Transmission intensity and impact of control policies on the foot and mouth epidemic in Great Britain

The interaction of disease transmission, mortality, and economic output over the first 2 years of the COVID-19 pandemic

BACKGROUND

The COVID-19 pandemic has caused over 7.02 million deaths as of January 2024 and profoundly affected most countries' Gross Domestic Product (GDP). Here, we study the interaction of SARS-CoV-2 transmission, mortality, and economic output between January 2020 and December 2022 across 25 European countries.

METHODS

We use a Bayesian mixed effects model with auto-regressive terms to estimate the temporal relationships between disease transmission, excess deaths, changes in economic output, transit mobility and non-pharmaceutical interventions (NPIs) across countries.

RESULTS

Disease transmission intensity (logRt) decreases GDP and increases excess deaths, where the latter association is longer-lasting. Changes in GDP as well as prior week transmission intensity are both negatively associated with each other (-0.241, 95% CrI: -0.295 - -0.189). We find evidence of risk-averse behaviour, as changes in transit and prior week transmission intensity are negatively associated (-0.055, 95% CrI: -0.074 to -0.036). Our results highlight a complex cost-benefit trade-off from individual NPIs. For example, banning international travel is associated with both increases in GDP (0.014, 0.002-0.025) and decreases in excess deaths (-0.014, 95% CrI: -0.028 - -0.001). Country-specific random effects, such as the poverty rate, are positively associated with excess deaths while the UN government effectiveness index is negatively associated with excess deaths.

INTERPRETATION

The interplay between transmission intensity, excess deaths, population mobility and economic output is highly complex, and none of these factors can be considered in isolation. Our results reinforce the intuitive idea that significant economic activity arises from diverse person-to-person interactions. Our analysis quantifies and highlights that the impact of disease on a given country is complex and multifaceted. Long-term economic impairments are not fully captured by our model, as well as long-term disease effects (Long COVID).

Enforcing Temporal Consistency in Migration History Inference

In addition to undergoing evolution, members of biological populations may also migrate between locations. Examples include the spread of tumor cells from the primary tumor to distant metastases or the spread of pathogens from one host to another. One may represent migration histories by assigning a location label to each vertex of a given phylogenetic tree such that an edge connecting vertices with distinct locations represents a migration. Some biological populations undergo comigration, a phenomenon where multiple taxa from distinct lineages simultaneously comigrate from one location to another. In this work, we show that a previous problem statement for inferring migration histories that are parsimonious in terms of migrations and comigrations may lead to temporally inconsistent solutions. To remedy this deficiency, we introduce precise definitions of temporal consistency of comigrations in a phylogenetic tree, leading to three successive problems. First, we formulate the temporally consistent comigration problem to check if a set of comigrations is temporally consistent and provide a linear time algorithm for solving this problem. Second, we formulate the parsimonious consistent comigrations (PCC) problem, which aims to find comigrations given a location labeling of a phylogenetic tree. We show that PCC is NP-hard. Third, we formulate the parsimonious consistent comigration history (PCCH) problem, which infers the migration history given a phylogenetic tree and locations of its extant vertices only. We show that PCCH is NP-hard as well. On the positive side, we propose integer linear programming models to solve the PCC and PCCH problems. We demonstrate our algorithms on simulated and real data.

Inferring transmission routes for foot-and-mouth disease virus within a cattle herd using approximate Bayesian computation

To control an outbreak of an infectious disease it is essential to understand the different routes of transmission and how they contribute to the overall spread of the pathogen. With this information, policy makers can choose the most efficient methods of detection and control during an outbreak. Here we assess the contributions of direct contact and environmental contamination to the transmission of foot-and-mouth disease virus (FMDV) in a cattle herd using an individual-based model that includes both routes. Model parameters are inferred using approximate Bayesian computation with sequential Monte Carlo sampling (ABC-SMC) applied to data from transmission experiments and the 2007 epidemic in Great Britain. This demonstrates that the parameters derived from transmission experiments are applicable to outbreaks in the field, at least for closely related strains. Under the assumptions made in the model we show that environmental transmission likely contributes a majority of infections within a herd during an outbreak, although there is a lot of variation between simulated outbreaks. The accumulation of environmental contamination not only causes infections within a farm, but also has the potential to spread between farms via fomites. We also demonstrate the importance and effectiveness of rapid detection of infected farms in reducing transmission between farms, whether via direct contact or the environment.

Modeling target-density-based cull strategies to contain foot-and-mouth disease outbreaks

Total ring depopulation is sometimes used as a management strategy for emerging infectious diseases in livestock, which raises ethical concerns regarding the potential slaughter of large numbers of healthy animals. We evaluated a farm-density-based ring culling strategy to control foot-and-mouth disease (FMD) in the United Kingdom (UK), which may allow for some farms within rings around infected premises (IPs) to escape depopulation. We simulated this reduced farm density, or "target density", strategy using a spatially-explicit, stochastic, state-transition algorithm. We modeled FMD spread in four counties in the UK that have different farm demographics, using 740,000 simulations in a full-factorial analysis of epidemic impact measures (i.e., culled animals, culled farms, and epidemic length) and cull strategy parameters (i.e., target farm density, daily farm cull capacity, and cull radius). All of the cull strategy parameters listed above were drivers of epidemic impact. Our simulated target density strategy was usually more effective at combatting FMD compared with traditional total ring depopulation when considering mean culled animals and culled farms and was especially effective when daily farm cull capacity was low. The differences in epidemic impact measures among the counties are likely driven by farm demography, especially differences in cattle and farm density. To prevent over-culling and the associated economic, organizational, ethical, and psychological impacts, the target density strategy may be worth considering in decision-making processes for future control of FMD and other diseases.

Limited efficacy of forward contact tracing in epidemics

Infectious diseases that spread silently through asymptomatic or pre-symptomatic infections represent a challenge for policy makers. A traditional way of achieving isolation of silent infectors from the community is through forward contact tracing, aimed at identifying individuals that might have been infected by a known infected person. In this work we investigate how efficient this measure is in preventing a disease from becoming endemic. We introduce an SIS-based compartmental model where symptomatic individuals may self-isolate and trigger a contact tracing process aimed at quarantining asymptomatic infected individuals. Imperfect adherence and delays affect both measures. We derive the epidemic threshold analytically and find that contact tracing alone can only lead to a very limited increase of the threshold. We quantify the effect of imperfect adherence and the impact of incentivizing asymptomatic and symptomatic populations to adhere to isolation. Our analytical results are confirmed by simulations on complex networks and by the numerical analysis of a much more complex model incorporating more realistic in-host disease progression.

Modeling of networked populations when data is sampled or missing

Networked populations consist of inhomogeneous individuals connected via relational ties. The individuals typically vary in multivariate attributes. In some cases primary interest focuses on individual attributes and in others the understanding of the social structure of the ties. In many circumstances both are of interest, as is their relationship. In this paper we consider this last, most general, case. We model the joint distribution of social ties and individual attributes when the population is only partially observed. Of central interest is when the population is surveyed using a network sampling design. A second situation is when data about a subset of the ties and/or the individual attributes is unintentionally missing. Exponential-family random network models (ERNM)s are capable of specifying a joint statistical representation of both the ties of a network and individual attributes. This class of models allow the nodal attributes to be modeled as stochastic processes, expanding the range and realism of exponential-family approaches to network modeling. In this paper we develop a theory of inference for ERNMs when only part of the network is observed, as well as specific methodology for partially observed networks, including non-ignorable mechanisms for network-based sampling designs. In particular, we consider data collected via contact tracing, of considerable importance to infectious disease epidemiology and public health.

