Dynamics of the 2001 UK foot and mouth epidemic: stochastic dispersal in a heterogeneous landscape

Analysis of within-pen and between-pen fenceline temporal contact networks in confined feedlot cattle

Though contact networks are important for describing the dynamics for disease transmission and intervention applications, individual animal contact and barriers between animal populations, such as fences, are not often utilized in the construction of these models. The objective of this study was to use contact network analysis to quantify contacts within two confined pens of feedlot cattle and the shared "fenceline" area between the pens at varying temporal resolutions and contact duration to better inform the construction of network-based disease transmission models for cattle within confined-housing systems. Two neighboring pens of feedlot steers were tagged with Real-Time Location System (RTLS) tags. Within-pen contacts were defined with a spatial threshold (SpTh) of 0.71 m and a minimum contact duration (MCD) of either 10 seconds (10 s), 30 seconds (30 s), or 60 seconds (60 s). For the fenceline network location readings were included within an area extending from 1 m on either side of the shared fence. "Fenceline" contacts could only occur between a steer from each pen. Static, undirected, weighted contact networks for within-pen networks and the between-pen network were generated for the full study duration and for daily (24-h), 6-h period, and hourly networks to better assess network heterogeneity. For the full study duration network, the two within-pen networks were densely homogenous. The within-pen networks showed more heterogeneity when smaller timescales (6-h period and hourly) were applied. When contacts were defined with a MCD of 30 s or 60 s, the total number of contacts seen in each network decreased, indicating that most of the contacts observed in our networks may have been transient passing contacts. Cosine similarity was moderate and stable across days for within pen networks. Of the 90 total tagged steers between the two pens, 86 steers (46 steers from Pen 2 and 40 steers from Pen 3) produced at least one contact across the shared fenceline. The total network density for the network created across the shared fenceline between the two pens was 17%, with few contacts at shorter timescales and for MCD of 30 s or 60 s. Overall, the contact networks created here from high-resolution spatial and temporal contact observation data provide estimates for a contact network within commercial US feedlot pens and the contact network created between two neighboring pens of cattle. These networks can be used to better inform pathogen transmission models on social contact networks.

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.

A systematic review of mechanistic models used to study avian influenza virus transmission and control

The global spread of avian influenza A viruses in domestic birds is causing increasing socioeconomic devastation. Various mechanistic models have been developed to better understand avian influenza transmission and evaluate the effectiveness of control measures in mitigating the socioeconomic losses caused by these viruses. However, the results of models of avian influenza transmission and control have not yet been subject to a comprehensive review. Such a review could help inform policy makers and guide future modeling work. To help fill this gap, we conducted a systematic review of the mechanistic models that have been applied to field outbreaks. Our three objectives were to: (1) describe the type of models and their epidemiological context, (2) list estimates of commonly used parameters of low pathogenicity and highly pathogenic avian influenza transmission, and (3) review the characteristics of avian influenza transmission and the efficacy of control strategies according to the mechanistic models. We reviewed a total of 46 articles. Of these, 26 articles estimated parameters by fitting the model to data, one evaluated the effectiveness of control strategies, and 19 did both. Values of the between-individual reproduction number ranged widely: from 2.18 to 86 for highly pathogenic avian influenza viruses, and from 4.7 to 45.9 for low pathogenicity avian influenza viruses, depending on epidemiological settings, virus subtypes and host species. Other parameters, such as the durations of the latent and infectious periods, were often taken from the literature, limiting the models' potential insights. Concerning control strategies, many models evaluated culling (n = 15), while vaccination received less attention (n = 6). According to the articles reviewed, optimal control strategies varied between virus subtypes and local conditions, and depended on the overall objective of the intervention. For instance, vaccination was optimal when the objective was to limit the overall number of culled flocks. In contrast, pre-emptive culling was preferred for reducing the size and duration of an epidemic. Early implementation consistently improved the overall efficacy of interventions, highlighting the need for effective surveillance and epidemic preparedness.

How important is the spatial movement of people in attempts to eliminate the transmission of human helminth infections by mass drug administration?

Human mobility contributes to the spatial dynamics of many infectious diseases, and understanding these dynamics helps us to determine the most effective ways to intervene and plan surveillance. In this paper, we describe a novel transmission model for the spatial dynamics of hookworm, a parasitic worm which is a common infection across sub-Saharan Africa, East Asia and the Pacific islands. We fit our model, with and without mobility, to data obtained from a sub-county in Kenya, and validate the model's predictions against the decline in prevalence observed over the course of a clustered randomized control trial evaluating methods of administering mass chemotherapy. We find that our model which incorporates human mobility is able to reproduce the observed patterns in decline of prevalence during the TUMIKIA trial, and additionally, that the widespread bounce-back of infection may be possible over many years, depending on the rates of people movement between villages. The results have important implications for the design of mass chemotherapy programmes for the elimination of human helminth transmission. This article is part of the theme issue 'Challenges and opportunities in the fight against neglected tropical diseases: a decade from the London Declaration on NTDs'.

Incorporating heterogeneity in farmer disease control behaviour into a livestock disease transmission model

Human behaviour is critical to effective responses to livestock disease outbreaks, especially with respect to vaccination uptake. Traditionally, mathematical models used to inform this behaviour have not taken heterogeneity in farmer behaviour into account. We address this by exploring how heterogeneity in farmers vaccination behaviour can be incorporated to inform mathematical models. We developed and used a graphical user interface to elicit farmers (n = 60) vaccination decisions to an unfolding fast-spreading epidemic and linked this to their psychosocial and behavioural profiles. We identified, via cluster analysis, robust patterns of heterogeneity in vaccination behaviour. By incorporating these vaccination behavioural groupings into a mathematical model for a fast-spreading livestock infection, using computational simulation we explored how the inclusion of heterogeneity in farmer disease control behaviour may impact epidemiological and economic focused outcomes. When assuming homogeneity in farmer behaviour versus configurations informed by the psychosocial profile cluster estimates, the modelled scenarios revealed a disconnect in projected distributions and threshold statistics across outbreak size, outbreak duration and economic metrics.

