tsiR: An R package for time-series Susceptible-Infected-Recovered models of epidemics

Climate, demography, immunology, and virology combine to drive two decades of dengue virus dynamics in Cambodia

The incidence of dengue virus disease has increased globally across the past half-century, with highest number of cases ever reported in 2019 and again in 2023. We analyzed climatological, epidemiological, and phylogenomic data to investigate drivers of two decades of dengue in Cambodia, an understudied endemic setting. Using epidemiological models fit to a 19-y dataset, we first demonstrate that climate-driven transmission alone is insufficient to explain three epidemics across the time series. We then use wavelet decomposition to highlight enhanced annual and multiannual synchronicity in dengue cycles between provinces in epidemic years, suggesting a role for climate in homogenizing dynamics across space and time. Assuming reported cases correspond to symptomatic secondary infections, we next use an age-structured catalytic model to estimate a declining force of infection for dengue through time, which elevates the mean age of reported cases in Cambodia. Reported cases in >70-y-old individuals in the 2019 epidemic are best explained when also allowing for waning multitypic immunity and repeat symptomatic infections in older patients. We support this work with phylogenetic analysis of 192 dengue virus (DENV) genomes that we sequenced between 2019 and 2022, which document emergence of DENV-2 Cosmopolitan Genotype-II into Cambodia. This lineage demonstrates phylogenetic homogeneity across wide geographic areas, consistent with invasion behavior and in contrast to high phylogenetic diversity exhibited by endemic DENV-1. Finally, we simulate an age-structured, mechanistic model of dengue dynamics to demonstrate how expansion of an antigenically distinct lineage that evades preexisting multitypic immunity effectively reproduces the older-age infections witnessed in our data.

Increasing intensity of enterovirus outbreaks projected with climate change

Pathogens of the enterovirus genus, including poliovirus and coxsackieviruses, typically circulate in the summer months suggesting a possible positive association between warmer weather and transmission. Here we evaluate the environmental and demographic drivers of enterovirus transmission, as well as the implications of climate change for future enterovirus circulation. We leverage pre-vaccination era data on polio in the US as well as data on two enterovirus A serotypes in China and Japan that are known to cause hand, foot, and mouth disease. Using mechanistic modeling and statistical approaches, we find that enterovirus transmission appears positively correlated with temperature although demographic factors, particularly the timing of school semesters, remain important. We use temperature projections from Coupled Model Intercomparison Project Phase 6 (CMIP6) to simulate future outbreaks under late 21st-century climate change for Chinese provinces. We find that outbreak size increases with climate change on average, though results differ across climate models depending on the degree of wintertime warming. In the worst-case scenario, we project peak outbreaks in some locations could increase by up to 40%.

Epidemiological impacts of post-infection mortality

Infectious diseases may cause some long-term damage to their host, leading to elevated mortality even after recovery. Mortality due to complications from so-called 'long COVID' is a stark illustration of this potential, but the impacts of such post-infection mortality (PIM) on epidemic dynamics are not known. Using an epidemiological model that incorporates PIM, we examine the importance of this effect. We find that in contrast to mortality during infection, PIM can induce epidemic cycling. The effect is due to interference between elevated mortality and reinfection through the previously infected susceptible pool. In particular, robust immunity (via decreased susceptibility to reinfection) reduces the likelihood of cycling; on the other hand, disease-induced mortality can interact with weak PIM to generate periodicity. In the absence of PIM, we prove that the unique endemic equilibrium is stable and therefore our key result is that PIM is an overlooked phenomenon that is likely to be destabilizing. Overall, given potentially widespread effects, our findings highlight the importance of characterizing heterogeneity in susceptibility (via both PIM and robustness of host immunity) for accurate epidemiological predictions. In particular, for diseases without robust immunity, such as SARS-CoV-2, PIM may underlie complex epidemiological dynamics especially in the context of seasonal forcing.

Application of a forecasting model to mitigate the consequences of unexpected RSV surge: Experience from the post-COVID-19 2021/22 winter season in a major metropolitan centre, Lyon, France

Background

The emergence of COVID-19 triggered the massive implementation of non-pharmaceutical interventions (NPI) which impacted the circulation of respiratory syncytial virus (RSV) during the 2020/2021 season.

Methods

A time-series susceptible-infected-recovered (TSIR) model was used early September 2021 to forecast the implications of this disruption on the future 2021/2022 RSV epidemic in Lyon urban population.

