Modelling norovirus dynamics within oysters emphasises potential food safety issues associated with current testing & depuration protocols.

Norovirus is a significant global cause of viral gastroenteritis, with raw oyster consumption often linked to such outbreaks due to their filter-feeding in harvest waters. National water quality and depuration/relaying times are often classified using Escherichia coli, a poor proxy for norovirus levels in shellfish. The current norovirus assay is limited to only the digestive tracts of oysters, meaning the total norovirus load of an oyster may differ from reported results. These limitations motivated this work, building upon previous modelling by the authors, and considers the sequestration of norovirus into observed and cryptic (unobservable) compartments within each oyster. Results show that total norovirus levels in shellfish batches exhibit distinct peaks during the early depuration stages, with each peak's magnitude dependent on the proportion of cryptic norovirus. These results are supported by depuration trial data and other studies, where viral levels often exhibit multiphase decays. This work's significant result is that any future norovirus legislation needs to consider not only the harvest site's water classification but also the total viral load present in oysters entering the market. We show that 62 h of depuration should be undertaken before any norovirus testing is conducted on oyster samples, being the time required for cryptic viral loads to have transited into the digestive tracts where they can be detected by current assay, or have exited the oyster.

SCoVMod - a spatially explicit mobility and deprivation adjusted model of first wave COVID-19 transmission dynamics.

Background: Mobility restrictions prevent the spread of infections to disease-free areas, and early in the coronavirus disease 2019 (COVID-19) pandemic, most countries imposed severe restrictions on mobility as soon as it was clear that containment of local outbreaks was insufficient to control spread. These restrictions have adverse impacts on the economy and other aspects of human health, and it is important to quantify their impact for evaluating their future value. Methods: Here we develop Scotland Coronavirus transmission Model (SCoVMod), a model for COVID-19 in Scotland, which presents unusual challenges because of its diverse geography and population conditions. Our fitted model captures spatio-temporal patterns of mortality in the first phase of the epidemic to a fine geographical scale. Results: We find that lockdown restrictions reduced transmission rates down to an estimated 12\% of its pre-lockdown rate. We show that, while the timing of COVID-19 restrictions influences the role of the transmission rate on the number of COVID-related deaths, early reduction in long distance movements does not. However, poor health associated with deprivation has a considerable association with mortality; the Council Area (CA) with the greatest health-related deprivation was found to have a mortality rate 2.45 times greater than the CA with the lowest health-related deprivation considering all deaths occurring outside of carehomes. Conclusions: We find that in even an early epidemic with poor case ascertainment, a useful spatially explicit model can be fit with meaningful parameters based on the spatio-temporal distribution of death counts. Our simple approach is useful to strategically examine trade-offs between travel related restrictions and physical distancing, and the effect of deprivation-related factors on outcomes.

Modelling plant health for policy.

Plant health is relatively poorly funded compared with animal and human health issues. However, we contend it is at least as complex and likely more so given the number of pests and hosts and that outbreaks occur in poorly monitored open systems. Modelling is often suggested as a method to better consider the threats to plant health to aid resource and time poor decision makers in their prioritisation of responses. However, like other areas of science, the modelling community has not always provided accessible and relevant solutions. We describe some potential solutions to developing plant health models in conjunction with decision makers based upon a recent example and illustrate how an increased emphasis on plant health is slowly expanding the potential role of modelling in decision making. We place the research in the Credibility, Relevance and Legitimacy (CRELE) framework and discuss the implications for future developments in co-construction of policy-linked models.

One model to rule them all? Modelling approaches across OneHealth for human, animal and plant epidemics.

One hundred years after the 1918 influenza outbreak, are we ready for the next pandemic? This paper addresses the need to identify and develop collaborative, interdisciplinary and cross-sectoral approaches to modelling of infectious diseases including the fields of not only human and veterinary medicine, but also plant epidemiology. Firstly, the paper explains the concepts on which the most common epidemiological modelling approaches are based, namely the division of a host population into susceptible, infected and removed (SIR) classes and the proportionality of the infection rate to the size of the susceptible and infected populations. It then demonstrates how these simple concepts have been developed into a vast and successful modelling framework that has been used in predicting and controlling disease outbreaks for over 100 years. Secondly, it considers the compartmental models based on the SIR paradigm within the broader concept of a 'disease tetrahedron' (comprising host, pathogen, environment and man) and uses it to review the similarities and differences among the fields comprising the 'OneHealth' approach. Finally, the paper advocates interactions between all fields and explores the future challenges facing modellers. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

A model for estimating pathogen variability in shellfish and predicting minimum depuration times.