The value of volunteer surveillance for the early detection of biological invaders

Early detection of invaders requires finding small numbers of individuals across large landscapes. It has been argued that the only feasible way to achieve the sampling effort needed for early detection of an invader is to involve volunteer groups (citizen scientists, passive surveyors, etc.). A key concern is that volunteers may have a considerable false-positive and false-negative rate. The question then becomes whether verification of a report from a volunteer is worth the effort. This question is the topic of this paper. Since we are interested in early detection we calculate the Z% upper limit of the one sided confidence interval of the incidence (fraction infected) and use the term maximum expected plausible incidence for this. We compare the maximum plausible incidence when the expert samples on their own, q_E∼, and the maximum plausible incidence when the expert only verifies cases reported by the volunteer surveyor to be infected, q_V∼. The maximum plausible incidences q_E∼ and q_V∼. are related as, q_V∼=θ_fp1-θ_fnq_E∼ where θ_fp and θ_fn are the false positive and false negative rate of the volunteer surveyor, respectively. We also show that the optimal monitoring programme consists of verifying only the cases reported by the volunteer surveyor if, T_XT_N<θ_fp1-θ_fn, where T_N is the time needed for a sample taken by the expert and T_X is the time needed for an expert to verify a case reported by a volunteer surveyor. Our results can be used to calculate the maximum plausible incidence of a plant disease based on reports of passive surveyors that have been verified by experts and data from experts sampling on their own. The results can also be used in the development phase of a surveillance project to assess whether including passive surveyor reports is useful in the early detection of exotic invaders.

Common features in spatial livestock disease transmission parameters

The risk of epidemic spread of diseases in livestock poses a threat to animal and often also human health. Important for the assessment of the effect of control measures is a statistical model quantification of between-farm transmission during epidemics. In particular, quantification of the between-farm transmission kernel has proven its importance for a range of different diseases in livestock. In this paper we explore if a comparison of the different transmission kernels yields further insight. Our comparison identifies common features that connect across the different pathogen-host combinations analyzed. We conjecture that these features are universal and thereby provide generic insights. Comparison of the shape of the spatial transmission kernel suggests that, in absence of animal movement bans, the distance dependence of transmission has a universal shape analogous to Lévy-walk model descriptions of human movement patterns. Also, our analysis suggests that interventions such as movement bans and zoning, through their impact on these movement patterns, change the shape of the kernel in a universal fashion. We discuss how the generic insights suggested can be of practical use for assessing risks of spread and optimizing control measures, in particular when outbreak data is scarce.

An exploration of within-herd dynamics of a transboundary livestock disease: A foot and mouth disease case study

Transboundary livestock diseases are a high priority for policy makers because of the serious economic burdens associated with infection. In order to make well informed preparedness and response plans, policy makers often utilize mathematical models to understand possible outcomes of different control strategies and outbreak scenarios. Many of these models focus on the transmission between herds and the overall trajectory of the outbreak. While the course of infection within herds has not been the focus of the majority of models, a thorough understanding of within-herd dynamics can provide valuable insight into a disease system by providing information on herd-level biological properties of the infection, which can be used to inform decision making in both endemic and outbreak settings and to inform larger between-herd models. In this study, we develop three stochastic simulation models to study within-herd foot and mouth disease dynamics and the implications of different empirical data-based assumptions about the timing of the onset of infectiousness and clinical signs. We also study the influence of herd size and the proportion of the herd that is initially infected on the outcome of the infection. We find that increasing herd size increases the duration of infectiousness and that the size of the herd plays a more significant role in determining this duration than the number of initially infected cattle in that herd. We also find that the assumptions made regarding the onset of infectiousness and clinical signs, which are based on contradictory empirical findings, can result in the predictions about when infection would be detectable differing by several days. Therefore, the disease progression used to characterize the course of infection in a single bovine host could have significant implications for determining when herds can be detected and subsequently controlled; the timing of which could influence the overall predicted trajectory of outbreaks.

Estimation of a Within-Herd Transmission Rate for African Swine Fever in Vietnam

We describe results from a panel study in which pigs from a 17-sow African swine fever (ASF) positive herd in Thái Bình province, Vietnam, were followed over time to record the date of onset of ASF signs and the date of death from ASF. Our objectives were to (1) fit a susceptible-exposed-infectious-removed disease model to the data with transmission coefficients estimated using approximate Bayesian computation; (2) provide commentary on how a model of this type might be used to provide decision support for disease control authorities. For the outbreak in this herd, the median of the average latent period was 10 days (95% HPD (highest posterior density interval): 2 to 19 days), and the median of the average duration of infectiousness was 3 days (95% HPD: 2 to 4 days). The estimated median for the transmission coefficient was 3.3 (95% HPD: 0.4 to 8.9) infectious contacts per ASF-infectious pig per day. The estimated median for the basic reproductive number, R₀, was 10 (95% HPD: 1.1 to 30). Our estimates of the basic reproductive number R₀ were greater than estimates of R₀ for ASF reported previously. The results presented in this study may be used to estimate the number of pigs expected to be showing clinical signs at a given number of days following an estimated incursion date. This will allow sample size calculations, with or without adjustment to account for less than perfect sensitivity of clinical examination, to be used to determine the appropriate number of pigs to examine to detect at least one with the disease. A second use of the results of this study would be to inform the equation-based within-herd spread components of stochastic agent-based and hybrid simulation models of ASF.

Main factors associated with foot-and-mouth disease virus infection during the 2001 FMD epidemic in Uruguay

Large epidemics provide the opportunity to understand the epidemiology of diseases under the specific conditions of the affected population. Whilst foot-and-mouth disease (FMD) epidemics have been extensively studied in developed countries, epidemics in developing countries have been sparsely studied. Here we address this limitation by systematically studying the 2001 epidemic in Uruguay where a total of 2,057 farms were affected. The objective of this study was to identify the risk factors (RF) associated with infection and spread of the virus within the country. The epidemic was divided into four periods: (1) the high-risk period (HRP) which was the period between the FMD virus introduction and detection of the index case; (2) the local control measures period (LCM) which encompassed the first control measures implemented before mass vaccination was adopted; (3) the first mass vaccination, and (4) the second mass vaccination round. A stochastic model was developed to estimate the time of initial infection for each of the affected farms. Our analyses indicated that during the HRP around 242 farms were probably already infected. In this period, a higher probability of infection was associated with: (1) animal movements [OR: 1.57 (95% CI: 1.19-2.06)]; (2) farms that combined livestock with crop production [OR: 1.93 (95% CI: 1.43-2.60)]; (3) large and medium farms compared to small farms (this difference was dependent on regional herd density); (4) the geographical location. Keeping cattle only (vs farms that kept also sheep) was a significant RF during the subsequent epidemic period (LCM), and remained as RF, together with large farms, for the entire epidemic. We further explored the RF associated with FMDV infection in farms that raised cattle by fitting another model to a data subset. We found that dairy farms had a higher probability of FMDV infection than beef farms during the HRP [OR: 1.81 (95% CI: 1.12-2.83)], and remained as RF until the end of the first round of vaccination. The delay in the detection of the index case associated with unrestricted animal movements during the HRP may have contributed to this large epidemic. This study contributes to the knowledge of FMD epidemiology in extensive production systems.

Temporal-spatial analysis of a foot-and-mouth disease model with spatial diffusion and vaccination

Foot-and-mouth disease is an acute, highly infectious, and economically significant transboundary animal disease. Vaccination is an efficient and cost-effective measure to prevent the transmission of this disease. The primary way that foot-and-mouth disease spreads is through direct contact with infected animals, although it can also spread through contact with contaminated environments. This paper uses a diffuse foot-and-mouth disease model to account for the efficacy of vaccination in managing the disease. First, we transform an age-space structured foot-and-mouth disease into a diffusive epidemic model with nonlocal infection coupling the latent period and the latent diffusive rate. The basic reproduction number, which determines the outbreak of the disease, is then explicitly formulated. Finally, numerical simulations demonstrate that increasing vaccine efficacy has a remarkable effect than increasing vaccine coverage.

