A modeling study of the impact of treatment policies on the evolution of resistance in sea lice on salmon farms.

Salmonid aquaculture is an important source of nutritious food with more than 2 million tonnes of fish produced each year (Food and Agriculture Organisation of the United Nations, 2019). In most salmon producing countries, sea lice represent a major barrier to the sustainability of salmonid aquaculture. This issue is exacerbated by widespread resistance to chemical treatments on both sides of the Atlantic. Regulation for sea lice management mostly involves reporting lice counts and treatment thresholds, which depending on interpretation may encourage preemptive treatments. We have developed a stochastic simulation model of sea lice infestation including the lice life-cycle, genetic resistance to treatment, a wildlife reservoir, salmon growth and stocking practices in the context of infestation, and coordination of treatment between farms. Farms report infestation levels to a central organisation, and may then cooperate or not when coordinated treatment is triggered. Treatment practice then impacts the level of resistance in the surrounding sea lice population. Our simulation finds that treatment drives selection for resistance and coordination between managers is key. We also find that position in the hydrologically-derived network of farms can impact individual farm infestation levels and the topology of this network can impact overall infestation and resistance. We show how coordination and triggering of treatment alongside varying hydrological topology of farm connections affects the evolution of lice resistance, and thus optimise salmon quality within socio-economic and environmental constraints. Network topology drives infestation levels in cages, treatments, and hence treatment-driven resistance. Thus farmer behaviour may be highly dependent on hydrologically position and local level of infestation.

Multidisciplinary ecosystem to study lifecourse determinants and prevention of early-onset burdensome multimorbidity (MELD-B) - protocol for a research collaboration.

Background: Most people living with multiple long-term condition multimorbidity (MLTC-M) are under 65 (defined as 'early onset'). Earlier and greater accrual of long-term conditions (LTCs) may be influenced by the timing and nature of exposure to key risk factors, wider determinants or other LTCs at different life stages. We have established a research collaboration titled 'MELD-B' to understand how wider determinants, sentinel conditions (the first LTC in the lifecourse) and LTC accrual sequence affect risk of early-onset, burdensome MLTC-M, and to inform prevention interventions. Aim: Our aim is to identify critical periods in the lifecourse for prevention of early-onset, burdensome MLTC-M, identified through the analysis of birth cohorts and electronic health records, including artificial intelligence (AI)-enhanced analyses. Design: We will develop deeper understanding of 'burdensomeness' and 'complexity' through a qualitative evidence synthesis and a consensus study. Using safe data environments for analyses across large, representative routine healthcare datasets and birth cohorts, we will apply AI methods to identify early-onset, burdensome MLTC-M clusters and sentinel conditions, develop semi-supervised learning to match individuals across datasets, identify determinants of burdensome clusters, and model trajectories of LTC and burden accrual. We will characterise early-life (under 18 years) risk factors for early-onset, burdensome MLTC-M and sentinel conditions. Finally, using AI and causal inference modelling, we will model potential 'preventable moments', defined as time periods in the life course where there is an opportunity for intervention on risk factors and early determinants to prevent the development of MLTC-M. Patient and public involvement is integrated throughout.

Modeling the effectiveness of targeting Rift Valley fever virus vaccination using imperfect network information.

Livestock movements contribute to the spread of several infectious diseases. Data on livestock movements can therefore be harnessed to guide policy on targeted interventions for controlling infectious livestock diseases, including Rift Valley fever (RVF)-a vaccine-preventable arboviral fever. Detailed livestock movement data are known to be useful for targeting control efforts including vaccination. These data are available in many countries, however, such data are generally lacking in others, including many in East Africa, where multiple RVF outbreaks have been reported in recent years. Available movement data are imperfect, and the impact of this uncertainty in the utility of movement data on informing targeting of vaccination is not fully understood. Here, we used a network simulation model to describe the spread of RVF within and between 398 wards in northern Tanzania connected by cattle movements, on which we evaluated the impact of targeting vaccination using imperfect movement data. We show that pre-emptive vaccination guided by only market movement permit data could prevent large outbreaks. Targeted control (either by the risk of RVF introduction or onward transmission) at any level of imperfect movement information is preferred over random vaccination, and any improvement in information reliability is advantageous to their effectiveness. Our modeling approach demonstrates how targeted interventions can be effectively used to inform animal and public health policies for disease control planning. This is particularly valuable in settings where detailed data on livestock movements are either unavailable or imperfect due to resource limitations in data collection, as well as challenges associated with poor compliance.