The aquaculture disease network model (AquaNet-Mod): A simulation model to evaluate disease spread and controls for the salmonid industry in England and Wales

Infectious disease causes significant mortality in wild and farmed systems, threatening biodiversity, conservation and animal welfare, as well as food security. To mitigate impacts and inform policy, tools such as mathematical models and computer simulations are valuable for predicting the potential spread and impact of disease. This paper describes the development of the Aquaculture Disease Network Model, AquaNet-Mod, and demonstrates its application to evaluating disease epidemics and the efficacy of control, using a Viral Haemorrhagic Septicaemia (VHS) case study. AquaNet-Mod is a data-driven, stochastic, state-transition model. Disease spread can occur via four different mechanisms, i) live fish movement, ii) river based, iii) short distance mechanical and iv) distance independent mechanical. Sites transit between three disease states: susceptible, clinically infected and subclinically infected. Disease spread can be interrupted by the application of disease mitigation measures and controls such as contact tracing, culling, fallowing and surveillance. Results from a VHS case study highlight the potential for VHS to spread to 96% of sites over a 10 year time horizon if no disease controls are applied. Epidemiological impact is significantly reduced when live fish movement restrictions are placed on the most connected sites and further still, when disease controls, representative of current disease control policy in England and Wales, are applied. The importance of specific disease control measures, particularly contact tracing and disease detection rate, are also highlighted. The merit of this model for evaluation of disease spread and the efficacy of controls, in the context of policy, along with potential for further application and development of the model, for example to include economic parameters, is discussed.

Novel pathogen introduction triggers rapid evolution in animal social movement strategies

Animal sociality emerges from individual decisions on how to balance the costs and benefits of being sociable. Novel pathogens introduced into wildlife populations should increase the costs of sociality, selecting against gregariousness. Using an individual-based model that captures essential features of pathogen transmission among social hosts, we show how novel pathogen introduction provokes the rapid evolutionary emergence and coexistence of distinct social movement strategies. These strategies differ in how they trade the benefits of social information against the risk of infection. Overall, pathogen-risk-adapted populations move more and have fewer associations with other individuals than their pathogen-risk-naive ancestors, reducing disease spread. Host evolution to be less social can be sufficient to cause a pathogen to be eliminated from a population, which is followed by a rapid recovery in social tendency. Our conceptual model is broadly applicable to a wide range of potential host-pathogen introductions and offers initial predictions for the eco-evolutionary consequences of wildlife pathogen spillover scenarios and a template for the development of theory in the ecology and evolution of animals' movement decisions.

Epicasting: An Ensemble Wavelet Neural Network for forecasting epidemics

Infectious diseases remain among the top contributors to human illness and death worldwide, among which many diseases produce epidemic waves of infection. The lack of specific drugs and ready-to-use vaccines to prevent most of these epidemics worsens the situation. These force public health officials and policymakers to rely on early warning systems generated by accurate and reliable epidemic forecasters. Accurate forecasts of epidemics can assist stakeholders in tailoring countermeasures, such as vaccination campaigns, staff scheduling, and resource allocation, to the situation at hand, which could translate to reductions in the impact of a disease. Unfortunately, most of these past epidemics exhibit nonlinear and non-stationary characteristics due to their spreading fluctuations based on seasonal-dependent variability and the nature of these epidemics. We analyze various epidemic time series datasets using a maximal overlap discrete wavelet transform (MODWT) based autoregressive neural network and call it Ensemble Wavelet Neural Network (EWNet) model. MODWT techniques effectively characterize non-stationary behavior and seasonal dependencies in the epidemic time series and improve the nonlinear forecasting scheme of the autoregressive neural network in the proposed ensemble wavelet network framework. From a nonlinear time series viewpoint, we explore the asymptotic stationarity of the proposed EWNet model to show the asymptotic behavior of the associated Markov Chain. We also theoretically investigate the effect of learning stability and the choice of hidden neurons in the proposal. From a practical perspective, we compare our proposed EWNet framework with twenty-two statistical, machine learning, and deep learning models for fifteen real-world epidemic datasets with three test horizons using four key performance indicators. Experimental results show that the proposed EWNet is highly competitive compared to the state-of-the-art epidemic forecasting methods.

Network analysis of pig movement data as an epidemiological tool: an Austrian case study

Animal movements represent a major risk for the spread of infectious diseases in the domestic swine population. In this study, we adopted methods from social network analysis to explore pig trades in Austria. We used a dataset of daily records of swine movements covering the period 2015-2021. We analyzed the topology of the network and its structural changes over time, including seasonal and long-term variations in the pig production activities. Finally, we studied the temporal dynamics of the network community structure. Our findings show that the Austrian pig production was dominated by small-sized farms while spatial farm density was heterogeneous. The network exhibited a scale-free topology but was very sparse, suggesting a moderate impact of infectious disease outbreaks. However, two regions (Upper Austria and Styria) may present a higher structural vulnerability. The network also showed very high assortativity between holdings from the same federal state. Dynamic community detection revealed a stable behavior of the clusters. Yet trade communities did not correspond to sub-national administrative divisions and may be an alternative zoning approach to managing infectious diseases. Knowledge about the topology, contact patterns, and temporal dynamics of the pig trade network can support optimized risk-based disease control and surveillance strategies.