Modeling nation-wide U.S. swine movement networks at the resolution of the individual premises

The spread of infectious livestock diseases is a major cause for concern in modern agricultural systems. In the dynamics of the transmission of such diseases, movements of livestock between herds play an important role. When constructing mathematical models used for activities such as forecasting epidemic development, evaluating mitigation strategies, or determining important targets for disease surveillance, including between-premises shipments is often a necessity. In the United States (U.S.), livestock shipment data is not routinely collected, and when it is, it is not readily available and mostly concerned with between-state shipments. To bridge this gap in knowledge and provide insight into the complete livestock shipment network structure, we have developed the U.S. Animal Movement Model (USAMM). Previously, USAMM has only existed for cattle shipments, but here we present a version for domestic swine. This new version of USAMM consists of a Bayesian model fit to premises demography, county-level livestock industry variables, and two limited data sets of between-state swine movements. The model scales up the data to simulate nation-wide networks of both within- and between-state shipments at the level of individual premises. Here we describe this shipment model in detail and subsequently explore its usefulness with a rudimentary predictive model of the prevalence of porcine epidemic diarrhea virus (PEDv) across the U.S. Additionally, in order to promote further research on livestock disease and other topics involving the movements of swine in the U.S., we also make 250 synthetic premises-level swine shipment networks with complete coverage of the entire conterminous U.S. freely available to the research community as a useful surrogate for the absent shipment data.

Estimation of the Serial Interval and the Effective Reproductive Number of COVID-19 Outbreak Using Contact Data in Burkina Faso, a Sub-Saharan African Country

The COVID-19 outbreak has spread all around the world in less than four months. However, the pattern of the epidemic was different according to the countries. We propose this paper to describe the transmission network and to estimate the serial interval and the reproductive number of the novel coronavirus disease (COVID-19) in Burkina Faso, a Sub-Saharan African country. Data from the COVID-19 response team was analyzed. Information on the 804 first detected cases were pulled together. From contact tracing information, 126 infector-infectee pairs were built. The principal infection clusters with their index cases were observed, principally the two major identified indexes in Burkina. However, the generations of infections were usually short (less than four). The serial interval was estimated to follow a gamma distribution with a shape parameter 1.04 (95% credibility interval: 0.69-1.57) and a scale parameter of 5.69 (95% credibility interval: 3.76-9.11). The basic reproductive number was estimated at 2.36 (95% confidence interval: 1.46-3.26). However, the effective reproductive number decreases very quickly, reaching a minimum value of 0.20 (95% confidence interval: 0.06-0.34). Estimated parameters are made available to monitor the outbreak in Sub-Saharan African countries. These show serial intervals like in the other continents but less infectiousness.

Dropping mortality by increasing connectivity in plant epidemics

Pathogen introduction in plant communities can cause serious impacts and biodiversity losses that may take a long time to manage and restore. Effective control of epidemic spreading in the wild is a problem of paramount importance because of its implications in conservation and potential economic losses. Understanding the mechanisms that hinder pathogen propagation is, therefore, crucial. Usual modelization approaches in epidemic spreading are based in compartmentalized models, without keeping track of pathogen concentrations during spreading. In this contribution we present and fully analyze a dynamical model for plant epidemic spreading based on pathogen abundances. The model, which is defined on top of network substrates, is amenable to a deep mathematical analysis in the absence of a limit in the amount of pathogen a plant can tolerate before dying. In the presence of such death threshold, we observe that the fraction of dead plants peaks at intermediate values of network connectivity, and mortality decreases for large average degrees. We discuss the implications of our results as mechanisms to halt infection propagation.

Forecasting for COVID-19 has failed

Epidemic forecasting has a dubious track-record, and its failures became more prominent with COVID-19. Poor data input, wrong modeling assumptions, high sensitivity of estimates, lack of incorporation of epidemiological features, poor past evidence on effects of available interventions, lack of transparency, errors, lack of determinacy, consideration of only one or a few dimensions of the problem at hand, lack of expertise in crucial disciplines, groupthink and bandwagon effects, and selective reporting are some of the causes of these failures. Nevertheless, epidemic forecasting is unlikely to be abandoned. Some (but not all) of these problems can be fixed. Careful modeling of predictive distributions rather than focusing on point estimates, considering multiple dimensions of impact, and continuously reappraising models based on their validated performance may help. If extreme values are considered, extremes should be considered for the consequences of multiple dimensions of impact so as to continuously calibrate predictive insights and decision-making. When major decisions (e.g. draconian lockdowns) are based on forecasts, the harms (in terms of health, economy, and society at large) and the asymmetry of risks need to be approached in a holistic fashion, considering the totality of the evidence.

Misinformation can prevent the suppression of epidemics

The effectiveness of non-pharmaceutical interventions, such as mask-wearing and social distancing, as control measures for pandemic disease relies upon a conscientious and well-informed public who are aware of and prepared to follow advice. Unfortunately, public health messages can be undermined by competing misinformation and conspiracy theories, spread virally through communities that are already distrustful of expert opinion. In this article, we propose and analyse a simple model of the interaction between disease spread and awareness dynamics in a heterogeneous population composed of both trusting individuals who seek better quality information and will take precautionary measures, and distrusting individuals who reject better quality information and have overall riskier behaviour. We show that, as the density of the distrusting population increases, the model passes through a phase transition to a state in which major outbreaks cannot be suppressed. Our work highlights the urgent need for effective interventions to increase trust and inform the public.

Challenges for modelling interventions for future pandemics

Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross-disciplinary collaboration together with close communication between scientists and policy makers.

Novel Epidemic Metrics to Communicate Outbreak Risk at the Municipality Level: Dengue and Zika in the Dominican Republic

Arboviruses remain a significant cause of morbidity, mortality and economic cost across the global human population. Epidemics of arboviral disease, such as Zika and dengue, also cause significant disruption to health services at local and national levels. This study examined 2014-2016 Zika and dengue epidemic data at the sub-national level to characterise transmission across the Dominican Republic. For each municipality, spatio-temporal mapping was used to characterise disease burden, while data were age and sex standardised to quantify burden distributions among the population. In separate analyses, time-ordered data were combined with the underlying disease migration interval distribution to produce a network of likely transmission chain events, displayed using transmission chain likelihood matrices. Finally, municipal-specific reproduction numbers (R_m) were established using a Wallinga-Teunis matrix. Dengue and Zika epidemics peaked during weeks 39-52 of 2015 and weeks 14-27 of 2016, respectively. At the provincial level, dengue attack rates were high in Hermanas Mirabal and San José de Ocoa (58.1 and 49.2 cases per 10,000 population, respectively), compared with the Zika burden, which was highest in Independencia and San José de Ocoa (21.2 and 13.4 cases per 10,000 population, respectively). Across municipalities, high disease burden was observed in Cotuí (622 dengue cases per 10,000 population) and Jimani (32 Zika cases per 10,000 population). Municipal infector-infectee transmission likelihood matrices identified seven 0% likelihood transmission events throughout the dengue epidemic and two 0% likelihood transmission events during the Zika epidemic. Municipality reproduction numbers (R_m) were consistently higher, and persisted for a greater duration, during the Zika epidemic (R_m = 1.0) than during the dengue epidemic (R_m < 1.0). This research highlights the importance of disease surveillance in land border municipalities as an early warning for infectious disease transmission. It also demonstrates that a high number of importation events are required to sustain transmission in endemic settings, and vice versa for newly emerged diseases. The inception of a novel epidemiological metric, R_m, reports transmission risk using standardised spatial units, and can be used to identify high transmission risk municipalities to better focus public health interventions for dengue, Zika and other infectious diseases.