Results

When compared to observed hospital-confirmed cases, the model successfully captured the early start, peak timing, and end of the 2021/2022 RSV epidemic. These simulations, added to other streams of surveillance data, shared and discussed among the local field experts were of great value to mitigate the consequences of this atypical RSV outbreak on our hospital paediatric department.

Conclusions

TSIR model, fitted to local hospital data covering large urban areas, can produce plausible post-COVID-19 RSV simulations. Collaborations between modellers and hospital management (who are both model users and data providers) should be encouraged in order to validate the use of dynamical models to timely allocate hospital resources to the future RSV epidemics.

Future trajectory of respiratory infections following the COVID-19 pandemic in Hong Kong

The accumulation of susceptible populations for respiratory infectious diseases (RIDs) when COVID-19-targeted non-pharmaceutical interventions (NPIs) were in place might pose a greater risk of future RID outbreaks. We examined the timing and magnitude of RID resurgence after lifting COVID-19-targeted NPIs and assessed the burdens on the health system. We proposed the Threshold-based Control Method (TCM) to identify data-driven solutions to maintain the resilience of the health system by re-introducing NPIs when the number of severe infections reaches a threshold. There will be outbreaks of all RIDs with staggered peak times after lifting COVID-19-targeted NPIs. Such a large-scale resurgence of RID patients will impose a significant risk of overwhelming the health system. With a strict NPI strategy, a TCM-initiated threshold of 600 severe infections can ensure a sufficient supply of hospital beds for all hospitalized severely infected patients. The proposed TCM identifies effective dynamic NPIs, which facilitate future NPI relaxation policymaking.

Drivers of respiratory syncytial virus seasonal epidemics in children under 5 years in Kilifi, coastal Kenya

Respiratory syncytial virus (RSV) causes significant childhood morbidity and mortality in the developing world. The determinants of RSV seasonality are of importance in designing interventions. They are poorly understood in tropical and sub-tropical regions in low- and middle-income countries. Our study utilized long-term surveillance data on cases of RSV associated with severe or very severe pneumonia in children aged 1 day to 59 months admitted to the Kilifi County Hospital. A generalized additive model was used to investigate the association between RSV admissions and meteorological variables (maximum temperature, rainfall, absolute humidity); weekly number of births within the catchment population; and school term dates. Furthermore, a time-series-susceptible-infected-recovered (TSIR) model was used to reconstruct an empirical transmission rate which was used as a dependent variable in linear regression and generalized additive models with meteorological variables and school term dates. Maximum temperature, absolute humidity, and weekly number of births were significantly associated with RSV activity in the generalized additive model. Results from the TSIR model indicated that maximum temperature and absolute humidity were significant factors. Rainfall and school term did not yield significant relationships. Our study indicates that meteorological parameters and weekly number of births potentially play a role in the RSV seasonality in this region. More research is required to explore the underlying mechanisms underpinning the observed relationships.

Impact of early phase COVID-19 precautionary behaviors on seasonal influenza in Hong Kong: A time-series modeling approach

Background

Before major non-pharmaceutical interventions were implemented, seasonal incidence of influenza in Hong Kong showed a rapid and unexpected reduction immediately following the early spread of COVID-19 in mainland China in January 2020. This decline was presumably associated with precautionary behavioral changes (e.g., wearing face masks and avoiding crowded places). Knowing their effectiveness on the transmissibility of seasonal influenza can inform future influenza prevention strategies.

Methods

We estimated the effective reproduction number (R _t ) of seasonal influenza in 2019/20 winter using a time-series susceptible-infectious-recovered (TS-SIR) model with a Bayesian inference by integrated nested Laplace approximation (INLA). After taking account of changes in underreporting and herd immunity, the individual effects of the behavioral changes were quantified.

Findings

The model-estimated mean R _t reduced from 1.29 (95%CI, 1.27-1.32) to 0.73 (95%CI, 0.73-0.74) after the COVID-19 community spread began. Wearing face masks protected 17.4% of people (95%CI, 16.3-18.3%) from infections, having about half of the effect as avoiding crowded places (44.1%, 95%CI, 43.5-44.7%). Within the current model, if more than 85% of people had adopted both behaviors, the initial R _t could have been less than 1.

Conclusion

Our model results indicate that wearing face masks and avoiding crowded places could have potentially significant suppressive impacts on influenza.