Modelling the spread and mitigation of an emerging vector-borne pathogen: Citrus greening in the U.S

Predictive models, based upon epidemiological principles and fitted to surveillance data, play an increasingly important role in shaping regulatory and operational policies for emerging outbreaks. Data for parameterising these strategically important models are often scarce when rapid actions are required to change the course of an epidemic invading a new region. We introduce and test a flexible epidemiological framework for landscape-scale disease management of an emerging vector-borne pathogen for use with endemic and invading vector populations. We use the framework to analyse and predict the spread of Huanglongbing disease or citrus greening in the U.S. We estimate epidemiological parameters using survey data from one region (Texas) and show how to transfer and test parameters to construct predictive spatio-temporal models for another region (California). The models are used to screen effective coordinated and reactive management strategies for different regions.

A foot and mouth disease ranking of risk using cattle transportation

Foot-and-mouth disease (FMD) is a highly infectious condition that affects domestic and wild cloven-hoofed animals. This disease has substantial economic consequences. Livestock movement is one of the primary causes of disease dissemination. The centrality properties of the livestock mobilization transportation network provide valuable information for surveillance and control of FMD. However, the same transportation network can be described by different centrality descriptions, making it challenging to prioritize the most vulnerable nodes in the transportation network. This work considers the construction of a single network risk ranking, which helps prioritize disease control measurements. Results show that the proposed ranking constructed on 2016 livestock mobilization data may predict an actual outbreak reported in the Cesar (Colombia) region in 2018, with a performance measured by the area under the receiver operating characteristic curve of 0.91. This result constitutes the first quantitative evidence of the predictive capacity of livestock transportation to target FMD outbreaks. This approach may help decision-makers devise strategies to control and prevent FMD.

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.

Mathematical Modelling of the Spatial Distribution of a COVID-19 Outbreak with Vaccination Using Diffusion Equation

The formulation of mathematical models using differential equations has become crucial in predicting the evolution of viral diseases in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China, which causes a severe and potentially fatal respiratory syndrome. Since then, it has been declared a pandemic by the World Health Organization and has spread around the globe. A reaction−diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process, in which different substances are transformed, and a diffusion process, which causes their distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic using the bias of reaction−diffusion equations. Both local and global asymptotic stability conditions for the equilibria were determined using a Lyapunov function, and the nature of the stability was determined using the Routh−Hurwitz criterion. Furthermore, we consider the conditions for the existence and uniqueness of the model solution and show the spatial distribution of the model compartments when the basic reproduction rate R0<1 and R0>1. Thereafter, we conducted a sensitivity analysis to determine the most sensitive parameters in the proposed model. We demonstrate the model’s effectiveness by performing numerical simulations and investigating the impact of vaccination, together with the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. Therefore, we offer to the public health policymakers a better understanding of COVID-19 management.

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.

Gastrointestinal helminths increase Bordetella bronchiseptica shedding and host variation in supershedding

Co-infected hosts, individuals that carry more than one infectious agent at any one time, have been suggested to facilitate pathogen transmission, including the emergence of supershedding events. However, how the host immune response mediates the interactions between co-infecting pathogens and how these affect the dynamics of shedding remains largely unclear. We used laboratory experiments and a modeling approach to examine temporal changes in the shedding of the respiratory bacterium Bordetella bronchiseptica in rabbits with one or two gastrointestinal helminth species. Experimental data showed that rabbits co-infected with one or both helminths shed significantly more B. bronchiseptica, by direct contact with an agar petri dish, than rabbits with bacteria alone. Co-infected hosts generated supershedding events of higher intensity and more frequently than hosts with no helminths. To explain this variation in shedding an infection-immune model was developed and fitted to rabbits of each group. Simulations suggested that differences in the magnitude and duration of shedding could be explained by the effect of the two helminths on the relative contribution of neutrophils and specific IgA and IgG to B. bronchiseptica neutralization in the respiratory tract. However, the interactions between infection and immune response at the scale of analysis that we used could not capture the rapid variation in the intensity of shedding of every rabbit. We suggest that fast and local changes at the level of respiratory tissue probably played a more important role. This study indicates that co-infected hosts are important source of variation in shedding, and provides a quantitative explanation into the role of helminths to the dynamics of respiratory bacterial infections.

Analysis of suspensions and recoveries of official foot and mouth disease free status of WOAH Members between 1996 and 2020

Foot and mouth disease was the first disease for which, in 1996, the World Organisation for Animal Health (WOAH; founded as OIE) established an official list of disease-free territories, which has helped to facilitate the trade of animals and animal products from those territories. Since that year, there have been a number of suspensions of FMD-free status which have impacted the livestock industry of the territories affected. The objective of this study is to identify factors associated with the time taken to recover FMD-free status after suspension. Historical applications submitted (between 1996 and the first semester of 2020) by WOAH Members for recognition and recovery of FMD-free status were used as the main source of data. Only FMD-free status suspensions caused by outbreaks were considered. Data on the Member's socio-economic characteristics, livestock production systems, FMD outbreak characteristics, and control strategies were targeted for the analysis. The period of time taken to recover FMD-free status was estimated using Kaplan-Meier survival curves. A Cox proportional hazard model was used to identify factors associated with the time taken to recover FMD-free status after suspension. A total of 163 territories were granted official FMD-free status during the study period. The study sample consisted of 45 FMD-free status suspensions. Africa and the Americas accounted for over 50% of FMD-free status suspensions, while over 70% of these occurred in formerly FMD-free territories where vaccination was not practiced. The study noted that implementing a stamping-out or vaccination and remove policy shortened the time to recover FMD-free status, compared with a vaccination and retain policy. Other variables associated with the outcome were the income level of the Member, Veterinary Service capacity, time taken to implement control measures, time taken until the disposal of the last FMD case, whether the territory bordered FMD-infected territories, and time elapsed since FMD freedom. This analysis will contribute toward the understanding of the main determinants affecting the time to recover the FMD free status of WOAH Members and policy processes for FMD control and elimination.