A model exploration of carrier and movement transmission as potential explanatory causes for the persistence of foot-and-mouth disease in endemic regions

Foot-and-mouth disease (FMD) is a virulent and economically important disease of livestock, still endemic in many areas of Asia and sub-Saharan Africa. Transmission from persistently infected livestock, also known as carriers, has been proposed as a mechanism to support the persistence of FMD in endemic regions. However, whether carrier livestock can infect susceptible animals is controversial; recovered virus is infectious and there are claims of field transmission, but it remains undemonstrated experimentally. Alternate hypotheses for persistence include the movement of livestock within and between regions, and fomite contamination of the environment. Using a stochastic compartmental ordinary differential equation (ODE) model, we investigate the minimum rates of carrier transmission necessary to contribute to the maintenance of FMD in a region, and compare this to the alternate mechanism of persistence through cattle shipments. We find that carrier transmission can theoretically support persistence even at transmission rates much lower than the highest realistic rates previously proposed, and that the parameters with the most effect on the feasibility of carrier-mediated persistence are the average duration of both the carrier phase and natural immunity. However, shipment-mediated persistence remains a viable alternate mechanism for persistence without carrier transmission.

Inference of malaria reproduction numbers in three elimination settings by combining temporal data and distance metrics

Individual-level geographic information about malaria cases, such as the GPS coordinates of residence or health facility, is often collected as part of surveillance in near-elimination settings, but could be more effectively utilised to infer transmission dynamics, in conjunction with additional information such as symptom onset time and genetic distance. However, in the absence of data about the flow of parasites between populations, the spatial scale of malaria transmission is often not clear. As a result, it is important to understand the impact of varying assumptions about the spatial scale of transmission on key metrics of malaria transmission, such as reproduction numbers. We developed a method which allows the flexible integration of distance metrics (such as Euclidian distance, genetic distance or accessibility matrices) with temporal information into a single inference framework to infer malaria reproduction numbers. Twelve scenarios were defined, representing different assumptions about the likelihood of transmission occurring over different geographic distances and likelihood of missing infections (as well as high and low amounts of uncertainty in this estimate). These scenarios were applied to four individual level datasets from malaria eliminating contexts to estimate individual reproduction numbers and how they varied over space and time. Model comparison suggested that including spatial information improved models as measured by second order AIC (ΔAICc), compared to time only results. Across scenarios and across datasets, including spatial information tended to increase the seasonality of temporal patterns in reproduction numbers and reduced noise in the temporal distribution of reproduction numbers. The best performing parameterisations assumed long-range transmission (> 200 km) was possible. Our approach is flexible and provides the potential to incorporate other sources of information which can be converted into distance or adjacency matrices such as travel times or molecular markers.

A Comparative Analysis of Statistical Methods to Estimate the Reproduction Number in Emerging Epidemics, With Implications for the Current Coronavirus Disease 2019 (COVID-19) Pandemic

BACKGROUND

As the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic continues its rapid global spread, quantification of local transmission patterns has been, and will continue to be, critical for guiding the pandemic response. Understanding the accuracy and limitations of statistical methods to estimate the basic reproduction number, R0, in the context of emerging epidemics is therefore vital to ensure appropriate interpretation of results and the subsequent implications for control efforts.

METHODS

Using simulated epidemic data, we assess the performance of 7 commonly used statistical methods to estimate R0 as they would be applied in a real-time outbreak analysis scenario: fitting to an increasing number of data points over time and with varying levels of random noise in the data. Method comparison was also conducted on empirical outbreak data, using Zika surveillance data from the 2015-2016 epidemic in Latin America and the Caribbean.

RESULTS

We find that most methods considered here frequently overestimate R0 in the early stages of epidemic growth on simulated data, the magnitude of which decreases when fitted to an increasing number of time points. This trend of decreasing bias over time can easily lead to incorrect conclusions about the course of the epidemic or the need for control efforts.

CONCLUSIONS

We show that true changes in pathogen transmissibility can be difficult to disentangle from changes in methodological accuracy and precision in the early stages of epidemic growth, particularly for data with significant over-dispersion. As localized epidemics of SARS-CoV-2 take hold around the globe, awareness of this trend will be important for appropriately cautious interpretation of results and subsequent guidance for control efforts.

o2geosocial: Reconstructing who-infected-whom from routinely collected surveillance data

Reconstructing the history of individual transmission events between cases is key to understanding what factors facilitate the spread of an infectious disease. Since conducting extended contact-tracing investigations can be logistically challenging and costly, statistical inference methods have been developed to reconstruct transmission trees from onset dates and genetic sequences. However, these methods are not as effective if the mutation rate of the virus is very slow, or if sequencing data is sparse. We developed the package o2geosocial to combine variables from routinely collected surveillance data with a simple transmission process model. The model reconstructs transmission trees when full genetic sequences are unavailable, or uninformative. Our model incorporates the reported age-group, onset date, location and genotype of infected cases to infer probabilistic transmission trees. The package also includes functions to summarise and visualise the inferred cluster size distribution. The results generated by o2geosocial can highlight regions where importations repeatedly caused large outbreaks, which may indicate a higher regional susceptibility to infections. It can also be used to generate the individual number of secondary transmissions, and show the features associated with individuals involved in high transmission events. The package is available for download from the Comprehensive R Archive Network (CRAN) and GitHub.

What can phylodynamics bring to animal health research?

Infectious diseases are a major burden to global economies, and public and animal health. To date, quantifying the spread of infectious diseases to inform policy making has traditionally relied on epidemiological data collected during epidemics. However, interest has grown in recent phylodynamic techniques to infer pathogen transmission dynamics from genetic data. Here, we provide examples of where this new discipline has enhanced disease management in public health and illustrate how it could be further applied in animal health. In particular, we describe how phylodynamics can address fundamental epidemiological questions, such as inferring key transmission parameters in animal populations and quantifying spillover events at the wildlife-livestock interface, and generate important insights for the design of more effective control strategies.

Temporal-spatial analysis of an age-space structured foot-and-mouth disease model with Dirichlet boundary condition

Foot-and-mouth disease is a highly contagious and economically devastating disease of cloven-hoofed animals. The historic occurrences of foot-and-mouth diseases led to huge economic losses and seriously threatened the livestock food security. In this paper, a novel age-space diffusive foot-and-mouth disease model with a Dirichlet boundary condition, coupling the virus-to-animals and animals-to-animals transmission routes, has been proposed. The basic reproduction number R₀ is defined as the spectral radius of a next generation operator K, which is calculated in an explicit form, and it serves as a vital value determining whether or not the disease persists. The existence of a unique trivial nonconstant steady state and at least one nonconstant endemic steady state of the system is established by a smart Lyapunov functional and the Kronoselskii fixed point theorem. An application to a foot-and-mouth outbreak in China is presented. The findings suggest that increasing the movements and disinfection of the environment for animals apparently reduce the risk of a foot-and-mouth infection.