The dynamics of scarlet fever in The Netherlands, 1906-1920: a historical analysis

Background. Scarlet fever, an infectious disease caused by Streptococcus pyogenes, largely disappeared in developed countries during the twentieth century. In recent years, scarlet fever is on the rise again, and there is a need for a better understanding of possible factors driving transmission. Methods. Using historical case notification data from the three largest cities in The Netherlands (Amsterdam, Rotterdam and The Hague) from 1906 to 1920, we inferred the transmission rate for scarlet fever using time-series susceptible-infected-recovered (TSIR) methods. Through additive regression modelling, we investigated the contributions of meteorological variables and school term times to transmission rates. Results. Estimated transmission rates varied by city, and were highest overall for Rotterdam, the most densely populated city at that time. High temperature, seasonal precipitation levels and school term timing were associated with transmission rates, but the roles of these factors were limited and not consistent over all three cities. Conclusions. While weather factors alone can only explain a small portion of the variability in transmission rates, these results help understand the historical dynamics of scarlet fever infection in an era with less advanced sanitation and no antibiotic treatment and may offer insights into the driving factors associated with its recent resurgence.

Global Change and Emerging Infectious Diseases

Our world is undergoing rapid planetary changes driven by human activities, often mediated by economic incentives and resource management, affecting all life on Earth. Concurrently, many infectious diseases have recently emerged or spread into new populations. Mounting evidence suggests that global change-including climate change, land-use change, urbanization, and global movement of individuals, species, and goods-may be accelerating disease emergence by reshaping ecological systems in concert with socioeconomic factors. Here, we review insights, approaches, and mechanisms by which global change drives disease emergence from a disease ecology perspective. We aim to spur more interdisciplinary collaboration with economists and identification of more effective and sustainable interventions to prevent disease emergence. While almost all infectious diseases change in response to global change, the mechanisms and directions of these effects are system specific, requiring new, integrated approaches to disease control that recognize linkages between environmental and economic sustainability and human and planetary health.

Comparing and linking machine learning and semi-mechanistic models for the predictability of endemic measles dynamics

Measles is one the best-documented and most-mechanistically-studied non-linear infectious disease dynamical systems. However, systematic investigation into the comparative performance of traditional mechanistic models and machine learning approaches in forecasting the transmission dynamics of this pathogen are still rare. Here, we compare one of the most widely used semi-mechanistic models for measles (TSIR) with a commonly used machine learning approach (LASSO), comparing performance and limits in predicting short to long term outbreak trajectories and seasonality for both regular and less regular measles outbreaks in England and Wales (E&W) and the United States. First, our results indicate that the proposed LASSO model can efficiently use data from multiple major cities and achieve similar short-to-medium term forecasting performance to semi-mechanistic models for E&W epidemics. Second, interestingly, the LASSO model also captures annual to biennial bifurcation of measles epidemics in E&W caused by susceptible response to the late 1940s baby boom. LASSO may also outperform TSIR for predicting less-regular dynamics such as those observed in major cities in US between 1932-45. Although both approaches capture short-term forecasts, accuracy suffers for both methods as we attempt longer-term predictions in highly irregular, post-vaccination outbreaks in E&W. Finally, we illustrate that the LASSO model can both qualitatively and quantitatively reconstruct mechanistic assumptions, notably susceptible dynamics, in the TSIR model. Our results characterize the limits of predictability of infectious disease dynamics for strongly immunizing pathogens with both mechanistic and machine learning models, and identify connections between these two approaches.

Generalized Susceptible-Exposed-Infectious-Recovered model and its contributing factors for analysing the death and recovery rates of the COVID-19 pandemic

COVID-19 is a highly contagious disease that has infected over 136 million people worldwide with over 2.9 million deaths as of 11 April 2021. In March 2020, the WHO declared COVID-19 as a pandemic and countries began to implement measures to control the spread of the virus. The spread and the death rates of the virus displayed dramatic differences among countries globally, showing that there are several factors affecting its spread and mortality. By utilizing the cumulative number of cases from John Hopkins University, the recovery rate, death rate, and the number of active, recovered, and death cases were simulated to analyse the trends and patterns within the chosen countries. 10 countries from 3 different case severity categories (high cases, medium cases, and low cases) and 5 continents (Asia, North America, South America, Europe, and Oceania) were studied. A generalized SEIR model which considers control measures such as isolation, and preventive measures such as vaccination is applied in this study. This model is able to capture not only the dynamics between the states, but also the time evolution of the states by using the fourth-order-Runge-Kutta process. This study found no significant patterns in the countries under the same case severity category, suggesting that there are other factors contributing to the pattern in these countries. One of the factors influencing the pattern in each country is the population's age. COVID-19 related deaths were found to be notably higher among older people, indicating that countries comprising of a larger proportion of older age groups have an increased risk of experiencing higher death rates. Tighter governmental control measures led to fewer infections and eventually reduced the number of death cases, while increasing the recovery rate, and early implementations were found to be far more effective in controlling the spread of the virus and produced better outcomes.

