Mathematical model of the 2010 foot-and-mouth disease epidemic in Japan and evaluation of control measures

Evaluation of foot and mouth disease control measures: Simulating two endemic areas of Thailand

Foot and mouth disease (FMD) is an important livestock disease in Thailand, with outbreaks occurring every year. However, the effects of FMD control measures in Thailand have received little research attention. Epidemiological models have been widely used to evaluate FMD outbreak control, but such a model has never been developed for Thailand. We constructed a stochastic between-farm transmission model to evaluate FMD control measures. The epidemiological unit of the model was the farm, which could be in different states: susceptible, latent, undetected infectious, detected infectious and recovered. The between-farm transmission was calculated by the sum of distance-dependent transmission and trade network transmission using parameters derived from FMD outbreaks in 2016-2017. We used this model to simulate the outbreaks with and without the implementation of the following control measures: culling all animals on infected farms, ring vaccination, animal movement restrictions and isolation of infected farms. The control measures were evaluated by estimating the number of secondarily infected farms and the outbreak duration for each scenario. The model was simulated in two study areas located in the Lamphaya Klang subdistrict (high farm density) and the Bo Phloi district (low farm density). The effects of control measures differed between the two study areas. When farm density was high, rigid control measures were required to prevent a major outbreak. Among all options, culling the animals on infected farms resulted in the lowest number of infected farms and the shortest outbreak duration. In contrast, for an area with a low farm density, less stringent control measures were sufficient to control the usually minor outbreaks. The results indicate that different areas require a different approach to control an outbreak of FMD.

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.

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.

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.

Pig farm vaccination against classical swine fever reduces the risk of transmission from wild boar

In 2018, classical swine fever (CSF) re-emerged in the Gifu Prefecture, central Japan, causing an on-going outbreak among wild boars and domestic pigs in the country. Consequently, oral vaccination for wild boar and compulsory vaccination for pig farms started in 2019. We have previously shown that, before vaccination in the Gifu Prefecture, the presence of CSF-infected wild boar near pig farms increased the risk of CSF transmission. This study aimed to re-evaluate the transmission risk from wild boars to pig farms under a vaccination program. The effectiveness of vaccination was evaluated by comparing the transmission risk estimated before and after the implementation of vaccinations. In this study, we focused on two affected areas, the Kanto (eastern Japan) and Kinki (west-central Japan) regions, in which eight of 11 infected farms were detected between the start of pig farm vaccinations and April 2021. Wild boar surveillance data from an area within a 50-km radius from the infected farms were used for analysis, consisting of 18,870 1-km grid cells (207 infected cells) in the Kanto region, and 15,677 cells (417 infected cells) in the Kinki region. The transmission rates in the post-vaccination period in the Kanto and Kinki regions were much lower than that in the pre-vaccination period in the Gifu Prefecture. The values of transmission kernels (h₀, transmission rate at 0 km) in the Kanto and Kinki regions decreased to 1% of the transmission kernel in the pre-vaccination period. In the pre-vaccination period, the risk of infection within 300 days was almost 95 % when one infected grid cell was detected within 1 km of a pig farm. Meanwhile, in the post-vaccination period, the risk of infection within 300 days was approximately 5% when several infected cells were detected within 1 km of a pig farm. Considering the limited effect of oral vaccination for wild boar due to distribution limitations in the Kanto and Kinki regions, vaccination on pig farms may seems to have mainly reduced the transmission risk from wild boar. However, despite the implementation of vaccination, the risk of infection on pig farms remains present due to the immunity gap of weaning pigs. Therefore, strict biosecurity measures on pig farms and an appropriate vaccination program are required to prevent and control CSF spread.

Regional Relative Risk, a Physics-Based Metric for Characterizing Airborne Infectious Disease Transmission

Airborne infectious disease transmission events occur over a wide range of spatial scales and can be an important means of disease transmission. Physics- and biology-based models can assist in predicting airborne transmission events, overall disease incidence, and disease control strategy efficacy. We describe a new theory that extends current approaches for the case in which an individual is infected by a single airborne particle, including the scenario in which numerous infectious particles are present in the air but only one causes infection. A single infectious particle can contain more than one pathogenic microorganism and be physically larger than the pathogen itself. This approach allows robust relative risk estimates even when there is wide variation in (i) individual exposures and (ii) the individual response to that exposure (the pathogen dose-response function can take any mathematical form and vary by individual). Based on this theory, we propose the regional relative risk-a new metric, distinct from the traditional relative risk metric, that compares the risk between two regions. In theory, these regions can range from individual rooms to large geographic areas. In this paper, we apply the regional relative risk metric to outdoor disease transmission events over spatial scales ranging from 50 m to 20 km, demonstrating that in many common cases minimal input information is required to use the metric. Also, we demonstrate that the model predictions are consistent with data from prior outbreaks. Future efforts could apply and validate this theory for other spatial scales, such as transmission within indoor environments. This work provides context for (i) the initial stages of an airborne disease outbreak and (ii) larger-scale disease spread, including unexpected low-probability disease "sparks" that potentially affect remote populations, a key practical issue in controlling airborne disease outbreaks. IMPORTANCE Airborne infectious disease transmission events occur over a wide range of spatial scales and can be important to disease outbreaks. We describe a new physics- and biology-based theory for the important case in which individuals are infected by a single airborne particle (even though numerous infectious particles can be emitted into the air and inhaled). Based on this theory, we propose a new epidemiological metric, regional relative risk, that compares the risk between two geographic regions (in theory, regions can range from individual rooms to large areas). Our modeling of transmission events predicts that for many scenarios of interest, minimal information is required to use this metric for locations 50 m to 20 km downwind. This prediction is consistent with data from prior disease outbreaks. Future efforts could apply and validate this theory for other spatial scales, such as indoor environments. Our results may be applicable to many airborne diseases a priori, as these results depend on the physics of airborne particulate dispersion.