Sheep scab transmission: a spatially explicit dynamic metapopulation model

Psoroptic mange (sheep scab), caused by the parasitic mite, Psoroptes ovis, is an important disease of sheep worldwide. It causes chronic animal welfare issues and economic losses. Eradication of scab has proved impossible in many sheep-rearing areas and recent reports of resistance to macrocyclic lactones, a key class of parasiticide, highlight the importance of improving approaches to scab management. To allow this, the current study aimed to develop a stochastic spatial metapopulation model for sheep scab transmission which can be adapted for use in any geographical region, exhibited here using data for Great Britain. The model uses agricultural survey and sheep movement data to geo-reference farms and capture realistic movement patterns. Reported data on sheep scab outbreaks from 1973 to 1991 were used for model fitting with Sequential Monte Carlo Approximate Bayesian Computation methods. The outbreak incidence predicted by the model was from the same statistical distribution as the reported outbreak data (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\chi }^{2}$$\end{document}χ2 = 115.3, p = 1) and the spatial location of sheep scab outbreaks predicted was positively correlated with the observed outbreak data by county (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}τ = 0.55, p < 0.001), confirming that the model developed is able to accurately capture the number of farms infected in a year, the seasonality of scab incidence and the spatial patterns seen in the data. This model gives insight into the transmission dynamics of sheep scab and will allow the exploration of more effective control strategies.

Causes of delayed outbreak responses and their impacts on epidemic spread

Livestock diseases have devastating consequences economically, socially and politically across the globe. In certain systems, pathogens remain viable after host death, which enables residual transmissions from infected carcasses. Rapid culling and carcass disposal are well-established strategies for stamping out an outbreak and limiting its impact; however, wait-times for these procedures, i.e. response delays, are typically farm-specific and time-varying due to logistical constraints. Failing to incorporate variable response delays in epidemiological models may understate outbreak projections and mislead management decisions. We revisited the 2001 foot-and-mouth epidemic in the United Kingdom and sought to understand how misrepresented response delays can influence model predictions. Survival analysis identified farm size and control demand as key factors that impeded timely culling and disposal activities on individual farms. Using these factors in the context of an existing policy to predict local variation in response times significantly affected predictions at the national scale. Models that assumed fixed, timely responses grossly underestimated epidemic severity and its long-term consequences. As a result, this study demonstrates how general inclusion of response dynamics and recognition of partial controllability of interventions can help inform management priorities during epidemics of livestock diseases.

Assessing intrastate shipments from interstate data and expert opinion

Live animal shipments are a potential route for transmitting animal diseases between holdings and are crucial when modelling spread of infectious diseases. Yet, complete contact networks are not available in all countries, including the USA. Here, we considered a 10% sample of Interstate Certificate of Veterinary Inspections from 1 year (2009). We focused on distance dependence in contacts and investigated how different functional forms affect estimates of unobserved intrastate shipments. To further enhance our predictions, we included responses from an expert elicitation survey about the proportion of shipments moving intrastate. We used hierarchical Bayesian modelling to estimate parameters describing the kernel and effects of expert data. We considered three functional forms of spatial kernels and the inclusion or exclusion of expert data. The resulting six models were ranked by widely applicable information criterion (WAIC) and deviance information criterion (DIC) and evaluated through within- and out-of-sample validation. We showed that predictions of intrastate shipments were mildly influenced by the functional form of the spatial kernel but kernel shapes that permitted a fat tail at large distances while maintaining a plateau-shaped behaviour at short distances better were preferred. Furthermore, our study showed that expert data may not guarantee enhanced predictions when expert estimates are disparate.

What the reproductive number R0 can and cannot tell us about COVID-19 dynamics

The reproductive number R (or R0, the initial reproductive number in an immune-naïve population) has long been successfully used to predict the likelihood of pathogen invasion, to gauge the potential severity of an epidemic, and to set policy around interventions. However, often ignored complexities have generated confusion around use of the metric. This is particularly apparent with the emergent pandemic virus SARS-CoV-2, the causative agent of COVID-19. We address some misconceptions about the predictive ability of the reproductive number, focusing on how it changes over time, varies over space, and relates to epidemic size by referencing the mathematical definition of R and examples from the current pandemic. We hope that a better appreciation of the uses, nuances, and limitations of R and R0 facilitates a better understanding of epidemic spread, epidemic severity, and the effects of interventions in the context of SARS-CoV-2.

A framework for surveillance of emerging pathogens at the human-animal interface: Pigs and coronaviruses as a case study

Pigs (Sus scrofa) may be important surveillance targets for risk assessment and risk-based control planning against emerging zoonoses. Pigs have high contact rates with humans and other animals, transmit similar pathogens as humans including CoVs, and serve as reservoirs and intermediate hosts for notable human pandemics. Wild and domestic pigs both interface with humans and each other but have unique ecologies that demand different surveillance strategies. Three fundamental questions shape any surveillance program: where, when, and how can surveillance be conducted to optimize the surveillance objective? Using theory of mechanisms of zoonotic spillover and data on risk factors, we propose a framework for determining where surveillance might begin initially to maximize a detection in each host species at their interface. We illustrate the utility of the framework using data from the United States. We then discuss variables to consider in refining when and how to conduct surveillance. Recent advances in accounting for opportunistic sampling designs and in translating serology samples into infection times provide promising directions for extracting spatio-temporal estimates of disease risk from typical surveillance data. Such robust estimates of population-level disease risk allow surveillance plans to be updated in space and time based on new information (adaptive surveillance) thus optimizing allocation of surveillance resources to maximize the quality of risk assessment insight.

Social structure defines spatial transmission of African swine fever in wild boar

The spatial spread of infectious disease is determined by spatial and social processes such as animal space use and family group structure. Yet, the impacts of social processes on spatial spread remain poorly understood and estimates of spatial transmission kernels (STKs) often exclude social structure. Understanding the impacts of social structure on STKs is important for obtaining robust inferences for policy decisions and optimizing response plans. We fit spatially explicit transmission models with different assumptions about contact structure to African swine fever virus surveillance data from eastern Poland from 2014 to 2015 and evaluated how social structure affected inference of STKs and spatial spread. The model with social structure provided better inference of spatial spread, predicted that approximately 80% of transmission events occurred within family groups, and that transmission was weakly female-biased (other models predicted weakly male-biased transmission). In all models, most transmission events were within 1.5 km, with some rare events at longer distances. Effective reproductive numbers were between 1.1 and 2.5 (maximum values between 4 and 8). Social structure can modify spatial transmission dynamics. Accounting for this additional contact heterogeneity in spatial transmission models could provide more robust inferences of STKs for policy decisions, identify best control targets and improve transparency in model uncertainty.

Assessing the interplay between travel patterns and SARS-CoV-2 outbreak in realistic urban setting

BACKGROUND

The dense social contact networks and high mobility in congested urban areas facilitate the rapid transmission of infectious diseases. Typical mechanistic epidemiological models are either based on uniform mixing with ad-hoc contact processes or need real-time or archived population mobility data to simulate the social networks. However, the rapid and global transmission of the novel coronavirus (SARS-CoV-2) has led to unprecedented lockdowns at global and regional scales, leaving the archived datasets to limited use.

FINDINGS

While it is often hypothesized that population density is a significant driver in disease propagation, the disparate disease trajectories and infection rates exhibited by the different cities with comparable densities require a high-resolution description of the disease and its drivers. In this study, we explore the impact of creation of containment zones on travel patterns within the city. Further, we use a dynamical network-based infectious disease model to understand the key drivers of disease spread at sub-kilometer scales demonstrated in the city of Ahmedabad, India, which has been classified as a SARS-CoV-2 hotspot. We find that in addition to the contact network and population density, road connectivity patterns and ease of transit are strongly correlated with the rate of transmission of the disease. Given the limited access to real-time traffic data during lockdowns, we generate road connectivity networks using open-source imageries and travel patterns from open-source surveys and government reports. Within the proposed framework, we then analyze the relative merits of social distancing, enforced lockdowns, and enhanced testing and quarantining mitigating the disease spread.