COVID-19: Forecasting confirmed cases and deaths with a simple time series model

Forecasting the outcome of outbreaks as early and as accurately as possible is crucial for decision-making and policy implementations. A significant challenge faced by forecasters is that not all outbreaks and epidemics turn into pandemics, making the prediction of their severity difficult. At the same time, the decisions made to enforce lockdowns and other mitigating interventions versus their socioeconomic consequences are not only hard to make, but also highly uncertain. The majority of modeling approaches to outbreaks, epidemics, and pandemics take an epidemiological approach that considers biological and disease processes. In this paper, we accept the limitations of forecasting to predict the long-term trajectory of an outbreak, and instead, we propose a statistical, time series approach to modelling and predicting the short-term behavior of COVID-19. Our model assumes a multiplicative trend, aiming to capture the continuation of the two variables we predict (global confirmed cases and deaths) as well as their uncertainty. We present the timeline of producing and evaluating 10-day-ahead forecasts over a period of four months. Our simple model offers competitive forecast accuracy and estimates of uncertainty that are useful and practically relevant.

The impact of COVID-19 non-pharmaceutical interventions on future respiratory syncytial virus transmission in South Africa

In response to the COVID-19 pandemic, the South African government employed various nonpharmaceutical interventions (NPIs) in order to reduce the spread of SARS-CoV-2. In addition to mitigating transmission of SARS-CoV-2, these public health measures have also functioned in slowing the spread of other endemic respiratory pathogens. Surveillance data from South Africa indicates low circulation of respiratory syncytial virus (RSV) throughout the 2020-2021 Southern Hemisphere winter seasons. Here we fit age-structured epidemiological models to national surveillance data to predict the 2022 RSV outbreak following two suppressed seasons. We project a 32% increase in the peak number of monthly hospitalizations among infants ≤ 2 years, with older infants (6-23 month olds) experiencing a larger portion of severe disease burden than typical. Our results suggest that hospital system readiness should be prepared for an intense RSV season in early 2022.

An integrated simulation framework for the prevention and mitigation of pandemics caused by airborne pathogens

In this work, we developed an integrated simulation framework for pandemic prevention and mitigation of pandemics caused by airborne pathogens, incorporating three sub-models, namely the spatial model, the mobility model, and the propagation model, to create a realistic simulation environment for the evaluation of the effectiveness of different countermeasures on the epidemic dynamics. The spatial model converts images of real cities obtained from Google Maps into undirected weighted graphs that capture the spatial arrangement of the streets utilized next for the mobility of individuals. The mobility model implements a stochastic agent-based approach, developed to assign specific routes to individuals moving in the city, through the use of stochastic processes, utilizing the weights of the underlying graph to deploy shortest path algorithms. The propagation model implements both the epidemiological model and the physical substance of the transmission of an airborne pathogen (in our approach, we investigate the transmission parameters of SARS-CoV-2). The deployment of a set of countermeasures was investigated in reducing the spread of the pathogen, where, through a series of repetitive simulation experiments, we evaluated the effectiveness of each countermeasure in pandemic prevention.

Existing human mobility data sources poorly predicted the spatial spread of SARS-CoV-2 in Madagascar

For emerging epidemics such as the COVID-19 pandemic, quantifying travel is a key component of developing accurate predictive models of disease spread to inform public health planning. However, in many LMICs, traditional data sets on travel such as commuting surveys as well as non-traditional sources such as mobile phone data are lacking, or, where available, have only rarely been leveraged by the public health community. Evaluating the accuracy of available data to measure transmission-relevant travel may be further hampered by limited reporting of suspected and laboratory confirmed infections. Here, we leverage case data collected as part of a COVID-19 dashboard collated via daily reports from the Malagasy authorities on reported cases of SARS-CoV-2 across the 22 regions of Madagascar. We compare the order of the timing of when cases were reported with predictions from a SARS-CoV-2 metapopulation model of Madagascar informed using various measures of connectivity including a gravity model based on different measures of distance, Internal Migration Flow data, and mobile phone data. Overall, the models based on mobile phone connectivity and the gravity-based on Euclidean distance best predicted the observed spread. The ranks of the regions most remote from the capital were more difficult to predict but interestingly, regions where the mobile phone connectivity model was more accurate differed from those where the gravity model was most accurate. This suggests that there may be additional features of mobility or connectivity that were consistently underestimated using all approaches but are epidemiologically relevant. This work highlights the importance of data availability and strengthening collaboration among different institutions with access to critical data - models are only as good as the data that they use, so building towards effective data-sharing pipelines is essential.