Spatial model of foot-and-mouth disease outbreak in an endemic area of Thailand

Foot-and-mouth disease (FDM) is a disease of cloven-hoofed animals with high costs in animal welfare and animal production. Up to now, transmission between farms in FMD-endemic areas has been given little attention. Between farm transmission can be quantified by distance independent transmission parameters and a spatial transmission kernel indicating the rate of transmission of an infected farm to susceptible farms depending on the distance. The spatial transmission kernel and distance-independent transmission parameters were estimated from data of an FMD outbreak in Lamphaya Klang subdistrict in Thailand between 2016 and 2017. The spatial between-farm transmission rate in Lamphaya Klang subdistrict was higher compared with the spatial between-farm transmission rate from FMDV in epidemic areas. The result can be explained by the larger size of the within-farm outbreak in the endemic area due to no culling. The inclusion of distance-independent transmission parameters improved the model fit, which suggests the presence of transmission sources from outside the area and spread within the area independent of the distance between farms. The remaining distance-dependent transmission was mainly local and could be due to over-the-fence transmission or other forms of contact between nearby farms. Farm size on the kernel positively affects the transmission rate, by increasing both infectivity and susceptibility with increasing farm size. The results showed that both distance-dependent transmission and distance-independent transmission were contributed to FMDV transmission in Lamphaya Klang outbreak. These transmission parameters help to gain knowledge about FMD transmission dynamic in the endemic area.

Scientific Opinion on the assessment of the control measures for category A diseases of Animal Health Law: Foot and Mouth Disease

EFSA received a mandate from the European Commission to assess the effectiveness of some of the control measures against diseases included in the Category A list according to Regulation (EU) 2016/429 on transmissible animal diseases ('Animal Health Law'). This opinion belongs to a series of opinions where these control measures will be assessed, with this opinion covering the assessment of control measures for foot and mouth disease (FMD). In this opinion, EFSA and the AHAW Panel of experts review the effectiveness of: i) clinical and laboratory sampling procedures, ii) monitoring period and iii) the minimum radius of the protection and surveillance zones, and the minimum length of time the measures should be applied in these zones. The general methodology used for this series of opinions has been published elsewhere; nonetheless, the transmission kernels used for the assessment of the minimum radius of the protection zone of 3 km and of the surveillance zone of 10 km are shown. Several scenarios for which these control measures had to be assessed were designed and agreed prior to the start of the assessment. The monitoring period of 21 days was assessed as effective, and it was concluded that the protection and the surveillance zones comprise > 99% of the infections from an affected establishment if transmission occurred. Recommendations, provided for each of the scenarios assessed, aim to support the European Commission in the drafting of further pieces of legislation, as well as for plausible ad hoc requests in relation to FMD.

A stochastic network-based model to simulate farm-level transmission of African swine fever virus in Vietnam

African swine fever virus is highly contagious, and mortality rates reach up to 100% depending on the host, virus dose, and the transmission routes. The main objective of this study was to develop a network-based simulation model for the farm-level transmission of ASF virus to evaluate the impact of changes in farm connectivity on ASF spread in Vietnam. A hypothetical population of 1,000 pig farms was created and used for the network-based simulation, where each farm represented a node, and the connection between farms represented an edge. The three scenarios modelled in this way (baseline, low, and high) evaluated the impact of connectivity on disease transmission. The median number of infected farms was higher as the connectivity increased (low: 659, baseline: 968 and high: 993). In addition, we evaluated the impact of the culling strategy on the number of infected farms. A total of four scenarios were simulated depending on the timing of culling after a farm was infected. We found that the timing of culling at 16, 12, 8, and 6 weeks had resulted in a reduction of the number of median infected farms by 81.92%, 91.63%, 100%, and 100%, respectively. Finally, our evaluation of the implication of stability of ties between farms indicated that if the farms were to have the same trading partners for at least six months could significantly reduce the median number of infected farms to two (95th percentile: 413) than in the basic model. Our study showed that pig movements among farms had a significant influence on the transmission dynamics of ASF virus. In addition, we found that the either timing of culling, reduction in the number of trading partners each farm had, or decreased mean contact rate during the outbreaks were essential to prevent or stop further outbreaks.

Modelling the transmission and vaccination strategy for porcine reproductive and respiratory syndrome virus

Many aspects of the porcine reproductive and respiratory syndrome virus (PRRSV) between-farm transmission dynamics have been investigated, but uncertainty remains about the significance of farm type and different transmission routes on PRRSV spread. We developed a stochastic epidemiological model calibrated on weekly PRRSV outbreaks accounting for the population dynamics in different pig production phases, breeding herds, gilt development units, nurseries and finisher farms, of three hog producer companies. Our model accounted for indirect contacts by the close distance between farms (local transmission), between-farm animal movements (pig flow) and reinfection of sow farms (re-break). The fitted model was used to examine the effectiveness of vaccination strategies and complementary interventions such as enhanced PRRSV detection and vaccination delays and forecast the spatial distribution of PRRSV outbreak. The results of our analysis indicated that for sow farms, 59% of the simulated infections were related to local transmission (e.g. airborne, feed deliveries, shared equipment) whereas 36% and 5% were related to animal movements and re-break, respectively. For nursery farms, 80% of infections were related to animal movements and 20% to local transmission; while at finisher farms, it was split between local transmission and animal movements. Assuming that the current vaccines are 1% effective in mitigating between-farm PRRSV transmission, weaned pigs vaccination would reduce the incidence of PRRSV outbreaks by 3%, indeed under any scenario vaccination alone was insufficient for completely controlling PRRSV spread. Our results also showed that intensifying PRRSV detection and/or vaccination pigs at placement increased the effectiveness of all simulated vaccination strategies. Our model reproduced the incidence and PRRSV spatial distribution; therefore, this model could also be used to map current and future farms at-risk. Finally, this model could be a useful tool for veterinarians, allowing them to identify the effect of transmission routes and different vaccination interventions to control PRRSV spread.

Assessment of reproductive and growth performance of pigs on commercial swine farms in southern Kyushu, Japan

The objective of the present study was to assess the productivity of pigs to investigate the time-dependent change in productivity and compare productivity according to breeding company group and porcine reproductive and respiratory syndrome (PRRS) status on commercial swine farms in southern Kyushu, Japan. Data used in the present study were 245 annual productivity records from 2014 to 2018 obtained from 72 farms. Average sow inventory was 481.2 sows. Mean numbers of pigs weaned per sow per year and market pigs sold per sow per year were 23.7 and 21.6, respectively. Pigs born alive per litter increased from 11.1 to 11.9 pigs from 2014 to 2018 (p < .05). Farms using domestic breeding companies had similar numbers in 2016 to those using international breeding companies, but fewer pigs in 2014, 2015, 2017, and 2018 (p < .05). Farms with an unknown or unstable PRRS status had fewer pigs born alive per litter and pigs weaned per sow per year than those with stable or negative PRRS statuses (11.2 ± 0.06 vs. 11.8 ± 0.08 pigs and 22.6 ± 0.38 vs. 25.0 ± 0.22 pigs, respectively; p < .05). These results can be used to establish feasible targets and standards of performance to identify problem areas and improve production.