The Importance of Livestock Demography and Infrastructure in Driving Foot and Mouth Disease Dynamics

Transboundary animal diseases, such as foot and mouth disease (FMD) pose a significant and ongoing threat to global food security. Such diseases can produce large, spatially complex outbreaks. Mathematical models are often used to understand the spatio-temporal dynamics and create response plans for possible disease introductions. Model assumptions regarding transmission behavior of premises and movement patterns of livestock directly impact our understanding of the ecological drivers of outbreaks and how to best control them. Here, we investigate the impact that these assumptions have on model predictions of FMD outbreaks in the U.S. using models of livestock shipment networks and disease spread. We explore the impact of changing assumptions about premises transmission behavior, both by including within-herd dynamics, and by accounting for premises type and increasing the accuracy of shipment predictions. We find that the impact these assumptions have on outbreak predictions is less than the impact of the underlying livestock demography, but that they are important for investigating some response objectives, such as the impact on trade. These results suggest that demography is a key ecological driver of outbreaks and is critical for making robust predictions but that understanding management objectives is also important when making choices about model assumptions.

Estimating SARS-CoV-2 variant fitness and the impact of interventions in England using statistical and geo-spatial agent-based models

The SARS-CoV-2 epidemic has been extended by the evolution of more transmissible viral variants. In autumn 2020, the B.1.177 lineage became the dominant variant in England, before being replaced by the B.1.1.7 (Alpha) lineage in late 2020, with the sweep occurring at different times in each region. This period coincided with a large number of non-pharmaceutical interventions (e.g. lockdowns) to control the epidemic, making it difficult to estimate the relative transmissibility of variants. In this paper, we model the spatial spread of these variants in England using a meta-population agent-based model which correctly characterizes the regional variation in cases and distribution of variants. As a test of robustness, we additionally estimated the relative transmissibility of multiple variants using a statistical model based on the renewal equation, which simultaneously estimates the effective reproduction number R. Relative to earlier variants, the transmissibility of B.1.177 is estimated to have increased by 1.14 (1.12-1.16) and that of Alpha by 1.71 (1.65-1.77). The vaccination programme starting in December 2020 is also modelled. Counterfactual simulations demonstrate that the vaccination programme was essential for reopening in March 2021, and that if the January lockdown had started one month earlier, up to 30 k (24 k-38 k) deaths could have been prevented. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Estimating SARS-CoV-2 variant fitness and the impact of interventions in England using statistical and geo-spatial agent-based models

The SARS-CoV-2 epidemic has been extended by the evolution of more transmissible viral variants. In autumn 2020, the B.1.177 lineage became the dominant variant in England, before being replaced by the B.1.1.7 (Alpha) lineage in late 2020, with the sweep occurring at different times in each region. This period coincided with a large number of non-pharmaceutical interventions (e.g. lockdowns) to control the epidemic, making it difficult to estimate the relative transmissibility of variants. In this paper, we model the spatial spread of these variants in England using a meta-population agent-based model which correctly characterizes the regional variation in cases and distribution of variants. As a test of robustness, we additionally estimated the relative transmissibility of multiple variants using a statistical model based on the renewal equation, which simultaneously estimates the effective reproduction number R. Relative to earlier variants, the transmissibility of B.1.177 is estimated to have increased by 1.14 (1.12-1.16) and that of Alpha by 1.71 (1.65-1.77). The vaccination programme starting in December 2020 is also modelled. Counterfactual simulations demonstrate that the vaccination programme was essential for reopening in March 2021, and that if the January lockdown had started one month earlier, up to 30 k (24 k-38 k) deaths could have been prevented. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

The African swine fever modelling challenge: Model comparison and lessons learnt

Robust epidemiological knowledge and predictive modelling tools are needed to address challenging objectives, such as: understanding epidemic drivers; forecasting epidemics; and prioritising control measures. Often, multiple modelling approaches can be used during an epidemic to support effective decision making in a timely manner. Modelling challenges contribute to understanding the pros and cons of different approaches and to fostering technical dialogue between modellers. In this paper, we present the results of the first modelling challenge in animal health - the ASF Challenge - which focused on a synthetic epidemic of African swine fever (ASF) on an island. The modelling approaches proposed by five independent international teams were compared. We assessed their ability to predict temporal and spatial epidemic expansion at the interface between domestic pigs and wild boar, and to prioritise a limited number of alternative interventions. We also compared their qualitative and quantitative spatio-temporal predictions over the first two one-month projection phases of the challenge. Top-performing models in predicting the ASF epidemic differed according to the challenge phase, host species, and in predicting spatial or temporal dynamics. Ensemble models built using all team-predictions outperformed any individual model in at least one phase. The ASF Challenge demonstrated that accounting for the interface between livestock and wildlife is key to increasing our effectiveness in controlling emerging animal diseases, and contributed to improving the readiness of the scientific community to face future ASF epidemics. Finally, we discuss the lessons learnt from model comparison to guide decision making.

Comparing the efficacy of control strategies for infectious disease outbreaks using field and simulation studies

Diseases characterized by long distance inoculum dispersal (LDD) are among the fastest spreading epidemics in both natural and managed landscapes. Management of such epidemics is extremely challenging because of asymptomatic infection extending at large spatial scales and frequent escape from the newly established disease sources. We compared the efficacy of area- and timing-based disease management strategies in artificially initiated field epidemics of wheat stripe rust and complemented with simulations from an updated version of the spatially explicit model EPIMUL, using model parameters relevant to field epidemics. The model was further used to expand the number of epidemic mitigations beyond that feasible to incorporate in the field. The field experiment was conducted for 2 years in two locations having different climatic conditions. Culling and protection treatments were applied at different times after epidemic initiation and to different spatial extents surrounding the outbreaks. In each experiment, treatments were replicated four times in plots 33.5 m long and 1.52 m wide with a 0.76 × 0.76 m inoculated focus centered within each plot. Disease gradients were assessed along the center lines of the plots at 1.52 m intervals both upwind and downwind from the focus. Both field and simulation results indicated that control measures applied over the entire population were highly effective in suppressing the epidemics by more than 99% but may not always be logistically and economically feasible at large spatial scales. Comparison between the variable sized treatment areas and application timings suggested that implementing contiguous premises (CP) cull at 1 day after first sporulation in the outbreak focus reduced rust by 52% and 60% in Corvallis and Madras, respectively. However, altering the cull size did not significantly affect the disease epidemic development, which suggested that early timing had a greater influence in suppressing the epidemics than did increased area of application. However, sufficiently large, treated areas may compensate for a delay in application timing to some extent. Results from these replicated treatments may help to devise appropriate management strategies for other LDD pathogens.