Respiratory syncytial virus outbreaks are predicted after the COVID-19 pandemic in Tokyo, Japan

The nonpharmaceutical interventions (NPIs) on COVID-19 can impact current and future dynamics of respiratory syncytial virus infections (RSV). In Tokyo, RSV activity declined by 97.9% (95%CI: 94.8% - 99.2%) during NPIs. A longer period of NPIs could expand susceptible populations, enhancing the potential for larger RSV outbreaks after NPIs ends.

Existing human mobility data sources poorly predicted the spatial spread of SARS-CoV-2 in Madagascar

For emerging epidemics such as the COVID-19 pandemic, quantifying travel is a key component of developing accurate predictive models of disease spread to inform public health planning. However, in many LMICs, traditional data sets on travel such as commuting surveys as well as non-traditional sources such as mobile phone data are lacking, or, where available, have only rarely been leveraged by the public health community. Evaluating the accuracy of available data to measure transmission-relevant travel may be further hampered by limited reporting of suspected and laboratory confirmed infections. Here, we leverage case data collected as part of a COVID-19 dashboard collated via daily reports from the Malagasy authorities on reported cases of SARS-CoV-2 across the 22 regions of Madagascar. We compare the order of the timing of when cases were reported with predictions from a SARS-CoV-2 metapopulation model of Madagascar informed using various measures of connectivity including a gravity model based on different measures of distance, Internal Migration Flow data, and mobile phone data. Overall, the models based on mobile phone connectivity and the gravity-based on Euclidean distance best predicted the observed spread. The ranks of the regions most remote from the capital were more difficult to predict but interestingly, regions where the mobile phone connectivity model was more accurate differed from those where the gravity model was most accurate. This suggests that there may be additional features of mobility or connectivity that were consistently underestimated using all approaches, but are epidemiologically relevant. This work highlights the importance of data availability and strengthening collaboration among different institutions with access to critical data - models are only as good as the data that they use, so building towards effective data-sharing pipelines is essential.

A time series-based statistical approach for outbreak spread forecasting: Application of COVID-19 in Greece

The aim of this paper is the generation of a time-series based statistical data-driven procedure in order to track an outbreak. At first are used univariate time series models in order to predict the evolution of the reported cases. Moreover, are considered combinations of the models in order to provide more accurate and robust results. Additionally, statistical probability distributions are considered in order to generate future scenarios. Final step is the build and use of an epidemiological model (tSIR) and the calculation of an epidemiological ratio (R₀) for estimating the termination of the outbreak. The time series models include Exponential Smoothing and ARIMA approaches from the classical models, also Feed-Forward Artificial Neural Networks and Multivariate Adaptive Regression Splines from the machine learning toolbox. Combinations include simple mean, Newbolt-Granger and Bates-Granger approaches. Finally, the tSIR model and the R₀ ratio are used for estimating the spread and the reversion of the pandemic. The suggested procedure is used to track the COVID-19 epidemic in Greece. This epidemic has appeared in China in December 2019 and has been widespread since then to all over the world. Greece is the center of this empirical study as is considered an early successful paradigm of resistance against the virus.

Tensor decomposition for infectious disease incidence data

Many demographic and ecological processes generate seasonal and other periodicities. Seasonality in infectious disease transmission can result from climatic forces such as temperature and humidity; variation in contact rates as a result of migration or school calendar; or temporary surges in birth rates. Seasonal drivers of acute immunizing infections can also drive longer-term fluctuations.Tensor decomposition has been used in many disciplines to uncover dominant trends in multi-dimensional data. We introduce tensors as a novel method for decomposing oscillatory infectious disease time series.We illustrate the reliability of the method by applying it to simulated data. We then present decompositions of measles data from England and Wales. This paper leverages simulations as well as much-studied data to illustrate the power of tensor decomposition to uncover dominant epidemic signals as well as variation in space and time. We then use tensor decomposition to uncover new findings and demonstrate the potential power of the method for disease incidence data. In particular, we are able to distinguish between annual and biennial signals across locations and shifts in these signals over time.Tensor decomposition is able to isolate variation in disease seasonality as a result of variation in demographic rates. The method allows us to discern variation in the strength of such signals by space and population size. Tensors provide an opportunity for a concise approach to uncovering heterogeneity in disease transmission across space and time in large datasets.