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.

Impact of truck contamination and information sharing on foot-and-mouth disease spreading in beef cattle production systems

As cattle movement data in the United States are scarce due to the absence of mandatory traceability programs, previous epidemic models for U.S. cattle production systems heavily rely on contact rates estimated based on expert opinions and survey data. These models are often based on static networks and ignore the sequence of movement, possibly overestimating the epidemic sizes. In this research, we adapt and employ an agent-based model that simulates beef cattle production and transportation in southwest Kansas to analyze the between-premises transmission of a highly contagious disease, foot-and-mouth disease. First, we assess the impact of truck contamination on the disease transmission with the truck agent following an independent clean-infected-clean cycle. Second, we add an information-sharing functionality such that producers/packers can trace back and forward their trade records to inform their trade partners during outbreaks. Scenario analysis results show that including indirect contact routes between premises via truck movements can significantly increase the amplitude of disease spread, compared with equivalent scenarios that only consider animal movement. Mitigation strategies informed by information sharing can effectively mitigate epidemics, highlighting the benefit of promoting information sharing in the cattle industry. In addition, we identify salient characteristics that must be considered when designing an information-sharing strategy, including the number of days to trace back and forward in the trade records and the role of different cattle supply chain stakeholders. Sensitivity analysis results show that epidemic sizes are sensitive to variations in parameters of the contamination period for a truck or a loading/unloading area of premises, and indirect contact transmission probability and future studies can focus on a more accurate estimation of these parameters.

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.

Outbreak response intervention models of vaccine-preventable diseases in humans and foot-and-mouth disease in livestock: a protocol for a systematic review

INTRODUCTION

Outbreaks of vaccine-preventable diseases continue to threaten public health, despite the proven effectiveness of vaccines. Interventions such as vaccination, social distancing and palliative care are usually implemented, either individually or in combination, to control these outbreaks. Mathematical models are often used to assess the impact of these interventions and for supporting outbreak response decision making. The objectives of this systematic review, which covers all human vaccine-preventable diseases, are to determine the relative impact of vaccination compared with other outbreak interventions, and to ascertain the temporal trends in the use of modelling in outbreak response decision making. We will also identify gaps and opportunities for future research through a comparison with the foot-and-mouth disease outbreak response modelling literature, which has good examples of the use of modelling to inform outbreak response intervention decision making.

METHODS AND ANALYSIS

We searched on PubMed, Scopus, Web of Science, Google Scholar and some preprint servers from the start of indexing to 15 January 2020. Inclusion: modelling studies, published in English, that use a mechanistic approach to evaluate the impact of an outbreak intervention. Exclusion: reviews, and studies that do not describe or use mechanistic models or do not describe an outbreak. We will extract data from the included studies such as their objectives, model types and composition, and conclusions on the impact of the intervention. We will ascertain the impact of models on outbreak response decision making through visualisation of time trends in the use of the models. We will also present our results in narrative style.

ETHICS AND DISSEMINATION

This systematic review will not require any ethics approval since it only involves scientific articles. The review will be disseminated in a peer-reviewed journal and at various conferences fitting its scope.

PROSPERO REGISTRATION NUMBER

CRD42020160803.

A Meta-Population Model of Potential Foot-and-Mouth Disease Transmission, Clinical Manifestation, and Detection Within U.S. Beef Feedlots

Foot-and-mouth disease (FMD) has not been reported in the U.S. since 1929. Recent outbreaks in previously FMD-free countries raise concerns about potential FMD introductions in the U.S. Mathematical modeling is the only tool for simulating infectious disease outbreaks in non-endemic territories. In the majority of prior studies, FMD virus (FMDv) transmission on-farm was modeled assuming homogenous animal mixing. This assumption is implausible for U.S. beef feedlots which are divided into multiple home-pens without contact between home-pens except fence line with contiguous home-pens and limited mixing in hospital pens. To project FMDv transmission and clinical manifestation in a feedlot, we developed a meta-population stochastic model reflecting the contact structure. Within a home-pen, the dynamics were represented assuming homogenous animal mixing by a modified SLIR (susceptible-latent-infectious-recovered) model with four additional compartments tracing cattle with subclinical or clinical FMD and infectious status. Virus transmission among home-pens occurred via cattle mixing in hospital-pen(s), cowboy pen rider movements between home-pens, airborne, and for contiguous home-pens fence-line and via shared water-troughs. We modeled feedlots with a one-time capacity of 4,000 (small), 12,000 (medium), and 24,000 (large) cattle. Common cattle demographics, feedlot layout, endemic infectious and non-infectious disease occurrence, and production management were reflected. Projected FMD-outbreak duration on a feedlot ranged from 49 to 82 days. Outbreak peak day (with maximum number of FMD clinical cattle) ranged from 24 (small) to 49 (large feedlot). Detection day was 4-12 post-FMD-introduction with projected 28, 9, or 4% of cattle already infected in a small, medium, or large feedlot, respectively. Depletion of susceptible cattle in a feedlot occurred by day 23-51 post-FMD-introduction. Parameter-value sensitivity analyses were performed for model outputs. Detection occurred sooner if there was a higher initial proportion of latent animals in the index home-pen. Shorter outbreaks were associated with a shorter latent period and higher bovine respiratory disease morbidity (impacting the in-hospital-pen cattle mixing occurrence). This first model of potential FMD dynamics on U.S. beef feedlots shows the importance of capturing within-feedlot cattle contact structure for projecting infectious disease dynamics. Our model provides a tool for evaluating FMD outbreak control strategies.