Process modelling of NHS cardiovascular waiting lists in response to the COVID-19 pandemic.

OBJECTIVE: To model the referral, diagnostic and treatment pathway for cardiovascular disease (CVD) in the English National Health Service (NHS) to provide commissioners and managers with a methodology to optimise patient flow and reduce waiting lists. STUDY DESIGN: A systems dynamics approach modelling the CVD healthcare system in England. The model is designed to capture current and predict future states of waiting lists. SETTING: Routinely collected, publicly available data streams of primary and secondary care, sourced from NHS Digital, NHS England, the Office of National Statistics and StatsWales. DATA COLLECTION AND EXTRACTION METHODS: The data used to train and validate the model were routinely collected and publicly available data. It was extracted and implemented in the model using the PySD package in python. RESULTS: NHS cardiovascular waiting lists in England have increased by over 40% compared with pre- COVID-19 levels. The rise in waiting lists was primarily due to restrictions in referrals from primary care, creating a bottleneck postpandemic. Predictive models show increasing point capacities within the system may paradoxically worsen downstream flow. While there is no simple rate-limiting step, the intervention that would most improve patient flow would be to increase consultant outpatient appointments. CONCLUSIONS: The increase in NHS CVD waiting lists in England can be captured using a systems dynamics approach, as can the future state of waiting lists in the presence of further shocks/interventions. It is important for those planning services to use such a systems-oriented approach because the feed-forward and feedback nature of patient flow through referral, diagnostics and treatment leads to counterintuitive effects of interventions designed to reduce waiting lists.

Local and wide-scale livestock movement networks inform disease control strategies in East Africa.

Livestock mobility exacerbates infectious disease risks across sub-Saharan Africa, but enables critical access to grazing and water resources, and trade. Identifying locations of high livestock traffic offers opportunities for targeted control. We focus on Tanzanian agropastoral and pastoral communities that account respectively for over 75% and 15% of livestock husbandry in eastern Africa. We construct networks of livestock connectivity based on participatory mapping data on herd movements reported by village livestock keepers as well as data from trading points to understand how seasonal availability of resources, land-use and trade influence the movements of livestock. In communities that practise agropastoralism, inter- and intra-village connectivity through communal livestock resources (e.g. pasture and water) was 1.9 times higher in the dry compared to the wet season suggesting greater livestock traffic and increased contact probability. In contrast, livestock from pastoral communities were 1.6 times more connected at communal locations during the wet season when they also tended to move farther (by 3 km compared to the dry season). Trade-linked movements were twice more likely from rural to urban locations. Urban locations were central to all networks, particularly those with potentially high onward movements, for example to abattoirs, livestock holding grounds, or other markets, including beyond national boundaries. We demonstrate how livestock movement information can be used to devise strategic interventions that target critical livestock aggregation points (i.e. locations of high centrality values) and times (i.e. prior to and after the wet season in pastoral and agropastoral areas, respectively). Such targeted interventions are a cost-effective approach to limit infection without restricting livestock mobility critical to sustainable livelihoods.

Ascertainment rate of SARS-CoV-2 infections from healthcare and community testing in the UK.

The proportion of SARS-CoV-2 infections ascertained through healthcare and community testing is generally unknown and expected to vary depending on natural factors and changes in test-seeking behaviour. Here we use population surveillance data and reported daily case numbers in the United Kingdom to estimate the rate of case ascertainment. We mathematically describe the relationship between the ascertainment rate, the daily number of reported cases, population prevalence, and the sensitivity of PCR and Lateral Flow tests as a function time since exposure. Applying this model to the data, we estimate that 20%-40% of SARS-CoV-2 infections in the UK were ascertained with a positive test with results varying by time and region. Cases of the Alpha variant were ascertained at a higher rate than the wild type variants circulating in the early pandemic, and higher again for the Delta variant and Omicron BA.1 sub-lineage, but lower for the BA.2 sub-lineage. Case ascertainment was higher in adults than in children. We further estimate the daily number of infections and compare this to mortality data to estimate that the infection fatality rate increased by a factor of 3 during the period dominated by the Alpha variant, and declined in line with the distribution of vaccines. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Getting the most out of maths: How to coordinate mathematical modelling research to support a pandemic, lessons learnt from three initiatives that were part of the COVID-19 response in the UK.