Norovirus is a major cause of viral gastroenteritis, with shellfish consumption being identified as one potential norovirus entry point into the human population. Minimising shellfish norovirus levels is therefore important for both the consumer's protection and the shellfish industry's reputation. One method used to reduce microbiological risks in shellfish is depuration; however, this process also presents additional costs to industry. Providing a mechanism to estimate norovirus levels during depuration would therefore be useful to stakeholders. This paper presents a mathematical model of the depuration process and its impact on norovirus levels found in shellfish. Two fundamental stages of norovirus depuration are considered: (i) the initial distribution of norovirus loads within a shellfish population and (ii) the way in which the initial norovirus loads evolve during depuration. Realistic assumptions are made about the dynamics of norovirus during depuration, and mathematical descriptions of both stages are derived and combined into a single model. Parameters to describe the depuration effect and norovirus load values are derived from existing norovirus data obtained from U.K. harvest sites. However, obtaining population estimates of norovirus variability is time-consuming and expensive; this model addresses the issue by assuming a 'worst case scenario' for variability of pathogens, which is independent of mean pathogen levels. The model is then used to predict minimum depuration times required to achieve norovirus levels which fall within possible risk management levels, as well as predictions of minimum depuration times for other water-borne pathogens found in shellfish. Times for Escherichia coli predicted by the model all fall within the minimum 42 hours required for class B harvest sites, whereas minimum depuration times for norovirus and FRNA+ bacteriophage are substantially longer. Thus this study provides relevant information and tools to assist norovirus risk managers with future control strategies.

Livestock Disease Management for Trading Across Different Regulatory Regimes.

The maintenance of livestock health depends on the combined actions of many different actors, both within and across different regulatory frameworks. Prior work recognised that private risk management choices have the ability to reduce the spread of infection to trading partners. We evaluate the efficiency of farmers' alternative biosecurity choices in terms of their own-benefits from unilateral strategies and quantify the impact they may have in filtering the disease externality of trade. We use bovine viral diarrhoea (BVD) in England and Scotland as a case study, since this provides an example of a situation where contrasting strategies for BVD management occur between selling and purchasing farms. We use an agent-based bioeconomic model to assess the payoff dependence of farmers connected by trade but using different BVD management strategies. We compare three disease management actions: test-cull, test-cull with vaccination and vaccination alone. For a two-farm trading situation, all actions carried out by the selling farm provide substantial benefits to the purchasing farm in terms of disease avoided, with the greatest benefit resulting from test-culling with vaccination on the selling farm. Likewise, unilateral disease strategies by purchasers can be effective in reducing disease risks created through trade. We conclude that regulation needs to balance the trade-off between private gains from those bearing the disease management costs and the positive spillover effects on others.

The Effects of Disease on Optimal Forest Rotation: A Generalisable Analytical Framework.

The arrival of novel pathogens and pests can have a devastating effect on the market values of forests. Calibrating management strategies/decisions to consider the effect of disease may help to reduce disease impacts on forests. Here, we use a novel generalisable, bioeconomic model framework, which combines an epidemiological compartmental model with a Faustmann optimal rotation length model, to explore the management decision of when to harvest a single rotation, even-aged, plantation forest under varying disease conditions. Sensitivity analysis of the rate of spread of infection and the effect of disease on the timber value reveals a key trade-off between waiting for the timber to grow and the infection spreading further. We show that the optimal rotation length, which maximises the net present value of the forest, is reduced when timber from infected trees has no value; but when the infection spreads quickly, and the value of timber from infected trees is non-zero, it can be optimal to wait until the disease-free optimal rotation length to harvest. Our original approach provides an exemplar framework showing how a bioeconomic model can be used to examine the effect of tree diseases on management strategies/decisions.

Payment for multiple forest benefits alters the effect of tree disease on optimal forest rotation length.

Forests deliver multiple benefits both to their owners and to wider society. However, a wave of forest pests and pathogens is threatening this worldwide. In this paper we examine the effect of disease on the optimal rotation length of a single-aged, single rotation forest when a payment for non-timber benefits, which is offered to private forest owners to partly internalise the social values of forest management, is included. Using a generalisable bioeconomic framework we show how this payment counteracts the negative economic effect of disease by increasing the optimal rotation length, and under some restrictive conditions, even makes it optimal to never harvest the forest. The analysis shows a range of complex interactions between factors including the rate of spread of infection and the impact of disease on the value of harvested timber and non-timber benefits. A key result is that the effect of disease on the optimal rotation length is dependent on whether the disease affects the timber benefit only compared to when it affects both timber and non-timber benefits. Our framework can be extended to incorporate multiple ecosystem services delivered by forests and details of how disease can affect their production, thus facilitating a wide range of applications.