FMD-VS: A virtual sensor to index FMD virus scattering

Foot-and-mouth disease (FMD) models—analytical models for tracking and analyzing FMD outbreaks—are known as dominant tools for examining the spread of the disease under various conditions and assessing the effectiveness of countermeasures. There has been some remarkable progress in modeling research since the UK epidemic in 2001. Several modeling methods have been introduced, developed, and are still growing. However, in 2010 when a FMD outbreak occurred in the Miyazaki prefecture, a crucial problem reported: Once a regional FMD outbreak occurs, municipal officials in the region must make various day-to-day decisions throughout this period of vulnerability. The deliverables of FMD modeling research in its current state appear insufficient to support the daily judgments required in such cases. FMD model can be an efficient support tool for prevention decisions. It requires being conversant with modeling and its preconditions. Therefore, most municipal officials with no knowledge or experience found full use of the model difficult. Given this limitation, the authors consider methods and systems to support users of FMD models who must make real-time epidemic-related judgments in the infected areas. We propose a virtual sensor, designated “FMD-VS,” to index FMD virus scattering in conditions where there is once a notion of FMD; and (2) shows how we apply the developed FMD-VS technique during an outbreak. In (1), we show our approach to constructing FMD-VS based on the existing FMD model and offer an analysis and evaluation method to assess its performance. We again present the results produced when the technique applied to 2010 infection data from the Miyazaki Prefecture. For (2), we outline the concept of a method that supports the prevention judgment of municipal officials and show how to use FMD-VS.

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.

Modelling infectious viral diseases in swine populations: a state of the art

Mathematical modelling is nowadays a pivotal tool for infectious diseases studies, completing regular biological investigations. The rapid growth of computer technology allowed for development of computational tools to address biological issues that could not be unravelled in the past. The global understanding of viral disease dynamics requires to account for all interactions at all levels, from within-host to between-herd, to have all the keys for development of control measures. A literature review was performed to disentangle modelling frameworks according to their major objectives and methodologies. One hundred and seventeen articles published between 1994 and 2020 were found to meet our inclusion criteria, which were defined to target papers representative of studies dealing with models of viral infection dynamics in pigs. A first descriptive analysis, using bibliometric indexes, permitted to identify keywords strongly related to the study scopes. Modelling studies were focused on particular infectious agents, with a shared objective: to better understand the viral dynamics for appropriate control measure adaptation. In a second step, selected papers were analysed to disentangle the modelling structures according to the objectives of the studies. The system representation was highly dependent on the nature of the pathogens. Enzootic viruses, such as swine influenza or porcine reproductive and respiratory syndrome, were generally investigated at the herd scale to analyse the impact of husbandry practices and prophylactic measures on infection dynamics. Epizootic agents (classical swine fever, foot-and-mouth disease or African swine fever viruses) were mostly studied using spatio-temporal simulation tools, to investigate the efficiency of surveillance and control protocols, which are predetermined for regulated diseases. A huge effort was made on model parameterization through the development of specific studies and methodologies insuring the robustness of parameter values to feed simulation tools. Integrative modelling frameworks, from within-host to spatio-temporal models, is clearly on the way. This would allow to capture the complexity of individual biological variabilities and to assess their consequences on the whole system at the population level. This would offer the opportunity to test and evaluate in silico the efficiency of possible control measures targeting specific epidemiological units, from hosts to herds, either individually or through their contact networks. Such decision support tools represent a strength for stakeholders to help mitigating infectious diseases dynamics and limiting economic consequences.

Identification of High-Risk Areas for the Spread of Highly Pathogenic Avian Influenza in Central Luzon, Philippines

Highly pathogenic avian influenza virus (HPAIV) is a major problem in the poultry industry. It is highly contagious and is associated with a high mortality rate. The Philippines experienced an outbreak of avian influenza (AI) in 2017. As there is always a risk of re-emergence, efforts to manage disease outbreaks should be optimal. Linked to this is the need for an effective surveillance procedure to capture disease outbreaks at their early stage. Risk-based surveillance is the most effective and economical approach to outbreak management. This study evaluated the potential of commercial poultry farms in Central Luzon to transmit HPAI by calculating their respective reproductive ratios (R0). The reproductive number for each farm is based on the spatial kernel and the infectious period. A risk map has been created based on the calculated R₀. There were 882 (76.63%) farms with R0 < 1. Farms with R0 ≥ 1 were all located in Pampanga Province. These farms were concentrated in the towns of San Luis (n = 12) and Candaba (n = 257). This study demonstrates the utility of mapping farm-level R0 estimates for informing HPAI risk management activities.

Transmission network reconstruction for foot-and-mouth disease outbreaks incorporating farm-level covariates

Transmission network modelling to infer ‘who infected whom’ in infectious disease outbreaks is a highly active area of research. Outbreaks of foot-and-mouth disease have been a key focus of transmission network models that integrate genomic and epidemiological data. The aim of this study was to extend Lau’s systematic Bayesian inference framework to incorporate additional parameters representing predominant species and numbers of animals held on a farm. Lau’s Bayesian Markov chain Monte Carlo algorithm was reformulated, verified and pseudo-validated on 100 simulated outbreaks populated with demographic data Japan and Australia. The modified model was then implemented on genomic and epidemiological data from the 2010 outbreak of foot-and-mouth disease in Japan, and outputs compared to those from the SCOTTI model implemented in BEAST2. The modified model achieved improvements in overall accuracy when tested on the simulated outbreaks. When implemented on the actual outbreak data from Japan, infected farms that held predominantly pigs were estimated to have five times the transmissibility of infected cattle farms and be 49% less susceptible. The farm-level incubation period was 1 day shorter than the latent period, the timing of the seeding of the outbreak in Japan was inferred, as were key linkages between clusters and features of farms involved in widespread dissemination of this outbreak. To improve accessibility the modified model has been implemented as the R package ‘BORIS’ for use in future outbreaks.

Optimal surveillance against foot-and-mouth disease: A sample average approximation approach

Decisions surrounding the presence of infectious diseases are typically made in the face of considerable uncertainty. However, the development of models to guide these decisions has been substantially constrained by computational difficulty. This paper focuses on the case of finding the optimal level of surveillance against a highly infectious animal disease where time, space and randomness are fully considered. We apply the Sample Average Approximation approach to solve our problem, and to control model dimension, we propose the use of an infection tree model, in combination with sensible ‘tree-pruning’ and parallel processing techniques. Our proposed model and techniques are generally applicable to a number of disease types, but we demonstrate the approach by solving for optimal surveillance levels against foot-and-mouth disease using bulk milk testing as an active surveillance protocol, during an epidemic, among 42,279 farms, fully characterised by their location, livestock type and size, in the state of Victoria, Australia.

