the average number of cases generated by an infected person at time t and is a key indicator of the spread of an epidemic. A timely estimation of Rt is a crucial tool to enable governmental organizations to adapt quickly to these changes and assess the consequences of their policies. The EpiEstim method is the most widely accepted method for estimating Rt But it estimates Rt with a significant temporal delay. Here, we propose a method, EpiInvert, that shows good agreement with EpiEstim, but that provides estimates of Rt several days in advance. We show that Rt can be estimated by inverting the renewal equation linking Rt with the observed incidence curve of new cases, it Our signal-processing approach to this problem yields both Rt and a restored it corrected for the "weekend effect" by applying a deconvolution and denoising procedure. The implementations of the EpiInvert and EpiEstim methods are fully open source and can be run in real time on every country in the world and every US state.

Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique

The COVID-19 pandemic has undergone frequent and rapid changes in its local and global infection rates, driven by governmental measures or the emergence of new viral variants. The reproduction number R_t indicates the average number of cases generated by an infected person at time t and is a key indicator of the spread of an epidemic. A timely estimation of R_t is a crucial tool to enable governmental organizations to adapt quickly to these changes and assess the consequences of their policies. The EpiEstim method is the most widely accepted method for estimating R_t But it estimates R_t with a significant temporal delay. Here, we propose a method, EpiInvert, that shows good agreement with EpiEstim, but that provides estimates of R_t several days in advance. We show that R_t can be estimated by inverting the renewal equation linking R_t with the observed incidence curve of new cases, i_t Our signal-processing approach to this problem yields both R_t and a restored i_t corrected for the "weekend effect" by applying a deconvolution and denoising procedure. The implementations of the EpiInvert and EpiEstim methods are fully open source and can be run in real time on every country in the world and every US state.

Influenza viruses and coronaviruses: Knowns, unknowns, and common research challenges

The development of safe and effective vaccines in a record time after the emergence of the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is a remarkable achievement, partly based on the experience gained from multiple viral outbreaks in the past decades. However, the Coronavirus Disease 2019 (COVID-19) crisis also revealed weaknesses in the global pandemic response and large gaps that remain in our knowledge of the biology of coronaviruses (CoVs) and influenza viruses, the 2 major respiratory viruses with pandemic potential. Here, we review current knowns and unknowns of influenza viruses and CoVs, and we highlight common research challenges they pose in 3 areas: the mechanisms of viral emergence and adaptation to humans, the physiological and molecular determinants of disease severity, and the development of control strategies. We outline multidisciplinary approaches and technological innovations that need to be harnessed in order to improve preparedeness to the next pandemic.