The effects of invasive pests and pathogens on strategies for forest diversification.

Diversification of the tree species composition of production forests is a frequently advocated strategy to increase resilience to pests and pathogens; however, there is a lack of a general framework to analyse the impact of economic and biological conditions on the optimal planting strategy in the presence of tree disease. To meet this need we use a novel bioeconomic model to quantitatively assess the effect of tree disease on the optimal planting proportion of two tree species. We find that diversifying the species composition can reduce the economic loss from disease even when the benefit from the resistant species is small. However, this key result is sensitive to a pathogen's characteristics (probability of arrival, time of arrival, rate of spread of infection) and the losses (damage of the disease to the susceptible species and reduced benefit of planting the resistant species). This study provides an exemplar framework which can be used to help understand the effect of a pathogen on forest management strategies.

Modelling the impact and control of an infectious disease in a plant nursery with infected plant material inputs.

The ornamental plant trade has been identified as a key introduction pathway for plant pathogens. Establishing effective biosecurity measures to reduce the risk of plant pathogen outbreaks in the live plant trade is therefore important. Management of invasive pathogens has been identified as a weakest link public good, and thus is reliant on the actions of individual private agents. This paper therefore provides an analysis of the impact of the private agents' biosecurity decisions on pathogen prevention and control within the plant trade. We model the impact that an infectious disease has on a plant nursery under a constant pressure of potentially infected input plant materials, like seeds and saplings, where the spread of the disease reduces the value of mature plants. We explore six scenarios to understand the influence of three key bioeconomic parameters; the disease's basic reproductive number, the loss in value of a mature plant from acquiring an infection and the cost-effectiveness of restriction. The results characterise the disease dynamics within the nursery and explore the trade-offs and synergies between the optimal level of efforts on restriction strategies (actions to prevent buying infected inputs), and on removal of infected plants in the nursery. For diseases that can be easily controlled, restriction and removal are substitutable strategies. In contrast, for highly infectious diseases, restriction and removal are often found to be complementary, provided that restriction is cost-effective and the optimal level of removal is non-zero.

Spontaneous social distancing in response to a simulated epidemic: a virtual experiment.

BACKGROUND: Studies of social distancing during epidemics have found that the strength of the response can have a decisive impact on the outcome. In previous work we developed a model of social distancing driven by individuals' risk attitude, a parameter which determines the extent to which social contacts are reduced in response to a given infection level. We showed by simulation that a strong response, driven by a highly cautious risk attitude, can quickly suppress an epidemic. However, a moderately cautious risk attitude gives weak control and, by prolonging the epidemic without reducing its impact, may yield a worse outcome than doing nothing. In real societies, social distancing may arise spontaneously from individual choices rather than being imposed centrally. There is little data available about this as opportunistic data collection during epidemics is difficult. Our study uses a simulated epidemic in a computer game setting to measure the social distancing response. METHODS: Two hundred thirty participants played a computer game simulating an epidemic on a spatial network. The player controls one individual in a population of 2500 (with others controlled by computer) and decides how many others to contact each day. To mimic real-world trade-offs, the player is motivated to make contact by being rewarded with points, while simultaneously being deterred by the threat of infection. Participants completed a questionnaire regarding psychological measures of health protection motivation. Finally, simulations were used to compare the experimentally-observed response to epidemics with no response. RESULTS: Participants reduced contacts in response to infection in a manner consistent with our model of social distancing. The experimentally observed response was too weak to halt epidemics quickly, resulting in a somewhat reduced attack rate and a substantially reduced peak attack rate, but longer duration and fewer social contacts, compared to no response. Little correlation was observed between participants' risk attitudes and the psychological measures. CONCLUSIONS: Our cognitive model of social distancing matches responses to a simulated epidemic. If these responses indicate real world behaviour, spontaneous social distancing can be expected to reduce peak attack rates. However, additional measures are needed if it is important to stop an epidemic quickly.

Protection motivation theory and social distancing behaviour in response to a simulated infectious disease epidemic.