Realistic assumptions about spatial locations and clustering of premises matter for models of foot-and-mouth disease spread in the United States

Spatially explicit livestock disease models require demographic data for individual farms or premises. In the U.S., demographic data are only available aggregated at county or coarser scales, so disease models must rely on assumptions about how individual premises are distributed within counties. Here, we addressed the importance of realistic assumptions for this purpose. We compared modeling of foot and mouth disease (FMD) outbreaks using simple randomization of locations to premises configurations predicted by the Farm Location and Agricultural Production Simulator (FLAPS), which infers location based on features such as topography, land-cover, climate, and roads. We focused on three premises-level Susceptible-Exposed-Infectious-Removed models available from the literature, all using the same kernel approach but with different parameterizations and functional forms. By computing the basic reproductive number of the infection (R₀) for both FLAPS and randomized configurations, we investigated how spatial locations and clustering of premises affects outbreak predictions. Further, we performed stochastic simulations to evaluate if identified differences were consistent for later stages of an outbreak. Using Ripley’s K to quantify clustering, we found that FLAPS configurations were substantially more clustered at the scales relevant for the implemented models, leading to a higher frequency of nearby premises compared to randomized configurations. As a result, R₀ was typically higher in FLAPS configurations, and the simulation study corroborated the pattern for later stages of outbreaks. Further, both R₀ and simulations exhibited substantial spatial heterogeneity in terms of differences between configurations. Thus, using realistic assumptions when de-aggregating locations based on available data can have a pronounced effect on epidemiological predictions, affecting if, where, and to what extent FMD may invade the population. We conclude that methods such as FLAPS should be preferred over randomization approaches.

When modeling the spread of infectious livestock diseases such as foot-and-mouth disease (FMD), the distance between premises is an important aspect. In the U.S., locations of premises are not available, forcing modelers to make assumptions about their coordinates. Such assumptions can be more or less crude and will impact the conclusions drawn from the model. To investigate the impact of such assumptions, we modeled outbreaks of FMD within the cattle population of the U.S. under two assumptions about premises locations. Their position was either randomly distributed within counties or informed by a state-of-the-art method developed specifically to simulate realistic locations of agricultural operations. We found that the higher degree of spatial clustering of premises associated with more realistic assumptions about locations leads to a substantially higher risk of outbreaks. Our results also show that the amount with which the risk is under-estimated by randomizing locations is unevenly distributed across the landscape. Together, these findings show a clear support for using informed methods to determine the spatial locations of premises and highlight the importance of spatial clustering when modeling FMD-like diseases.

Estimation of infection risk on pig farms in infected wild boar areas-Epidemiological analysis for the reemergence of classical swine fever in Japan in 2018

In September 2018, classical swine fever (CSF) reemerged in Japan after 26 years' absence. The first case was detected at a pig farm in Gifu Prefecture, in the center of Japan, and the disease spread to both domestic pigs and wild boar (Sus scrofa). The spread of CSF in wild boar is extremely difficult to control and is thus a great threat to domestic pig farms, and understanding the transmission risk from wild boar to domestic pigs is essential to implement effective control measures that will prevent domestic pig infection. Therefore, this study elucidates the transmission risk from wild boar to domestic pigs by introducing a transmission kernel that is dependent on the distance between infected wild boar and pig farms, and then estimating the risk area of infection from wild boar by describing the transmission probability. The study used epidemiological data from Gifu Prefecture in the period from September 2018 to March 2019, including a total of 171 1-km grid cells where an infected wild boar was detected and pig farm data from 13 infected and 34 uninfected farms. The estimated infection risk area within 28 days matched well with the observed data. The risk area widened gradually during the epidemic, and at the end of March, the risk area extended over a range of approximately 75 km from east to west and 40 km from north to south (almost 3000 km²). Ten out of the 13 infected farms and four out of the 34 uninfected farms were located within the high-risk area (>60 % infection probability). In contrast, one infected farm and 18 uninfected farms were located within the low-risk area (<5 % infection probability). When several infected grid cells were detected within 5 km of a pig farm, the risk of infection from wild boar within 28 days was more than 5 %. This analysis provides an estimate of the potential spatial range over which CSF virus can spread between wild boar and domestic pig farms, and can be used to inform the early detection of CSF-suspected pigs and the strengthening of biosecurity measures that will effectively prevent and control the disease based on the infection risk level.

Multi-scale dynamics of infectious diseases

To address the challenge of multiscale dynamics of infectious diseases, the Mathematical Biosciences Institute organized a workshop at The Ohio State University to bring together scientists from a variety of disciplines to share expertise gained through looking at infectious diseases across different scales. The researchers at the workshop, held in April 2018, were specifically looking at three model systems: foot-and-mouth disease, vector-borne diseases and enteric diseases. Although every multiscale model must be necessarily derived from a multiscale system, not every multiscale system has to lead to multiscale models. These three model systems seem to have produced a variety of both multiscale and integrated single-scale mechanistic models that have developed their own strengths and particular challenges. Here, we present papers from some of the workshop participants to show the breadth of the field.

Effects of regional differences and demography in modelling foot-and-mouth disease in cattle at the national scale

Foot-and-mouth disease (FMD) is a fast-spreading viral infection that can produce large and costly outbreaks in livestock populations. Transmission occurs at multiple spatial scales, as can the actions used to control outbreaks. The US cattle industry is spatially expansive, with heterogeneous distributions of animals and infrastructure. We have developed a model that incorporates the effects of scale for both disease transmission and control actions, applied here in simulating FMD outbreaks in US cattle. We simulated infection initiating in each of the 3049 counties in the contiguous US, 100 times per county. When initial infection was located in specific regions, large outbreaks were more likely to occur, driven by infrastructure and other demographic attributes such as premises clustering and number of cattle on premises. Sensitivity analyses suggest these attributes had more impact on outbreak metrics than the ranges of estimated disease parameter values. Additionally, although shipping accounted for a small percentage of overall transmission, areas receiving the most animal shipments tended to have other attributes that increase the probability of large outbreaks. The importance of including spatial and demographic heterogeneity in modelling outbreak trajectories and control actions is illustrated by specific regions consistently producing larger outbreaks than others.