Phylodynamic analysis of the highly pathogenic avian influenza H5N8 epidemic in France, 2016-2017

In 2016-2017, France experienced a devastating epidemic of highly pathogenic avian influenza (HPAI) H5N8, with more than 400 outbreaks reported in poultry farms. We analyzed the spatiotemporal dynamics of the epidemic using a structured-coalescent-based phylodynamic approach that combined viral genomic data (n = 196; one viral genome per farm) and epidemiological data. In the process, we estimated viral migration rates between départements (French administrative regions) and the temporal dynamics of the effective viral population size (Ne) in each département. Viral migration rates quantify viral spread between départements and Ne is a population genetic measure of the epidemic size and, in turn, is indicative of the within-département transmission intensity. We extended the phylodynamic analysis with a generalized linear model to assess the impact of multiple factors-including large-scale preventive culling and live-duck movement bans-on viral migration rates and Ne. We showed that the large-scale culling of ducks that was initiated on 4 January 2017 significantly reduced the viral spread between départements. No relationship was found between the viral spread and duck movements between départements. The within-département transmission intensity was found to be weakly associated with the intensity of duck movements within départements. Together, these results indicated that the virus spread in short distances, either between adjacent départements or within départements. Results also suggested that the restrictions on duck transport within départements might not have stopped the viral spread completely. Overall, we demonstrated the usefulness of phylodynamics in characterizing the dynamics of a HPAI epidemic and assessing control measures. This method can be adapted to investigate other epidemics of fast-evolving livestock pathogens.

Cattle transport network predicts endemic and epidemic foot-and-mouth disease risk on farms in Turkey

The structure of contact networks affects the likelihood of disease spread at the population scale and the risk of infection at any given node. Though this has been well characterized for both theoretical and empirical networks for the spread of epidemics on completely susceptible networks, the long-term impact of network structure on risk of infection with an endemic pathogen, where nodes can be infected more than once, has been less well characterized. Here, we analyze detailed records of the transportation of cattle among farms in Turkey to characterize the global and local attributes of the directed—weighted shipments network between 2007-2012. We then study the correlations between network properties and the likelihood of infection with, or exposure to, foot-and-mouth disease (FMD) over the same time period using recorded outbreaks. The shipments network shows a complex combination of features (local and global) that have not been previously reported in other networks of shipments; i.e. small-worldness, scale-freeness, modular structure, among others. We find that nodes that were either infected or at high risk of infection with FMD (within one link from an infected farm) had disproportionately higher degree, were more central (eigenvector centrality and coreness), and were more likely to be net recipients of shipments compared to those that were always more than 2 links away from an infected farm. High in-degree (i.e. many shipments received) was the best univariate predictor of infection. Low in-coreness (i.e. peripheral nodes) was the best univariate predictor of nodes always more than 2 links away from an infected farm. These results are robust across the three different serotypes of FMD observed in Turkey and during periods of low-endemic prevalence and high-prevalence outbreaks.

Contact network epidemiology has been extensively used in the context of infectious diseases, primarily focusing on epidemic diseases. In this paper we use detailed recorded data about cattle exchange between farms in Turkey from 2007 to 2012, to build, analyze and characterize the directed-weighted complex network of shipments of cattle. Additionally, using outbreaks data about recorded cases of foot-and-mouth disease (FMD) in Turkey, we assess the correlation between the “farm’s” position in the network (importance) and the risk of being infected with FMD, which has been endemic in Turkey for a long time. We find some network measures that are more likely to identify high-risk and low-risk farms (in-degree and in-coreness, respectively) when proposing strategies for surveillance or containment of an infectious disease.

Modelling livestock infectious disease control policy under differing social perspectives on vaccination behaviour

The spread of infection amongst livestock depends not only on the traits of the pathogen and the livestock themselves, but also on the veterinary health behaviours of farmers and how this impacts their implementation of disease control measures. Controls that are costly may make it beneficial for individuals to rely on the protection offered by others, though that may be sub-optimal for the population. Failing to account for socio-behavioural properties may produce a substantial layer of bias in infectious disease models. We investigated the role of heterogeneity in vaccine response across a population of farmers on epidemic outbreaks amongst livestock, caused by pathogens with differential speed of spread over spatial landscapes of farms for two counties in England (Cumbria and Devon). Under different compositions of three vaccine behaviour groups (precautionary, reactionary, non-vaccination), we evaluated from population- and individual-level perspectives the optimum threshold distance to premises with notified infection that would trigger responsive vaccination by the reactionary vaccination group. We demonstrate a divergence between population and individual perspectives in the optimal scale of reactive voluntary vaccination response. In general, minimising the population-level perspective cost requires a broader reactive uptake of the intervention, whilst optimising the outcome for the average individual increased the likelihood of larger scale disease outbreaks. When the relative cost of vaccination was low and the majority of premises had undergone precautionary vaccination, then adopting a perspective that optimised the outcome for an individual gave a broader spatial extent of reactive response compared to a perspective wanting to optimise outcomes for everyone in the population. Under our assumed epidemiological context, the findings identify livestock disease intervention receptiveness and cost combinations where one would expect strong disagreement between the intervention stringency that is best from the perspective of a stakeholder responsible for supporting the livestock industry compared to a sole livestock owner. Were such discord anticipated and achieving a consensus view across perspectives desired, the findings may also inform those managing veterinary health policy the requisite reduction in intervention cost and/or the required extent of nurturing beneficial community attitudes towards interventions.