SCOPE

Our results suggest that the declaration of micro-containment zones within the city with high road network density combined with enhanced testing can help in containing the outbreaks until clinical interventions become available.

Development and dissemination of infectious disease dynamic transmission models during the COVID-19 pandemic: what can we learn from other pathogens and how can we move forward?

The current COVID-19 pandemic has resulted in the unprecedented development and integration of infectious disease dynamic transmission models into policy making and public health practice. Models offer a systematic way to investigate transmission dynamics and produce short-term and long-term predictions that explicitly integrate assumptions about biological, behavioural, and epidemiological processes that affect disease transmission, burden, and surveillance. Models have been valuable tools during the COVID-19 pandemic and other infectious disease outbreaks, able to generate possible trajectories of disease burden, evaluate the effectiveness of intervention strategies, and estimate key transmission variables. Particularly given the rapid pace of model development, evaluation, and integration with decision making in emergency situations, it is necessary to understand the benefits and pitfalls of transmission models. We review and highlight key aspects of the history of infectious disease dynamic models, the role of rigorous testing and evaluation, the integration with data, and the successful application of models to guide public health. Rather than being an expansive history of infectious disease models, this Review focuses on how the integration of modelling can continue to be advanced through policy and practice in appropriate and conscientious ways to support the current pandemic response.

The world is its own best model: modelling and future pandemic planning in dentistry

The coronavirus SARS-CoV-2 pandemic has and continues to create a huge number of challenges to the global economy and its associated healthcare systems, including dentistry. In the early stages, we have had to rely on mathematical modelling and plans developed from previous healthcare emergencies. As the emergency develops, it is vitally important that policymakers understand the difference between the science and the real-world evidence so that policy can adapt rapidly to the changing environment. Effective management of future crises will require open channels of communication across the whole profession, not only to collect, clean, curate and evaluate data but also to assess the benefits and harms of any policy change.

The effects of the COVID-19 pandemic are not evenly spread throughout the population.

Errors in pandemic modelling are due to a combination of biased assumptions, and an underestimation of the variance and noise in real-world data.

Scientific research must be backed up by real-world evidence before it can be considered valid.

As evidence accumulates, policymakers should rapidly update guidance by keeping channels of communication open and frequently updated.

Anticipating future learning affects current control decisions: A comparison between passive and active adaptive management in an epidemiological setting

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Adaptive epidemic control.

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Using real-time outbreak information to improve epidemic control.

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Active Adaptive Management in an epidemiological setting.

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Analysing the interaction between control and monitoring during an epidemic.

Infectious disease epidemics present a difficult task for policymakers, requiring the implementation of control strategies under significant time constraints and uncertainty. Mathematical models can be used to predict the outcome of control interventions, providing useful information to policymakers in the event of such an epidemic. However, these models suffer in the early stages of an outbreak from a lack of accurate, relevant information regarding the dynamics and spread of the disease and the efficacy of control. As such, recommendations provided by these models are often incorporated in an ad hoc fashion, as and when more reliable information becomes available. In this work, we show that such trial-and-error-type approaches to management, which do not formally take into account the resolution of uncertainty and how control actions affect this, can lead to sub-optimal management outcomes. We compare three approaches to managing a theoretical epidemic: a non-adaptive management (AM) approach that does not use real-time outbreak information to adapt control, a passive AM approach that incorporates real-time information if and when it becomes available, and an active AM approach that explicitly incorporates the future resolution of uncertainty through gathering real-time information into its initial recommendations. The structured framework of active AM encourages the specification of quantifiable objectives, models of system behaviour and possible control and monitoring actions, followed by an iterative learning and control phase that is able to employ complex control optimisations and resolve system uncertainty. The result is a management framework that is able to provide dynamic, long-term projections to help policymakers meet the objectives of management. We investigate in detail the effect of different methods of incorporating up-to-date outbreak information. We find that, even in a highly simplified system, the method of incorporating new data can lead to different results that may influence initial policy decisions, with an active AM approach to management providing better information that can lead to more desirable outcomes from an epidemic.

Transmission Network of Measles During the Yamagata Outbreak in Japan, 2017

Background

A measles outbreak involving 60 cases occurred in Yamagata, Japan in 2017. Using two different mathematical models for different datasets, we aimed to estimate measles transmissibility over time and explore any heterogeneous transmission patterns.

Methods

The first model relied on the temporal distribution for date of illness onset for cases, and a generation-dependent model was applied to the data. Another model focused on the transmission network. Using the illness-onset date along with the serial interval and geographical location of exposure, we reconstructed a transmission network with 19 unknown links. We then compared the number of secondary transmissions with and without clinical symptoms or laboratory findings.

Results

Using a generation-dependent model (assuming three generations other than the index case), the reproduction number (R) over generations 0, 1, and 2 were 25.3, 1.3, and <0.1, respectively, explicitly yielding the transmissibility over each generation. The network data enabled us to demonstrate that both the mean and the variance for the number of secondary transmissions per primary case declined over time. Comparing primary cases with and without secondary transmission, high viral shedding was the only significant determinant (P < 0.01).

Conclusions

The R declined abruptly over subsequent generations. Use of network data revealed the distribution of the number of secondary transmissions per primary case and also allowed us to identify possible secondary transmission risk factors. High viral shedding from the throat mucosa was identified as a potential predictor of secondary transmission.

Challenges to the Application of Spatially Explicit Stochastic Simulation Models for Foot-and-Mouth Disease Control in Endemic Settings: A Systematic Review

Simulation modeling has become common for estimating the spread of highly contagious animal diseases. Several models have been developed to mimic the spread of foot-and-mouth disease (FMD) in specific regions or countries, conduct risk assessment, analyze outbreaks using historical data or hypothetical scenarios, assist in policy decisions during epidemics, formulate preparedness plans, and evaluate economic impacts. Majority of the available FMD simulation models were designed for and applied in disease-free countries, while there has been limited use of such models in FMD endemic countries. This paper's objective was to report the findings from a study conducted to review the existing published original research literature on spatially explicit stochastic simulation (SESS) models of FMD spread, focusing on assessing these models for their potential use in endemic settings. The goal was to identify the specific components of endemic FMD needed to adapt these SESS models for their potential application in FMD endemic settings. This systematic review followed the PRISMA guidelines, and three databases were searched, which resulted in 1176 citations. Eighty citations finally met the inclusion criteria and were included in the qualitative synthesis, identifying nine unique SESS models. These SESS models were assessed for their potential application in endemic settings. The assessed SESS models can be adapted for use in FMD endemic countries by modifying the underlying code to include multiple cocirculating serotypes, routine prophylactic vaccination (RPV), and livestock population dynamics to more realistically mimic the endemic characteristics of FMD. The application of SESS models in endemic settings will help evaluate strategies for FMD control, which will improve livestock health, provide economic gains for producers, help alleviate poverty and hunger, and will complement efforts to achieve the Sustainable Development Goals.

Mathematical Quantification of Transmission in Experiments: FMDV Transmission in Pigs Can Be Blocked by Vaccination and Separation

Quantitative understanding of transmission with and without control measures is important for the control of infectious diseases because it helps to determine which of these measures (or combinations thereof) will be effective to reduce transmission. In this paper, the statistical methods used to estimate transmission parameters are explained. To show how these methods can be used we reviewed literature for papers describing foot-and-mouth disease virus (FMDV) transmission in pigs and we used the data to estimate transmission parameters. The analysis showed that FMDV transmits very well when pigs have direct contact. Transmission, however, is reduced when a physical barrier separates infected and susceptible non-vaccinated pigs. Vaccination of pigs can prevent infection when virus is administered by a single intradermal virus injection in the bulb of the heel, but it cannot prevent infection when pigs are directly exposed to either non-vaccinated or vaccinated FMDV infected pigs. Physical separation combined with vaccination is observed to block transmission. Vaccination and separation can make a significant difference in the estimated number of new infections per day. Experimental transmission studies show that the combined effect of vaccination and physical separation can significantly reduce transmission (R < 1), which is a very relevant result for the control of between-farm transmission.