Environmental persistence of foot-and-mouth disease virus applied to endemic regions

The consequences of foot-and-mouth disease impact regional economies and food security through animal mortality and morbidity, trade restrictions and burdens to veterinary infrastructure. Despite efforts to control the disease, some regions, mostly in warmer climates, persistently report disease outbreaks. Consequently, it is necessary to understand how environmental factors influence transmission, of this economically devastating disease. Extensive research covers basic aetiology and transmission potential of livestock and livestock products for foot-and-mouth disease virus (FMDV), with a subset evaluating environmental survival. However, this subset, completed in the early to mid-20th century in Northern Europe and the United States, is not easily generalized to today's endemic locations. This review uncovered 20 studies, to assess current knowledge and analyse the effects of environmental variables on FMDV survival, using a Cox proportional hazards (Coxph) model. However, the dataset is limited, for example pH was included in three studies and only five studies reported both relative humidity (RH) and temperature. After dropping pH from the analysis, our results suggest that temperature alone does not describe FMDV survival; instead, interactions between RH and temperature have broader impacts across various conditions. For instance, FMDV is expected to survive longer during the wet season (survival at day 50 is ~90% at 16°C and 86% RH) versus the dry season (survival at day 50 approaches 0% at 16°C and 37.5% RH) or comparatively in the UK versus the Southwestern United States. Additionally, survival on vegetation topped 70% on day 75 when conditions exceeded 20°C with high RH (86%), drastically higher than the survival on inanimate surfaces at the same temperature and RH (~0%). This is important in tropical regions, where high temperatures can persist throughout the year, but RH varies. Therefore, parameter estimates, for disease modelling and control in endemic areas, require environmental survival data from a wider range of conditions.

Reconstructing a transmission network and identifying risk factors of secondary transmissions in the 2010 foot-and-mouth disease outbreak in Japan

Research aimed at understanding transmission networks, representing a network of "who infected whom" for an infectious disease outbreak, have been actively conducted in recent years. Transmission network models incorporating epidemiological and genetic data are valuable for elucidating disease transmission pathways. In this study, we reconstructed the transmission network of the foot-and-mouth disease (FMD) epidemic in Japan in 2010, and explored farm-level risk factors associated with increased risk of secondary transmission. A published, systematic Bayesian transmission network model was applied to epidemiological data of 292 infected farms and whole genome sequence data of 104 of the infected farms. This model can make inferences for known infected farms even lacking genetic data. After estimating the consensus network, the accuracy of the network was examined by comparison with epidemiological data. Then, risk factors inferred to have been sources of secondary transmission were explored using zero-inflated Poisson regression model. As far as we are aware, this study represents the largest FMD outbreak transmission network to be published by such means combining epidemiological and genetic data. The consensus network reasonably generated the epidemiological links, which were estimated from the actual epidemiological investigation. Among 292 farms, 101 farms (35%) were inferred to have been the sources of secondary transmission, and amongst these farms, the median number of secondary cases was 2 (min:1-max:18) farms. The farm-type (small and large -sized pig farms), the number of days from onset to notification, and the number of susceptible farms within a 1-km radius were significantly associated with secondary transmission. Transmission network modelling enabled inference of the connections between infected farms during the FMD epidemic and identified important factors for controlling the risk of secondary transmission. This study demonstrated that the predominant susceptible species held on a farm, farm size, and animal density were associated with increased onwards transmission.

The implementation of cattle market closure strategies to mitigate the foot-and-mouth disease epidemics: A contact modeling approach

Foot-and-mouth disease (FMD) is one of the most endemic diseases in livestock worldwide. The disease occurrence generally results in a huge economic impact. The virus may distribute across countries or even continents along the contact network of animal movements. The present study, therefore, aimed to explore a cattle movement network originated in Tak, a Thailand-Myanmar bordered province and to demonstrate how FMDV spread among the nodes of market, source and destination. Subsequently, we examined the effectiveness of market closure intervention. The market-market (M-M) network was constructed to highlight the inter-market connections and the FMDV was modeled to spread along the trade chain. Four market closure scenarios based on rapidness and duration of implementation were examined. Our results indicate that two of the three major markets located in the province were highly connected and a strongly connected component was identified. The intra-provincial animal movements, which were currently overlooked, should be moved into sights as most of the high-risk sources for FMD epidemics were recognized in a close proximity to the cattle markets. Simultaneously, remote destinations across the country were identified. The inter-provincial animal movement control must be strengthened once FMD outbreak is notified. Based on our simulations, closing markets with low inter-market connectivity may not prevent the spread of FMDV. A selective market closure strategy targeting highly connected markets together with cattle trader tracking system was an alternative approach. However, socio-economic consequences regarding this intervention must be considered.

Spatial transmission of H5N2 highly pathogenic avian influenza between Minnesota poultry premises during the 2015 outbreak

The spatial spread of highly pathogenic avian influenza (HPAI) H5N2 during the 2015 outbreak in the U.S. state of Minnesota was analyzed through the estimation of a spatial transmission kernel, which quantifies the infection hazard an infectious premises poses to an uninfected premises some given distance away. Parameters were estimated using a maximum likelihood method for the entire outbreak as well as for two phases defined by the daily number of newly detected HPAI-positive premises. The results indicate both a strong dependence of the likelihood of transmission on distance and a significant distance-independent component of outbreak spread for the overall outbreak. The results further suggest that HPAI spread differed during the later phase of the outbreak. The estimated spatial transmission kernel was used to compare the Minnesota outbreak with previous HPAI outbreaks in the Netherlands and Italy to contextualize the Minnesota transmission kernel results and make additional inferences about HPAI transmission during the Minnesota outbreak. Lastly, the spatial transmission kernel was used to identify high risk areas for HPAI spread in Minnesota. Risk maps were also used to evaluate the potential impact of an early marketing strategy implemented by poultry producers in a county in Minnesota during the outbreak, with results providing evidence that the strategy was successful in reducing the potential for HPAI spread.