The impact of COVID-19 nonpharmaceutical interventions on the future dynamics of endemic infections

Nonpharmaceutical interventions (NPIs) have been employed to reduce the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), yet these measures are already having similar effects on other directly transmitted, endemic diseases. Disruptions to the seasonal transmission patterns of these diseases may have consequences for the timing and severity of future outbreaks. Here we consider the implications of SARS-CoV-2 NPIs for two endemic infections circulating in the United States of America: respiratory syncytial virus (RSV) and seasonal influenza. Using laboratory surveillance data from 2020, we estimate that RSV transmission declined by at least 20% in the United States at the start of the NPI period. We simulate future trajectories of both RSV and influenza, using an epidemic model. As susceptibility increases over the NPI period, we find that substantial outbreaks of RSV may occur in future years, with peak outbreaks likely occurring in the winter of 2021-2022. Longer NPIs, in general, lead to larger future outbreaks although they may display complex interactions with baseline seasonality. Results for influenza broadly echo this picture, but are more uncertain; future outbreaks are likely dependent on the transmissibility and evolutionary dynamics of circulating strains.

Immune life history, vaccination, and the dynamics of SARS-CoV-2 over the next 5 years

The future trajectory of the coronavirus disease 2019 (COVID-19) pandemic hinges on the dynamics of adaptive immunity against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2); however, salient features of the immune response elicited by natural infection or vaccination are still uncertain. We use simple epidemiological models to explore estimates for the magnitude and timing of future COVID-19 cases, given different assumptions regarding the protective efficacy and duration of the adaptive immune response to SARS-CoV-2, as well as its interaction with vaccines and nonpharmaceutical interventions. We find that variations in the immune response to primary SARS-CoV-2 infections and a potential vaccine can lead to markedly different immune landscapes and burdens of critically severe cases, ranging from sustained epidemics to near elimination. Our findings illustrate likely complexities in future COVID-19 dynamics and highlight the importance of immunological characterization beyond the measurement of active infections for adequately projecting the immune landscape generated by SARS-CoV-2 infections.

A Time-Dependent SIR Model for COVID-19 With Undetectable Infected Persons

In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks the transmission and recovering rate at time [Formula: see text]. Using the data provided by China authority, we show our one-day prediction errors are almost less than [Formula: see text]. The turning point and the total number of confirmed cases in China are predicted under our model. To analyze the impact of the undetectable infections on the spread of disease, we extend our model by considering two types of infected persons: detectable and undetectable infected persons. Whether there is an outbreak is characterized by the spectral radius of a [Formula: see text] matrix. If [Formula: see text], then the spectral radius of that matrix is greater than 1, and there is an outbreak. We plot the phase transition diagram of an outbreak and show that there are several countries on the verge of COVID-19 outbreaks on Mar. 2, 2020. To illustrate the effectiveness of social distancing, we analyze the independent cascade model for disease propagation in a configuration random network. We show two approaches of social distancing that can lead to a reduction of the effective reproduction number [Formula: see text].

A marginal moment matching approach for fitting endemic-epidemic models to underreported disease surveillance counts

Count data are often subject to underreporting, especially in infectious disease surveillance. We propose an approximate maximum likelihood method to fit count time series models from the endemic-epidemic class to underreported data. The approach is based on marginal moment matching where underreported processes are approximated through completely observed processes from the same class. Moreover, the form of the bias when underreporting is ignored or taken into account via multiplication factors is analyzed. Notably, we show that this leads to a downward bias in model-based estimates of the effective reproductive number. A marginal moment matching approach can also be used to account for reporting intervals which are longer than the mean serial interval of a disease. The good performance of the proposed methodology is demonstrated in simulation studies. An extension to time-varying parameters and reporting probabilities is discussed and applied in a case study on weekly rotavirus gastroenteritis counts in Berlin, Germany.