Bayesian reconstruction of transmission trees from genetic sequences and uncertain infection times

Genetic sequence data of pathogens are increasingly used to investigate transmission dynamics in both endemic diseases and disease outbreaks. Such research can aid in the development of appropriate interventions and in the design of studies to evaluate them. Several computational methods have been proposed to infer transmission chains from sequence data; however, existing methods do not generally reliably reconstruct transmission trees because genetic sequence data or inferred phylogenetic trees from such data contain insufficient information for accurate estimation of transmission chains. Here, we show by simulation studies that incorporating infection times, even when they are uncertain, can greatly improve the accuracy of reconstruction of transmission trees. To achieve this improvement, we propose a Bayesian inference methods using Markov chain Monte Carlo that directly draws samples from the space of transmission trees under the assumption of complete sampling of the outbreak. The likelihood of each transmission tree is computed by a phylogenetic model by treating its internal nodes as transmission events. By a simulation study, we demonstrate that accuracy of the reconstructed transmission trees depends mainly on the amount of information available on times of infection; we show superiority of the proposed method to two alternative approaches when infection times are known up to specified degrees of certainty. In addition, we illustrate the use of a multiple imputation framework to study features of epidemic dynamics, such as the relationship between characteristics of nodes and average number of outbound edges or inbound edges, signifying possible transmission events from and to nodes. We apply the proposed method to a transmission cluster in San Diego and to a dataset from the 2014 Sierra Leone Ebola virus outbreak and investigate the impact of biological, behavioral, and demographic factors.

Challenges and opportunities for using national animal datasets to support foot-and-mouth disease control

National level databases of animal numbers, locations and movements provide the essential foundations for disease preparedness, outbreak investigations and control activities. These activities are particularly important for managing and mitigating the risks of high-impact transboundary animal disease outbreaks such as foot-and-mouth disease (FMD), which can significantly affect international trade access and domestic food security. In countries where livestock production systems are heavily subsidized by the government, producers are often required to provide detailed animal movement and demographic data as a condition of business. In the remaining countries, it can be difficult to maintain these types of databases and impossible to estimate the extent of missing or inaccurate information due to the absence of gold standard datasets for comparison. Consequently, competent authorities are often required to make decisions about disease preparedness and control based on available data, which may result in suboptimal outcomes for their livestock industries. It is important to understand the limitations of poor data quality as well as the range of methods that have been developed to compensate in both disease-free and endemic situations. Using FMD as a case example, this review first discusses the different activities that competent authorities use farm-level animal population data for to support (1) preparedness activities in disease-free countries, (2) response activities during an acute outbreak in a disease-free country, and (3) eradication and control activities in an endemic country. We then discuss (4) data requirements needed to support epidemiological investigations, surveillance, and disease spread modelling both in disease-free and endemic countries.

Local lockdowns outperform global lockdown on the far side of the COVID-19 epidemic curve

In the late stages of an epidemic, infections are often sporadic and geographically distributed. Spatially structured stochastic models can capture these important features of disease dynamics, thereby allowing a broader exploration of interventions. Here we develop a stochastic model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission among an interconnected group of population centers representing counties, municipalities, and districts (collectively, "counties"). The model is parameterized with demographic, epidemiological, testing, and travel data from Ontario, Canada. We explore the effects of different control strategies after the epidemic curve has been flattened. We compare a local strategy of reopening (and reclosing, as needed) schools and workplaces county by county, according to triggers for county-specific infection prevalence, to a global strategy of province-wide reopening and reclosing, according to triggers for province-wide infection prevalence. For trigger levels that result in the same number of COVID-19 cases between the two strategies, the local strategy causes significantly fewer person-days of closure, even under high intercounty travel scenarios. However, both cases and person-days lost to closure rise when county triggers are not coordinated and when testing rates vary among counties. Finally, we show that local strategies can also do better in the early epidemic stage, but only if testing rates are high and the trigger prevalence is low. Our results suggest that pandemic planning for the far side of the COVID-19 epidemic curve should consider local strategies for reopening and reclosing.

Real-Time Standard Analysis of Disease Investigation (SADI)-A Toolbox Approach to Inform Disease Outbreak Response

An incursion of an important exotic transboundary animal disease requires a prompt and intensive response. The routine analysis of up-to-date data, as near to real time as possible, is essential for the objective assessment of the patterns of disease spread or effectiveness of control measures and the formulation of alternative control strategies. In this paper, we describe the Standard Analysis of Disease Investigation (SADI), a toolbox for informing disease outbreak response, which was developed as part of New Zealand's biosecurity preparedness. SADI was generically designed on a web-based software platform, Integrated Real-time Information System (IRIS). We demonstrated the use of SADI for a hypothetical foot-and-mouth disease (FMD) outbreak scenario in New Zealand. The data standards were set within SADI, accommodating a single relational database that integrated the national livestock population data, outbreak data, and tracing data. We collected a well-researched, standardised set of 16 epidemiologically relevant analyses for informing the FMD outbreak response, including farm response timelines, interactive outbreak/network maps, stratified epidemic curves, estimated dissemination rates, estimated reproduction numbers, and areal attack rates. The analyses were programmed within SADI to automate the process to generate the reports at a regular interval (daily) using the most up-to-date data. Having SADI prepared in advance and the process streamlined for data collection, analysis and reporting would free a wider group of epidemiologists during an actual disease outbreak from solving data inconsistency among response teams, daily “number crunching,” or providing largely retrospective analyses. Instead, the focus could be directed into enhancing data collection strategies, improving data quality, understanding the limitations of the data available, interpreting the set of analyses, and communicating their meaning with response teams, decision makers and public in the context of the epidemic.

Evaluation of strategies using simulation model to control a potential outbreak of highly pathogenic avian influenza among poultry farms in Central Luzon, Philippines

The Philippines confirmed its first epidemic of Highly Pathogenic Avian Influenza (HPAI) on August 11, 2017. It ended in November of 2017. Despite the successful management of the epidemic, reemergence is a continuous threat. The aim of this study was to conduct a mathematical model to assess the spatial transmission of HPAI among poultry farms in Central Luzon. Different control strategies and the current government protocol of 1 km radius pre-emptive culling (PEC) from infected farms were evaluated. The alternative strategies include 0.5km PEC, 1.5km PEC, 2 km PEC, 2.5 km PEC, and 3 km PEC, no pre-emptive culling (NPEC). The NPEC scenario was further modeled with a time of government notification set at 24hours, 48 hours, and 72 hours after the detection. Disease spread scenarios under each strategy were generated using an SEIR (susceptible-exposed-infectious-removed) stochastic model. A spatial transmission kernel was calculated and used to represent all potential routes of infection between farms. We assumed that the latent period occurs between 1–2 days, disease detection at 5–7 days post-infection, notification of authorities at 5–7 days post-detection and start of culling at 1–3 days post notification. The epidemic scenarios were compared based on the number of infected farms, the total number of culled farms, and the duration of the epidemic. Our results revealed that the current protocol is the most appropriate option compared with the other alternative interventions considered among farms with reproductive ratio (R_i) > 1. Shortening the culling radius to 0.5 km increased the duration of the epidemic. Further increase in the PEC zone decreased the duration of the epidemic but may not justify the increased number of farms to be culled. Nonetheless, the no-pre-emptive culling (NPEC) strategy can be an effective alternative to the current protocol if farm managers inform the government immediately within 24 hours of observation of the presence of HPAI in their farms. Moreover, if notification is made on days 1–3 after the detection, the scale and length of the outbreak have been significantly reduced. In conclusion, this study provided a comparison of various control measures for confronting the spread of HPAI infection using the simulation model. Policy makers can use this information to enhance the effectiveness of the current control strategy.