Clinical and infection dynamics of foot-and-mouth disease in beef feedlot cattle: An expert survey

Parameterizing mathematical models of foot-and-mouth disease virus (FMDv) transmission is challenging due to knowledge gaps on the variable dynamics in susceptible populations. Expert opinion surveys are an approach to gather data on topics where no data have been reported. The objective of this study was to collect-via an expert-opinion survey-key parameter values of the potential FMD natural history and transmissibility in beef feedlot cattle in the U.S. Experts with experience working with FMD in endemic and non-endemic settings were targeted. Parameters surveyed were: duration of infection and disease stages, proportions of animals with specific clinical manifestations, duration and extent of the reduction in feed consumption, and probabilities of severe clinical disease and FMDv transmission. We surveyed the parameter values for infections by strains of different virulence, different infection doses, and routes of transmission. Twenty-seven experts from around the world agreed to participate and 16 (59%) completed the survey. The expert responses to individual questions were resampled via Monte Carlo simulations; to the resulting distributions, candidate theoretical distributions were fitted using the maximum likelihood method and the sought parameter values estimated based on the best-fit distributions. Of the infection stages, the estimates of the expected FMD latent period in beef feedlot ranged from 1.7 to 5.3 days and the infectious period from 5.6 to 10.9 days. Of the disease stages, the estimated incubation period ranged from 2.9 to 6.1 days, subclinical period from 1.2 to 2.8 days, and clinical period from 4.2 to 7.5 days. Probability of developing clinical disease after infection varied from 82% (IQ range 90-70%) with high-virulent to 63% (IQ range 89-60%) with low-virulent strains. Reduction in feed consumption was estimated to last 5 (SD ± 2) days in cattle infected by a low-virulent FMDv strain and 7 (SD ± 2) days for high virulent strains. The study results can be used in combination with experimental and outbreak investigation data to parameterize FMDv-transmission models to evaluate intervention responses during hypothetical FMD epidemics in beef feedlot populations in the U.S.

Need for speed: An optimized gridding approach for spatially explicit disease simulations

Numerical models for simulating outbreaks of infectious diseases are powerful tools for informing surveillance and control strategy decisions. However, large-scale spatially explicit models can be limited by the amount of computational resources they require, which poses a problem when multiple scenarios need to be explored to provide policy recommendations. We introduce an easily implemented method that can reduce computation time in a standard Susceptible-Exposed-Infectious-Removed (SEIR) model without introducing any further approximations or truncations. It is based on a hierarchical infection process that operates on entire groups of spatially related nodes (cells in a grid) in order to efficiently filter out large volumes of susceptible nodes that would otherwise have required expensive calculations. After the filtering of the cells, only a subset of the nodes that were originally at risk are then evaluated for actual infection. The increase in efficiency is sensitive to the exact configuration of the grid, and we describe a simple method to find an estimate of the optimal configuration of a given landscape as well as a method to partition the landscape into a grid configuration. To investigate its efficiency, we compare the introduced methods to other algorithms and evaluate computation time, focusing on simulated outbreaks of foot-and-mouth disease (FMD) on the farm population of the USA, the UK and Sweden, as well as on three randomly generated populations with varying degree of clustering. The introduced method provided up to 500 times faster calculations than pairwise computation, and consistently performed as well or better than other available methods. This enables large scale, spatially explicit simulations such as for the entire continental USA without sacrificing realism or predictive power.

Numerical models for simulating the outbreak of infectious disease are powerful tools that can be used to inform policy decisions by simulating outbreaks and control actions. However, they rely on considerable computational power to explore all outcomes and scenarios of interest. Focusing on model types commonly used for livestock diseases, we here introduce novel algorithms for efficient computation, alongside techniques to optimize them based on simplifying assumptions. Through simulations of FMD outbreak in the US, the UK and Sweden, as well as in computer generated landscapes, we test how these methods perform under realistic conditions. We find that our optimization techniques works well, and when the introduced algorithms are implemented with these optimizations, computation time can be reduced by more than two orders of magnitude compared to pairwise calculations. We propose that the considered algorithms—which are straight forward to implement—will be useful for simulation of a wide range of diseases, and will promote the use of simulation models for policy recommendation.

Data-Driven Risk Assessment from Small Scale Epidemics: Estimation and Model Choice for Spatio-Temporal Data with Application to a Classical Swine Fever Outbreak

Livestock epidemics have the potential to give rise to significant economic, welfare, and social costs. Incursions of emerging and re-emerging pathogens may lead to small and repeated outbreaks. Analysis of the resulting data is statistically challenging but can inform disease preparedness reducing potential future losses. We present a framework for spatial risk assessment of disease incursions based on data from small localized historic outbreaks. We focus on between-farm spread of livestock pathogens and illustrate our methods by application to data on the small outbreak of Classical Swine Fever (CSF) that occurred in 2000 in East Anglia, UK. We apply models based on continuous time semi-Markov processes, using data-augmentation Markov Chain Monte Carlo techniques within a Bayesian framework to infer disease dynamics and detection from incompletely observed outbreaks. The spatial transmission kernel describing pathogen spread between farms, and the distribution of times between infection and detection, is estimated alongside unobserved exposure times. Our results demonstrate inference is reliable even for relatively small outbreaks when the data-generating model is known. However, associated risk assessments depend strongly on the form of the fitted transmission kernel. Therefore, for real applications, methods are needed to select the most appropriate model in light of the data. We assess standard Deviance Information Criteria (DIC) model selection tools and recently introduced latent residual methods of model assessment, in selecting the functional form of the spatial transmission kernel. These methods are applied to the CSF data, and tested in simulated scenarios which represent field data, but assume the data generation mechanism is known. Analysis of simulated scenarios shows that latent residual methods enable reliable selection of the transmission kernel even for small outbreaks whereas the DIC is less reliable. Moreover, compared with DIC, model choice based on latent residual assessment correlated better with predicted risk.

Evaluation of the Control Strategy for the 2010 Foot-and-Mouth Disease Outbreak in Japan Using Disease Simulation

In 2010, Japan experienced a foot-and-mouth disease (FMD) epidemic where 292 premises were infected over a period of 75 days. The epidemic was controlled by stamping-out and vaccination, applied 5 weeks after the first confirmation of disease within a 10 km radius of identified infected places. This study aimed at identifying the role of emergency vaccination to epidemic control while adjusting for the dynamic pattern of local spread, and assessing alternative vaccination strategies, using a disease simulation model. Our results indicate that the overall hazard of local spread remained high throughout the silent spread phase and the first two weeks post-detection, with significant reduction occurring from week 3 onwards. The estimated effectiveness of emergency vaccination quantified as reduction in the hazard of infection was at most 81% and 44% for cattle and pig farms, respectively. The vaccination strategy reduced the simulated median number of IPs by 22%, epidemic duration by 64% and culling duration by 52%, but increased the total number of infected or vaccinated premises subject to culling by 144% compared with no vaccination. The simulation indicated that vaccination starting 2 weeks earlier (3 weeks post-first detection) with a smaller vaccination radius (3 km) was more effective for eradication of the epidemic compared with the actually implemented strategy.