The COVID-19 pandemic has shown how crucial human behaviour is in controlling the spread of an infectious disease. The same is true of livestock, where farmer behaviour is critical to reduce the spread of an infection to enhance animal welfare and reduce economic losses. An ongoing concern for livestock owners is therefore ensuring they have adequate disease management procedures. However, what an individual farmer considers an appropriate way to control an infection in their own livestock may not be the best way to prevent an infection for every farmer’s livestock in the population. We describe a mathematical model combining epidemiological and behavioural elements to study the tension between individual and population-level control of livestock diseases. Applied to representative livestock systems in two counties in England (Cumbria and Devon), and splitting farmers into three types of vaccine behaviour groups (precautionary, reactionary, non-vaccination), we show what individual farmers see as an effective way to reduce infection is not the same as would benefit every farmer. The preferred response to protect every farmer’s livestock is to encourage wider uptake of reactive vaccination, whereas optimising the spatial extent of reactive vaccination for the average individual increases the chance of larger disease outbreaks.

Fock-space approach to stochastic susceptible-infected-recovered models

We investigate the stochastic susceptible-infected-recovered (SIR) model of infectious disease dynamics in the Fock-space approach. In contrast to conventional SIR models based on ordinary differential equations for the subpopulation sizes of S, I, and R individuals, the stochastic SIR model is driven by a master equation governing the transition probabilities among the system's states defined by SIR occupation numbers. In the Fock-space approach the master equation is recast in the form of a real-valued Schrödinger-type equation with a second quantization Hamiltonian-like operator describing the infection and recovery processes. We find exact analytic expressions for the Hamiltonian eigenvalues for any population size N. We present small- and large-N results for the average numbers of SIR individuals and basic reproduction number. For small N we also obtain the probability distributions of SIR states, epidemic sizes and durations, which cannot be found from deterministic SIR models. Our Fock-space approach to stochastic SIR models introduces a powerful set of tools to calculate central quantities of epidemic processes, especially for relatively small populations where statistical fluctuations not captured by conventional deterministic SIR models play a crucial role.

Genetic diversity and connectivity of the Ostreid herpesvirus 1 populations in France: A first attempt to phylogeographic inference for a marine mollusc disease

The genetic diversity of viral populations is a key driver of the spatial and temporal diffusion of viruses; yet, studying the diversity of whole genomes from natural populations still remains a challenge. Phylodynamic approaches are commonly used for RNA viruses harboring small genomes but have only rarely been applied to DNA viruses with larger genomes. Here, we used the Pacific oyster mortality syndrome (a disease that affects oyster farms around the world) as a model to study the genetic diversity of its causative agent, the Ostreid herpesvirus 1 (OsHV-1) in the three main French oyster-farming areas. Using ultra-deep sequencing on individual moribund oysters and an innovative combination of bioinformatics tools, we de novo assembled twenty-one OsHV-1 new genomes. Combining quantification of major and minor genetic variations, phylogenetic analysis, and ancestral state reconstruction of discrete traits approaches, we assessed the connectivity of OsHV-1 viral populations between the three oyster-farming areas. Our results suggest that the Marennes-Oléron Bay represents the main source of OsHV-1 diversity, from where the virus has dispersed to other farming areas, a scenario consistent with current practices of oyster transfers in France. We demonstrate that phylodynamic approaches can be applied to aquatic DNA viruses to determine how epidemiological, immunological, and evolutionary processes act and potentially interact to shape their diversity patterns.

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.

Delays in Epidemic Outbreak Control Cost Disproportionately Large Treatment Footprints to Offset

Epidemic outbreak control often involves a spatially explicit treatment area (quarantine, inoculation, ring cull) that covers the outbreak area and adjacent regions where hosts are thought to be latently infected. Emphasis on space however neglects the influence of treatment timing on outbreak control. We conducted field and in silico experiments with wheat stripe rust (WSR), a long-distance dispersed plant disease, to understand interactions between treatment timing and area interact to suppress an outbreak. Full-factorial field experiments with three different ring culls (outbreak area only to a 25-fold increase in treatment area) at three different disease control timings (1.125, 1.25, and 1.5 latent periods after initial disease expression) indicated that earlier treatment timing had a conspicuously greater suppressive effect than the area treated. Disease spread computer simulations over a broad range of influential epidemic parameter values (R0, outbreak disease prevalence, epidemic duration) suggested that potentially unrealistically large increases in treatment area would be required to compensate for even small delays in treatment timing. Although disease surveillance programs are costly, our results suggest that treatments early in an epidemic disease outbreak require smaller areas to be effective, which may ultimately compensate for the upfront costs of proactive disease surveillance programs.

Bayesian nonparametric inference for heterogeneously mixing infectious disease models

Mathematical models of infectious disease transmission continue to play a vital role in understanding, mitigating, and preventing outbreaks. The vast majority of epidemic models in the literature are parametric, meaning that they contain inherent assumptions about how transmission occurs in a population. However, such assumptions can be lacking in appropriate biological or epidemiological justification and in consequence lead to erroneous scientific conclusions and misleading predictions. We propose a flexible Bayesian nonparametric framework that avoids the need to make strict model assumptions about the infection process and enables a far more data-driven modeling approach for inferring the mechanisms governing transmission. We use our methods to enhance our understanding of the transmission mechanisms of the 2001 UK foot and mouth disease outbreak.