Latent likelihood ratio tests for assessing spatial kernels in epidemic models

One of the most important issues in the critical assessment of spatio-temporal stochastic models for epidemics is the selection of the transmission kernel used to represent the relationship between infectious challenge and spatial separation of infected and susceptible hosts. As the design of control strategies is often based on an assessment of the distance over which transmission can realistically occur and estimation of this distance is very sensitive to the choice of kernel function, it is important that models used to inform control strategies can be scrutinised in the light of observation in order to elicit possible evidence against the selected kernel function. While a range of approaches to model criticism is in existence, the field remains one in which the need for further research is recognised. In this paper, building on earlier contributions by the authors, we introduce a new approach to assessing the validity of spatial kernels—the latent likelihood ratio tests—which use likelihood-based discrepancy variables that can be used to compare the fit of competing models, and compare the capacity of this approach to detect model mis-specification with that of tests based on the use of infection-link residuals. We demonstrate that the new approach can be used to formulate tests with greater power than infection-link residuals to detect kernel mis-specification particularly when the degree of mis-specification is modest. This new tests avoid the use of a fully Bayesian approach which may introduce undesirable complications related to computational complexity and prior sensitivity.

The Prediction of Infectious Diseases: A Bibliometric Analysis

OBJECTIVE

The outbreak of infectious diseases has a negative influence on public health and the economy. The prediction of infectious diseases can effectively control large-scale outbreaks and reduce transmission of epidemics in rapid response to serious public health events. Therefore, experts and scholars are increasingly concerned with the prediction of infectious diseases. However, a knowledge mapping analysis of literature regarding the prediction of infectious diseases using rigorous bibliometric tools, which are supposed to offer further knowledge structure and distribution, has been conducted infrequently. Therefore, we implement a bibliometric analysis about the prediction of infectious diseases to objectively analyze the current status and research hotspots, in order to provide a reference for related researchers.

METHODS

We viewed "infectious disease*" and "prediction" or "forecasting" as search theme in the core collection of Web of Science from inception to 1 May 2020. We used two effective bibliometric tools, i.e., CiteSpace (Drexel University, Philadelphia, PA, USA) and VOSviewer (Leiden University, Leiden, The Netherlands) to objectively analyze the data of the prediction of infectious disease domain based on related publications, which can be downloaded from the core collection of Web of Science. Then, the leading publications of the prediction of infectious diseases were identified to detect the historical progress based on collaboration analysis, co-citation analysis, and co-occurrence analysis.

RESULTS

1880 documents that met the inclusion criteria were extracted from Web of Science in this study. The number of documents exhibited a growing trend, which can be expressed an increasing number of experts and scholars paying attention to the field year by year. These publications were published in 427 different journals with 11 different document types, and the most frequently studied types were articles 1618 (83%). In addition, as the most productive country, the United States has provided a lot of scientific research achievements in the field of infectious diseases.

CONCLUSION

Our study provides a systematic and objective view of the field, which can be useful for readers to evaluate the characteristics of publications involving the prediction of infectious diseases and for policymakers to take timely scientific responses.

Trade-off between local transmission and long-range dispersal drives infectious disease outbreak size in spatially structured populations

Transmission of infectious diseases between immobile hosts (e.g., plants, farms) is strongly dependent on the spatial distribution of hosts and the distance-dependent probability of transmission. As the interplay between these factors is poorly understood, we use spatial process and transmission modelling to investigate how epidemic size is shaped by host clustering and spatial range of transmission. We find that for a given degree of clustering and individual-level infectivity, the probability that an epidemic occurs after an introduction is generally higher if transmission is predominantly local. However, local transmission also impedes transfer of the infection to new clusters. A consequence is that the total number of infections is maximal if the range of transmission is intermediate. In highly clustered populations, the infection dynamics is strongly determined by the probability of transmission between clusters of hosts, whereby local clusters act as multiplier of infection. We show that in such populations, a metapopulation model sometimes provides a good approximation of the total epidemic size, using probabilities of local extinction, the final size of infections in local clusters, and probabilities of cluster-to-cluster transmission. As a real-world example we analyse the case of avian influenza transmission between poultry farms in the Netherlands.

Transmission of infectious diseases between immobile hosts depends on the transmission characteristics of the infection and on the spatial distribution of hosts. Examples include infectious diseases of plants that are spread by wind or via vectors (e.g., Asiatic citrus canker spread between citrus trees), diseases that are transmitted between local host populations (e.g., sylvatic plague transmitted between rodents living in burrows), diseases of production animals that are spread between farms (e.g., avian influenza in poultry transmitted from farm to farm). We use spatial transmission modelling to investigate how the total number of infections over the course of an epidemic is determined by host clustering and spatial range of transmission. We find that for a given degree of clustering and infectivity of hosts, the number of infections is maximal if the spatial range of transmission is intermediate. In highly clustered populations we show that epidemic size can be approximated by a metapopulation model, illustrating that in such populations the transmission dynamics is dominated by transmission between clusters of hosts.

Probabilistic reconstruction of measles transmission clusters from routinely collected surveillance data

Pockets of susceptibility resulting from spatial or social heterogeneity in vaccine coverage can drive measles outbreaks, as cases imported into such pockets are likely to cause further transmission and lead to large transmission clusters. Characterizing the dynamics of transmission is essential for identifying which individuals and regions might be most at risk. As data from detailed contact-tracing investigations are not available in many settings, we developed an R package called o2geosocial to reconstruct the transmission clusters and the importation status of the cases from their age, location, genotype and onset date. We compared our inferred cluster size distributions to 737 transmission clusters identified through detailed contact-tracing in the USA between 2001 and 2016. We were able to reconstruct the importation status of the cases and found good agreement between the inferred and reference clusters. The results were improved when the contact-tracing investigations were used to set the importation status before running the model. Spatial heterogeneity in vaccine coverage is difficult to measure directly. Our approach was able to highlight areas with potential for local transmission using a minimal number of variables and could be applied to assess the intensity of ongoing transmission in a region.

Algorithmic discovery of dynamic models from infectious disease data

Theoretical models are typically developed through a deductive process where a researcher formulates a system of dynamic equations from hypothesized mechanisms. Recent advances in algorithmic methods can discover dynamic models inductively-directly from data. Most previous research has tested these methods by rediscovering models from synthetic data generated by the already known model. Here we apply Sparse Identification of Nonlinear Dynamics (SINDy) to discover mechanistic equations for disease dynamics from case notification data for measles, chickenpox, and rubella. The discovered models provide a good qualitative fit to the observed dynamics for all three diseases, However, the SINDy chickenpox model appears to overfit the empirical data, and recovering qualitatively correct rubella dynamics requires using power spectral density in the goodness-of-fit criterion. When SINDy uses a library of second-order functions, the discovered models tend to include mass action incidence and a seasonally varying transmission rate-a common feature of existing epidemiological models for childhood infectious diseases. We also find that the SINDy measles model is capable of out-of-sample prediction of a dynamical regime shift in measles case notification data. These results demonstrate the potential for algorithmic model discovery to enrich scientific understanding by providing a complementary approach to developing theoretical models.