Evidence for Emergency Vaccination Having Played a Crucial Role to Control the 1965/66 Foot-and-Mouth Disease Outbreak in Switzerland

Foot-and-mouth disease (FMD) is a highly contagious disease that caused several large outbreaks in Europe in the last century. The last important outbreak in Switzerland took place in 1965/66 and affected more than 900 premises and more than 50,000 animals were slaughtered. Large-scale emergency vaccination of the cattle and pig population has been applied to control the epidemic. In recent years, many studies have used infectious disease models to assess the impact of different disease control measures, including models developed for diseases exotic for the specific region of interest. Often, the absence of real outbreak data makes a validation of such models impossible. This study aimed to evaluate whether a spatial, stochastic simulation model (the Davis Animal Disease Simulation model) can predict the course of a Swiss FMD epidemic based on the available historic input data on population structure, contact rates, epidemiology of the virus, and quality of the vaccine. In addition, the potential outcome of the 1965/66 FMD epidemic without application of vaccination was investigated. Comparing the model outcomes to reality, only the largest 10% of the simulated outbreaks approximated the number of animals being culled. However, the simulation model highly overestimated the number of culled premises. While the outbreak duration could not be well reproduced by the model compared to the 1965/66 epidemic, it was able to accurately estimate the size of the area infected. Without application of vaccination, the model predicted a much higher mean number of culled animals than with vaccination, demonstrating that vaccination was likely crucial in disease control for the Swiss FMD outbreak in 1965/66. The study demonstrated the feasibility to analyze historical outbreak data with modern analytical tools. However, it also confirmed that predicted epidemics from a most carefully parameterized model cannot integrate all eventualities of a real epidemic. Therefore, decision makers need to be aware that infectious disease models are useful tools to support the decision-making process but their results are not equal valuable as real observations and should always be interpreted with caution.

Data-Driven Models of Foot-and-Mouth Disease Dynamics: A Review

Foot-and-mouth disease virus (FMDV) threatens animal health and leads to considerable economic losses worldwide. Progress towards minimizing both veterinary and financial impact of the disease will be made with targeted disease control policies. To move towards targeted control, specific targets and detailed control strategies must be defined. One approach for identifying targets is to use mathematical and simulation models quantified with accurate and fine-scale data to design and evaluate alternative control policies. Nevertheless, published models of FMDV vary in modelling techniques and resolution of data incorporated. In order to determine which models and data sources contain enough detail to represent realistic control policy alternatives, we performed a systematic literature review of all FMDV dynamical models that use host data, disease data or both data types. For the purpose of evaluating modelling methodology, we classified models by control strategy represented, resolution of models and data, and location modelled. We found that modelling methodology has been well developed to the point where multiple methods are available to represent detailed and contact-specific transmission and targeted control. However, detailed host and disease data needed to quantify these models are only available from a few outbreaks. To address existing challenges in data collection, novel data sources should be considered and integrated into models of FMDV transmission and control. We suggest modelling multiple endemic areas to advance local control and global control and better understand FMDV transmission dynamics. With incorporation of additional data, models can assist with both the design of targeted control and identification of transmission drivers across geographic boundaries.

Potential impact of species and livestock density on the epidemic size and effectiveness of control measures for foot-and-mouth disease in Japan

The characteristics of a livestock area, including farm density and animal species, influence the spread of foot-and-mouth disease (FMD). In this study, the impact of livestock area on FMD epidemics was examined using an FMD transmission model. For this simulation, three major livestock areas were selected: the 2010 FMD epidemic area in Japan as the baseline area (BS), a cattle and pig mixed production area (CP) and a cattle production area (C). Simulation results demonstrated that under the 24-hr culling policy, only 12% of epidemics among 1,000 simulations were abated within 100 days in the CP area, whereas 90% of the epidemics ceased in the BS area. In the C area, all epidemics were successfully contained within 100 days. Evaluation of additional control measures in the CP area showed that the 0.5-km pre-emptive culling, even when only targeting pig farms, raised the potential for successful containment to 94%. A 10-km vaccination on day 7 or 14 after initial detection was also effective in halting the epidemics (80%), but accompanied a large number of culled or vaccinated farms. The combined strategy of 10-km vaccination and 0.5-km pre-emptive culling targeting pig farms succeeded in containing all epidemics within 100 days. The present study suggests the importance of preparedness for the 24-hr culling policy and additional control measures when an FMD outbreak occurs in a densely populated area. Considering the characteristics of the livestock area is important in planning FMD control strategies.

Post-traumatic stress disorder in participants of foot-and-mouth disease epidemic control in Miyazaki, Japan, in 2010

Foot-and-mouth disease (FMD) occurred in Miyazaki, Japan, in 2010, and 290,000 animals were culled. This paper describes the mental distress of the volunteers who had been dispatched to Miyazaki for disease control two years after the epidemic. It also assesses risk factors for post-traumatic stress disorder (PTSD). A participatory appraisal and self-administered questionnaire survey were conducted in 2012 for those who were dispatched to Miyazaki in 2010. The Impact of Event Scale-Revised (IES-R) was used as an indicator of PTSD, and univariate and multivariable analyses were performed. Of the 875 respondents, 1.3% had higher IES-R scores than the cut-off point (25), which is suggestive of PTSD. Mental stresses during and soon after FMD control and after two years were described. Four risk factors associated with high IES-R scores were found: transporting culled animals (P<0.01), stress during FMD control (P<0.01) and at the time of the survey (P<0.01), and lack of someone to talk to about FMD-associated stress at the time of the survey (P<0.01). Veterinarians, livestock technicians and clerical officers involved in FMD control still suffer from mental stress two years later. Public services should provide an opportunity for them to consult with mental health specialists. These findings should be used to better prepare workers who deal with infectious diseases of animals, especially when they must be culled. The establishment of a collaborative framework between veterinary and mental health services is recommended.

Evaluation of the transmission risk of foot-and-mouth disease in Japan

The transmission risk of foot-and-mouth disease (FMD) in Japan was evaluated using a mathematical FMD transmission model. The distance-based transmission rate between farms, which was parameterized using the FMD epidemic data in 2010 in Japan, was used to calculate the local-level reproduction numbers-expected numbers of secondary infections caused by one infected farm-for all cattle and pig farms in the country, which were then visualized as a risk map. The risk map demonstrated the spatial heterogeneity of transmission risk in the country and identified risk areas with higher possibility of disease spread. This result suggests that, particularly in high-risk areas, it is important to prepare for the smooth and efficient implementation of control measures against FMD outbreaks.