Infectious disease transmission models require assumptions about how the pathogen spreads between individuals. These assumptions may be somewhat arbitrary, particularly when it comes to describing how transmission varies between individuals of different types or in different locations, and may in turn lead to incorrect conclusions or policy decisions. We develop a general Bayesian nonparametric framework for transmission modeling that removes the need to make such specific assumptions with regard to the infection process. We use multioutput Gaussian process prior distributions to model different infection rates in populations containing multiple types of individuals. Further challenges arise because the transmission process itself is unobserved, and large outbreaks can be computationally demanding to analyze. We address these issues by data augmentation and a suitable efficient approximation method. Simulation studies using synthetic data demonstrate that our framework gives accurate results. We analyze an outbreak of foot and mouth disease in the United Kingdom, quantifying the spatial transmission mechanism between farms with different combinations of livestock.

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.

The costs and benefits of primary prevention of zoonotic pandemics

The lives lost and economic costs of viral zoonotic pandemics have steadily increased over the past century. Prominent policymakers have promoted plans that argue the best ways to address future pandemic catastrophes should entail, "detecting and containing emerging zoonotic threats." In other words, we should take actions only after humans get sick. We sharply disagree. Humans have extensive contact with wildlife known to harbor vast numbers of viruses, many of which have not yet spilled into humans. We compute the annualized damages from emerging viral zoonoses. We explore three practical actions to minimize the impact of future pandemics: better surveillance of pathogen spillover and development of global databases of virus genomics and serology, better management of wildlife trade, and substantial reduction of deforestation. We find that these primary pandemic prevention actions cost less than 1/20th the value of lives lost each year to emerging viral zoonoses and have substantial cobenefits.

Antigenic escape selects for the evolution of higher pathogen transmission and virulence

Despite the propensity for complex and non-equilibrium dynamics in nature, eco-evolutionary analytical theory typically assumes that populations are at equilibria. In particular, pathogens often show antigenic escape from host immune defences, leading to repeated epidemics, fluctuating selection and diversification, but we do not understand how this impacts the evolution of virulence. We model the impact of antigenic drift and escape on the evolution of virulence in a generalized pathogen and apply a recently introduced oligomorphic methodology that captures the dynamics of the mean and variance of traits, to show analytically that these non-equilibrium dynamics select for the long-term persistence of more acute pathogens with higher virulence. Our analysis predicts both the timings and outcomes of antigenic shifts leading to repeated epidemics and predicts the increase in variation in both antigenicity and virulence before antigenic escape. There is considerable variation in the degree of antigenic escape that occurs across pathogens and our results may help to explain the difference in virulence between related pathogens including, potentially, human influenzas. Furthermore, it follows that these pathogens will have a lower R₀, with clear implications for epidemic behaviour, endemic behaviour and control. More generally, our results show the importance of examining the evolutionary consequences of non-equilibrium dynamics.

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.

When and why direct transmission models can be used for environmentally persistent pathogens

Variants of the susceptible-infected-removed (SIR) model of Kermack & McKendrick (1927) enjoy wide application in epidemiology, offering simple yet powerful inferential and predictive tools in the study of diverse infectious diseases across human, animal and plant populations. Direct transmission models (DTM) are a subset of these that treat the processes of disease transmission as comprising a series of discrete instantaneous events. Infections transmitted indirectly by persistent environmental pathogens, however, are examples where a DTM description might fail and are perhaps better described by models that comprise explicit environmental transmission routes, so-called environmental transmission models (ETM). In this paper we discuss the stochastic susceptible-exposed-infected-removed (SEIR) DTM and susceptible-exposed-infected-removed-pathogen (SEIR-P) ETM and we show that the former is the timescale separation limit of the latter, with ETM host-disease dynamics increasingly resembling those of a DTM when the pathogen’s characteristic timescale is shortened, relative to that of the host population. Using graphical posterior predictive checks (GPPC), we investigate the validity of the SEIR model when fitted to simulated SEIR-P host infection and removal times. Such analyses demonstrate how, in many cases, the SEIR model is robust to departure from direct transmission. Finally, we present a case study of white spot disease (WSD) in penaeid shrimp with rates of environmental transmission and pathogen decay (SEIR-P model parameters) estimated using published results of experiments. Using SEIR and SEIR-P simulations of a hypothetical WSD outbreak management scenario, we demonstrate how relative shortening of the pathogen timescale comes about in practice. With atttempts to remove diseased shrimp from the population every 24h, we see SEIR and SEIR-P model outputs closely conincide. However, when removals are 6-hourly, the two models’ mean outputs diverge, with distinct predictions of outbreak size and duration.

Mathematical models of the spread and progression of communicable disease in populations are important tools in efforts to prevent and control outbreaks. A common class of disease models assume that infection is transmitted directly from infectious to susceptible individuals when they are in close proximity—so called direct transmission models. These are used widely and have proven invaluable as simplified descriptions of a wide array of infectious diseases in diverse populations. However, many pathogens spread through indirect, environmental routes of transmission, for example via contact with contaminated water sources in the case of cholera, or inhalation of infectious airborne droplets for respiratory infections, such as Covid-19.

We show that direct transmission models work well for such pathogens with short environmental lifetimes and where hosts shed pathogens into the environment at high rates. This means that we do not require information about environmental pathogen levels to understand the behaviour of outbreaks caused by these pathogens. When shedding rates are also low, e.g., with macroparasitic infections, or when variable environmental factors play a role in transmissibility, then explicit modelling of both the pathogen and environmental transmission will provide a more accurate picture than a direct transmission approximation.