Fast estimation of time-varying infectious disease transmission rates

Compartmental epidemic models have been used extensively to study the historical spread of infectious diseases and to inform strategies for future control. A critical parameter of any such model is the transmission rate. Temporal variation in the transmission rate has a profound influence on disease spread. For this reason, estimation of time-varying transmission rates is an important step in identifying mechanisms that underlie patterns in observed disease incidence and mortality. Here, we present and test fast methods for reconstructing transmission rates from time series of reported incidence. Using simulated data, we quantify the sensitivity of these methods to parameters of the data-generating process and to mis-specification of input parameters by the user. We show that sensitivity to the user's estimate of the initial number of susceptible individuals-considered to be a major limitation of similar methods-can be eliminated by an efficient, "peak-to-peak" iterative technique, which we propose. The method of transmission rate estimation that we advocate is extremely fast, for even the longest infectious disease time series that exist. It can be used independently or as a fast way to obtain better starting conditions for computationally expensive methods, such as iterated filtering and generalized profiling.

Structure, space and size: competing drivers of variation in urban and rural measles transmission

A key concern in public health is whether disparities exist between urban and rural areas. One dimension of potential variation is the transmission of infectious diseases. In addition to potential differences between urban and rural local dynamics, the question of whether urban and rural areas participate equally in national dynamics remains unanswered. Specifically, urban and rural areas may diverge in local transmission as well as spatial connectivity, and thus risk for receiving imported cases. Finally, the potential confounding relationship of spatial proximity with size and urban/rural district type has not been addressed by previous research. It is rare to have sufficient data to explore these questions thoroughly. We use exhaustive weekly case reports of measles in 954 urban and 468 rural districts of the UK (1944–1965) to compare both local disease dynamics as well as regional transmission. We employ the time-series susceptible–infected–recovered model to estimate disease transmission, epidemic severity, seasonality and import dependence. Congruent with past results, we observe a clear dependence on population size for the majority of these measures. We use a matched-pair strategy to compare proximate urban and rural districts and control for possible spatial confounders. This analytical strategy reveals a modest difference between urban and rural areas. Rural areas tend to be characterized by more frequent, smaller outbreaks compared to urban counterparts. The magnitude of the difference is slight and the results primarily reinforce the importance of population size, both in terms of local and regional transmission. In sum, urban and rural areas demonstrate remarkable epidemiological similarity in this recent UK context.

Time series analysis of temporal trends in hemorrhagic fever with renal syndrome morbidity rate in China from 2005 to 2019

Hemorrhagic fever with renal syndrome (HFRS) is seriously endemic in China with 70%~90% of the notified cases worldwide and showing an epidemic tendency of upturn in recent years. Early detection for its future epidemic trends plays a pivotal role in combating this threat. In this scenario, our study investigates the suitability for application in analyzing and forecasting the epidemic tendencies based on the monthly HFRS morbidity data from 2005 through 2019 using the nonlinear model-based self-exciting threshold autoregressive (SETAR) and logistic smooth transition autoregressive (LSTAR) methods. The experimental results manifested that the SETAR and LSTAR approaches presented smaller values among the performance measures in both two forecasting subsamples, when compared with the most extensively used seasonal autoregressive integrated moving average (SARIMA) method, and the former slightly outperformed the latter. Descriptive statistics showed an epidemic tendency of downturn with average annual percent change (AAPC) of −5.640% in overall HFRS, however, an upward trend with an AAPC = 1.213% was observed since 2016 and according to the forecasts using the SETAR, it would seemingly experience an outbreak of HFRS in China in December 2019. Remarkably, there were dual-peak patterns in HFRS incidence with a strong one occurring in November until January of the following year, additionally, a weak one in May and June annually. Therefore, the SETAR and LSTAR approaches may be a potential useful tool in analyzing the temporal behaviors of HFRS in China.

Climatological, virological and sociological drivers of current and projected dengue fever outbreak dynamics in Sri Lanka

The largest ever Sri Lankan dengue outbreak of 2017 provides an opportunity for investigating the relative contributions of climatological, epidemiological and sociological drivers on the epidemic patterns of this clinically important vector-borne disease. To do so, we develop a climatologically driven disease transmission framework for dengue virus using spatially resolved temperature and precipitation data as well as the time-series susceptible-infected-recovered (SIR) model. From this framework, we first demonstrate that the distinct climatological patterns encountered across the island play an important role in establishing the typical yearly temporal dynamics of dengue, but alone are unable to account for the epidemic case numbers observed in Sri Lanka during 2017. Using a simplified two-strain SIR model, we demonstrate that the re-introduction of a dengue virus serotype that had been largely absent from the island in previous years may have played an important role in driving the epidemic, and provide a discussion of the possible roles for extreme weather events and human mobility patterns on the outbreak dynamics. Lastly, we provide estimates for the future burden of dengue across Sri Lanka using the Coupled Model Intercomparison Phase 5 climate projections. Critically, we demonstrate that climatological and serological factors can act synergistically to yield greater projected case numbers than would be expected from the presence of a single driver alone. Altogether, this work provides a holistic framework for teasing apart and analysing the various complex drivers of vector-borne disease outbreak dynamics.