Epidemics of respiratory infectious disease remain one of the most serious health risks facing the population. Non-pharmaceutical interventions (e.g. hand-washing or wearing face masks) can have a significant impact on the course of an infectious disease epidemic. The current study investigated whether protection motivation theory (PMT) is a useful framework for understanding social distancing behaviour (i.e. the tendency to reduce social contacts) in response to a simulated infectious disease epidemic. There were 230 participants (109 males, 121 females, mean age 32.4 years) from the general population who completed self-report measures assessing the components of PMT. In addition, participants completed a computer game which simulated an infectious disease epidemic in order to provide a measure of social distancing behaviour. The regression analyses revealed that none of the PMT variables were significant predictors of social distancing behaviour during the simulation task. However, fear (ß = .218, p < .001), response efficacy (ß = .175, p < .01) and self-efficacy (ß = .251, p < .001) were all significant predictors of intention to engage in social distancing behaviour. Overall, the PMT variables (and demographic factors) explain 21.2% of the variance in intention. The findings demonstrated that PMT was a useful framework for understanding intention to engage in social distancing behaviour, but not actual behaviour during the simulated epidemic. These findings may reflect an intention-behaviour gap in relation to social distancing behaviour.

Efficient control of epidemics spreading on networks: balance between treatment and recovery.

We analyse two models describing disease transmission and control on regular and small-world networks. We use simulations to find a control strategy that minimizes the total cost of an outbreak, thus balancing the costs of disease against that of the preventive treatment. The models are similar in their epidemiological part, but differ in how the removed/recovered individuals are treated. The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease. However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment) the models give similar results. Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models.

Controlling epidemic spread by social distancing: do it well or not at all.

BACKGROUND: Existing epidemiological models have largely tended to neglect the impact of individual behaviour on the dynamics of diseases. However, awareness of the presence of illness can cause people to change their behaviour by, for example, staying at home and avoiding social contacts. Such changes can be used to control epidemics but they exact an economic cost. Our aim is to study the costs and benefits of using individual-based social distancing undertaken by healthy individuals as a form of control. METHODS: Our model is a standard SIR model superimposed on a spatial network, without and with addition of small-world interactions. Disease spread is controlled by allowing susceptible individuals to temporarily reduce their social contacts in response to the presence of infection within their local neighbourhood. We ascribe an economic cost to the loss of social contacts, and weigh this against the economic benefit gained by reducing the impact of the epidemic. We study the sensitivity of the results to two key parameters, the individuals' attitude to risk and the size of the awareness neighbourhood. RESULTS: Depending on the characteristics of the epidemic and on the relative economic importance of making contacts versus avoiding infection, the optimal control is one of two extremes: either to adopt a highly cautious control, thereby suppressing the epidemic quickly by drastically reducing contacts as soon as disease is detected; or else to forego control and allow the epidemic to run its course. The worst outcome arises when control is attempted, but not cautiously enough to cause the epidemic to be suppressed. The next main result comes from comparing the size of the neighbourhood of which individuals are aware to that of the neighbourhood within which transmission can occur. The control works best when these sizes match and is particularly ineffective when the awareness neighbourhood is smaller than the infection neighbourhood. The results are robust with respect to inclusion of long-range, small-world links which destroy the spatial structure, regardless of whether individuals can or cannot control them. However, addition of many non-local links eventually makes control ineffective. CONCLUSIONS: These results have implications for the design of control strategies using social distancing: a control that is too weak or based upon inaccurate knowledge, may give a worse outcome than doing nothing.

Understanding disease control: influence of epidemiological and economic factors.

We present a model of disease transmission on a regular and small world network and compare different control options. Comparison is based on a total cost of epidemic, including cost of palliative treatment of ill individuals and preventive cost aimed at vaccination or culling of susceptible individuals. Disease is characterized by pre-symptomatic phase, which makes detection and control difficult. Three general strategies emerge: global preventive treatment, local treatment within a neighborhood of certain size and only palliative treatment with no prevention. While the choice between the strategies depends on a relative cost of palliative and preventive treatment, the details of the local strategy and, in particular, the size of the optimal treatment neighborhood depend on the epidemiological factors. The required extent of prevention is proportional to the size of the infection neighborhood, but depends on time till detection and time till treatment in a non-nonlinear (power) law. The optimal size of control neighborhood is also highly sensitive to the relative cost, particularly for inefficient detection and control application. These results have important consequences for design of prevention strategies aiming at emerging diseases for which parameters are not nessecerly known in advance.

Searching for the most cost-effective strategy for controlling epidemics spreading on regular and small-world networks.