Optimal surveillance against bioinvasions: a sample average approximation method applied to an agent-based spread model

Trade-offs exist between the point of early detection and the future cost of controlling any invasive species. Finding optimal levels of early detection, with post-border active surveillance, where time, space and randomness are explicitly considered, is computationally challenging. We use a stochastic programming model to find the optimal level of surveillance and predict damages, easing the computational challenge by combining a sample average approximation (SAA) approach and parallel processing techniques. The model is applied to the case of Asian Papaya Fruit Fly (PFF), a highly destructive pest, in Queensland, Australia. To capture the non-linearity in PFF spread, we use an agent-based model (ABM), which is calibrated to a highly detailed land-use raster map (50 m × 50 m) and weather-related data, validated against a historical outbreak. The combination of SAA and ABM sets our work apart from the existing literature. Indeed, despite its increasing popularity as a powerful analytical tool, given its granularity and capability to model the system of interest adequately, the complexity of ABM limits its application in optimizing frameworks due to considerable uncertainty about solution quality. In this light, the use of SAA ensures quality in the optimal solution (with a measured optimality gap) while still being able to handle large-scale decision-making problems. With this combination, our application suggests that the optimal (economic) trap grid size for PFF in Queensland is ˜0.7 km, much smaller than the currently implemented level of 5 km. Although the current policy implies a much lower surveillance cost per year, compared with the $2.08 million under our optimal policy, the expected total cost of an outbreak is $23.92 million, much higher than the optimal policy of roughly $7.74 million.

Endemic persistence of a highly contagious pathogen: Foot-and-mouth disease in its wildlife host

Extremely contagious pathogens are a global biosecurity threat because of their high burden of morbidity and mortality, as well as their capacity for fast-moving epidemics that are difficult to quell. Understanding the mechanisms enabling persistence of highly transmissible pathogens in host populations is thus a central problem in disease ecology. Through a combination of experimental and theoretical approaches, we investigated how highly contagious foot-and-mouth disease viruses persist in the African buffalo, which serves as their wildlife reservoir. We found that viral persistence through transmission among acutely infected hosts alone is unlikely. However, the inclusion of occasional transmission from persistently infected carriers reliably rescues the most infectious viral strain from fade-out. Additional mechanisms such as antigenic shift, loss of immunity, or spillover among host populations may be required for persistence of less transmissible strains.

Disease control as an optimization problem

In the context of epidemiology, policies for disease control are often devised through a mixture of intuition and brute-force, whereby the set of logically conceivable policies is narrowed down to a small family described by a few parameters, following which linearization or grid search is used to identify the optimal policy within the set. This scheme runs the risk of leaving out more complex (and perhaps counter-intuitive) policies for disease control that could tackle the disease more efficiently. In this article, we use techniques from convex optimization theory and machine learning to conduct optimizations over disease policies described by hundreds of parameters. In contrast to past approaches for policy optimization based on control theory, our framework can deal with arbitrary uncertainties on the initial conditions and model parameters controlling the spread of the disease, and stochastic models. In addition, our methods allow for optimization over policies which remain constant over weekly periods, specified by either continuous or discrete (e.g.: lockdown on/off) government measures. We illustrate our approach by minimizing the total time required to eradicate COVID-19 within the Susceptible-Exposed-Infected-Recovered (SEIR) model proposed by Kissler et al. (March, 2020).

Simulating the impacts of interregional mobility restriction on the spatial spread of COVID-19 in Japan

A spatial susceptible-exposed-infectious-recovered (SEIR) model is developed to analyze the effects of restricting interregional mobility on the spatial spread of the coronavirus disease 2019 (COVID-19) infection in Japan. National and local governments have requested that residents refrain from traveling between prefectures during the state of emergency. However, the extent to which restricting interregional mobility prevents infection expansion is unclear. The spatial SEIR model describes the spatial spread pattern of COVID-19 infection when people commute or travel to a prefecture in the daytime and return to their residential prefecture at night. It is assumed that people are exposed to an infection risk during their daytime activities. The spatial spread of COVID-19 infection is simulated by integrating interregional mobility data. According to the simulation results, interregional mobility restrictions can prevent the geographical expansion of the infection. On the other hand, in urban prefectures with many infectious individuals, residents are exposed to higher infection risk when their interregional mobility is restricted. The simulation results also show that interregional mobility restrictions play a limited role in reducing the total number of infected individuals in Japan, suggesting that other non-pharmaceutical interventions should be implemented to reduce the epidemic size.

Gastrointestinal nematode and Eimeria spp. infections in dairy cattle along a rural-urban gradient

Endoparasite infections can lead to considerable economic losses in dairy cattle due to decreases in milk yield and quality. Environmental and host-related factors contribute to endoparasite infection intensity and probability. Moreover, advancing urbanization influences parasite infection dynamics in livestock due to close human-animal cohabitation and changes in animal housing conditions. The aim of the present study was to investigate social-ecological effects on gastrointestinal nematode (GIN) and Eimeria spp. infections in dairy cattle along a rural-urban gradient in the emerging Indian megacity Bangalore. In this regard, 726 faecal samples from 441 dairy cattle of different ages and physiological stages were collected from 101 farms and examined at three visits between June 2017 and April 2018. Based on a survey stratification index (SSI) comprising built-up density and distance to the city center, we assigned the farms to urban, mixed and rural areas. GIN eggs were identified in the faeces of 243 cattle (33.5%; 95% confidence interval [CI]: 30.1-36.9%), and Eimeria spp. oocysts in the faeces of 151 cattle (20.8%; 95% CI: 17.9-23.7%). Co-infection rates of GIN and Eimeria spp. were 8.5 to 12.2% higher in rural compared to urban and mixed areas. The SSI effect significantly influenced Eimeria spp. infection probability and oocyst per gram of faeces (OpG; P < 0.001) with an infection probability and OpG higher than 26% and 40% for cattle kept in rural areas compared to cattle from urban areas. However, the SSI effect was not significant for the infection probability of GIN and for GIN eggs per gram of faeces (EpG). Infection probabilities and EpG/OpG were significantly higher in calves and heifers compared to lactating and dry cows. Moreover, we estimated significantly lower OpG values in summer compared to the other seasons. No differences were estimated for GIN and Eimeria spp. infection probabilities and EpG/OpG with regard to pasture access and breed. The variations in endoparasite infection intensity and probability observed along the rural-urban gradient of Bangalore reflect the variability in dairy husbandry systems governed by the social-ecological context.