Coexisting attractors in the context of cross-scale population dynamics: measles in London as a case study

Patterns of measles infection in large urban populations have long been considered the paradigm of synchronized nonlinear dynamics. Indeed, recurrent epidemics appear approximately mass-action despite underlying heterogeneity. However, using a subset of rich, newly digitized mortality data (1897–1906), we challenge that proposition. We find that sub-regions of London exhibited a mixture of simultaneous annual and biennial dynamics, while the aggregate city-level dynamics appears firmly annual. Using a simple stochastic epidemic model and maximum-likelihood inference methods, we show that we can capture this observed variation in periodicity. We identify agreement between theory and data, indicating that both changes in periodicity and epidemic coupling between regions can follow relatively simple rules; in particular we find local variation in seasonality drives periodicity. Our analysis underlines that multiple attractors can coexist in a strongly mixed population and follow theoretical predictions.

Epidemic dynamics of respiratory syncytial virus in current and future climates

A key question for infectious disease dynamics is the impact of the climate on future burden. Here, we evaluate the climate drivers of respiratory syncytial virus (RSV), an important determinant of disease in young children. We combine a dataset of county-level observations from the US with state-level observations from Mexico, spanning much of the global range of climatological conditions. Using a combination of nonlinear epidemic models with statistical techniques, we find consistent patterns of climate drivers at a continental scale explaining latitudinal differences in the dynamics and timing of local epidemics. Strikingly, estimated effects of precipitation and humidity on transmission mirror prior results for influenza. We couple our model with projections for future climate, to show that temperature-driven increases to humidity may lead to a northward shift in the dynamic patterns observed and that the likelihood of severe outbreaks of RSV hinges on projections for extreme rainfall.

Long-term dynamics of measles in London: Titrating the impact of wars, the 1918 pandemic, and vaccination

A key question in ecology is the relative impact of internal nonlinear dynamics and external perturbations on the long-term trajectories of natural systems. Measles has been analyzed extensively as a paradigm for consumer-resource dynamics due to the oscillatory nature of the host-pathogen life cycle, the abundance of rich data to test theory, and public health relevance. The dynamics of measles in London, in particular, has acted as a prototypical test bed for such analysis using incidence data from the pre-vaccination era (1944–1967). However, during this timeframe there were few external large-scale perturbations, limiting an assessment of the relative impact of internal and extra demographic perturbations to the host population. Here, we extended the previous London analyses to include nearly a century of data that also contains four major demographic changes: the First and Second World Wars, the 1918 influenza pandemic, and the start of a measles mass vaccination program. By combining mortality and incidence data using particle filtering methods, we show that a simple stochastic epidemic model, with minimal historical specifications, can capture the nearly 100 years of dynamics including changes caused by each of the major perturbations. We show that the majority of dynamic changes are explainable by the internal nonlinear dynamics of the system, tuned by demographic changes. In addition, the 1918 influenza pandemic and World War II acted as extra perturbations to this basic epidemic oscillator. Our analysis underlines that long-term ecological and epidemiological dynamics can follow very simple rules, even in a non-stationary population subject to significant perturbations and major secular changes.

The impact of intrinsic versus external drivers of transmission on long-term dynamics is an open question in complex systems studies. In particular, when and where dynamics become chaotic has crucial implications for control efforts. Here, we extended the well-studied London measles data to include nearly a century of novel data (1897–1991) that also contains five major demographic changes: the First and Second World Wars, the wartime evacuation of London, the 1918 influenza pandemic, and the start of a measles mass vaccination program. We found that a simple stochastic epidemic model, with minimal historical specifications, can capture the nearly 100 years of dynamics including changes caused by each of the major perturbations. We further illustrated that the majority of dynamic changes are explainable by the internal nonlinear dynamics of the system, tuned by demographic changes. Notably however, the 1918 influenza pandemic and evacuation acted as external perturbations to this basic epidemic oscillator. Yet, in the wake of these massive shifts, the overall system remained stable (Lyapunov exponent < 0), underlining how long-term ecological and epidemiological dynamics can follow very simple rules, even in a non-stationary population subject to significant perturbations and major secular changes.