We present a combined epidemiological and economic model for control of diseases spreading on local and small-world networks. The disease is characterized by a pre-symptomatic infectious stage that makes detection and control of cases more difficult. The effectiveness of local (ring-vaccination or culling) and global control strategies is analysed by comparing the net present values of the combined cost of preventive treatment and illness. The optimal strategy is then selected by minimizing the total cost of the epidemic. We show that three main strategies emerge, with treating a large number of individuals (global strategy, GS), treating a small number of individuals in a well-defined neighbourhood of a detected case (local strategy) and allowing the disease to spread unchecked (null strategy, NS). The choice of the optimal strategy is governed mainly by a relative cost of palliative and preventive treatments. If the disease spreads within the well-defined neighbourhood, the local strategy is optimal unless the cost of a single vaccine is much higher than the cost associated with hospitalization. In the latter case, it is most cost-effective to refrain from prevention. Destruction of local correlations, either by long-range (small-world) links or by inclusion of many initial foci, expands the range of costs for which the NS is most cost-effective. The GS emerges for the case when the cost of prevention is much lower than the cost of treatment and there is a substantial non-local component in the disease spread. We also show that local treatment is only desirable if the disease spreads on a small-world network with sufficiently few long-range links; otherwise it is optimal to treat globally. In the mean-field case, there are only two optimal solutions, to treat all if the cost of the vaccine is low and to treat nobody if it is high. The basic reproduction ratio, R(0), does not depend on the rate of responsive treatment in this case and the disease always invades (but might be stopped afterwards). The details of the local control strategy, and in particular the optimal size of the control neighbourhood, are determined by the epidemiology of the disease. The properties of the pathogen might not be known in advance for emerging diseases, but the broad choice of the strategy can be made based on economic analysis only.

Cucumber mosaic virus and its 2b RNA silencing suppressor modify plant-aphid interactions in tobacco.

The cucumber mosaic virus (CMV) 2b protein not only inhibits anti-viral RNA silencing but also quenches transcriptional responses of plant genes to jasmonic acid, a key signalling molecule in defence against insects. This suggested that it might affect interactions between infected plants and aphids, insects that transmit CMV. We found that infection of tobacco with a 2b gene deletion mutant (CMVΔ2b) induced strong resistance to aphids (Myzus persicae) while CMV infection fostered aphid survival. Using electrical penetration graph methodology we found that higher proportions of aphids showed sustained phloem ingestion on CMV-infected plants than on CMVΔ2b-infected or mock-inoculated plants although this did not increase the rate of growth of individual aphids. This indicates that while CMV infection or certain viral gene products might elicit aphid resistance, the 2b protein normally counteracts this during a wild-type CMV infection. Our findings suggest that the 2b protein could indirectly affect aphid-mediated virus transmission.

Modelling control of epidemics spreading by long-range interactions.

We have studied the spread of epidemics characterized by a mixture of local and non-local interactions. The infection spreads on a two-dimensional lattice with the fixed nearest neighbour connections. In addition, long-range dynamical links are formed by moving agents (vectors). Vectors perform random walks, with step length distributed according to a thick-tail distribution. Two distributions are considered in this paper, an alpha-stable distribution describing self-similar vector movement, yet characterized by an infinite variance and an exponential power characterized by a large but finite variance. Such long-range interactions are hard to track and make control of epidemics very difficult. We also allowed for cryptic infection, whereby an infected individual on the lattice can be infectious prior to showing any symptoms of infection or disease. To account for such cryptic spread, we considered a control strategy in which not only detected, i.e. symptomatic, individuals but also all individuals within a certain control neighbourhood are treated upon the detection of disease. We show that it is possible to eradicate the disease by using such purely local control measures, even in the presence of long-range jumps. In particular, we show that the success of local control and the choice of the optimal strategy depend in a non-trivial way on the dispersal patterns of the vectors. By characterizing these patterns using the stability index of the alpha-stable distribution to change the power-law behaviour or the exponent characterizing the decay of an exponential power distribution, we show that infection can be successfully contained using relatively small control neighbourhoods for two limiting cases for long-distance dispersal and for vectors that are much more limited in their dispersal range.

Testing the impact of climate variability on European plant diversity: 320,000 years of water-energy dynamics and its long-term influence on plant taxonomic richness.

Models examining the present-day relationship between macro-scale patterns in terrestrial species richness and variables of water and energy demonstrate that a combined water-energy model is a good predictor of richness in mid-to-high latitude regions. However, the power of the individual water and energy variables to explain this richness through time has never been explored. Here, we assess how well energy and water can predict long-term variations in plant richness using a 320,000-year fossil pollen data set from Hungary. Results demonstrate that a combined water-energy model best explains the variation in plant diversity through time. However, this long temporal record also demonstrates that amplitude of energy variation appears to be a strong determinant of richness. Decreased richness correlates with increased climate variability and certain species appear to be more susceptible according to their ecological traits. These findings have important implications for predicting richness at times of increasing climate variability.