In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modelling community in the UK to be pushed to its limits. At the same time, mathematical modellers across the country were keen to use their knowledge and skills to support the COVID-19 modelling effort. However, this sudden great interest in epidemiological modelling needed to be coordinated to provide much-needed support, and to limit the burden on epidemiological modellers already very stretched for time. In this paper we describe three initiatives set up in the UK in spring 2020 to coordinate the mathematical sciences research community in supporting mathematical modelling of COVID-19. Each initiative had different primary aims and worked to maximise synergies between the various projects. We reflect on the lessons learnt, highlighting the key roles of pre-existing research collaborations and focal centres of coordination in contributing to the success of these initiatives. We conclude with recommendations about important ways in which the scientific research community could be better prepared for future pandemics. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Visualization for epidemiological modelling: challenges, solutions, reflections and recommendations.

We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs-a series of ideas, approaches and methods taken from existing visualization research and practice-deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. See https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

FAIR data pipeline: provenance-driven data management for traceable scientific workflows.

Modern epidemiological analyses to understand and combat the spread of disease depend critically on access to, and use of, data. Rapidly evolving data, such as data streams changing during a disease outbreak, are particularly challenging. Data management is further complicated by data being imprecisely identified when used. Public trust in policy decisions resulting from such analyses is easily damaged and is often low, with cynicism arising where claims of 'following the science' are made without accompanying evidence. Tracing the provenance of such decisions back through open software to primary data would clarify this evidence, enhancing the transparency of the decision-making process. Here, we demonstrate a Findable, Accessible, Interoperable and Reusable (FAIR) data pipeline. Although developed during the COVID-19 pandemic, it allows easy annotation of any data as they are consumed by analyses, or conversely traces the provenance of scientific outputs back through the analytical or modelling source code to primary data. Such a tool provides a mechanism for the public, and fellow scientists, to better assess scientific evidence by inspecting its provenance, while allowing scientists to support policymakers in openly justifying their decisions. We believe that such tools should be promoted for use across all areas of policy-facing research. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

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.

Genomic epidemiology of SARS-CoV-2 in a university outbreak setting and implications for public health planning.

Whole genome sequencing of SARS-CoV-2 has occurred at an unprecedented scale, and can be exploited for characterising outbreak risks at the fine-scale needed to inform control strategies. One setting at continued risk of COVID-19 outbreaks are higher education institutions, associated with student movements at the start of term, close living conditions within residential halls, and high social contact rates. Here we analysed SARS-CoV-2 whole genome sequences in combination with epidemiological data to investigate a large cluster of student cases associated with University of Glasgow accommodation in autumn 2020, Scotland. We identified 519 student cases of SARS-CoV-2 infection associated with this large cluster through contact tracing data, with 30% sequencing coverage for further analysis. We estimated at least 11 independent introductions of SARS-CoV-2 into the student population, with four comprising the majority of detected cases and consistent with separate outbreaks. These four outbreaks were curtailed within a week following implementation of control measures. The impact of student infections on the local community was short-term despite an underlying increase in community infections. Our study highlights the need for context-specific information in the formation of public health policy for higher educational settings.

Livestock movement informs the risk of disease spread in traditional production systems in East Africa.

In Africa, livestock are important to local and national economies, but their productivity is constrained by infectious diseases. Comprehensive information on livestock movements and contacts is required to devise appropriate disease control strategies; yet, understanding contact risk in systems where herds mix extensively, and where different pathogens can be transmitted at different spatial and temporal scales, remains a major challenge. We deployed Global Positioning System collars on cattle in 52 herds in a traditional agropastoral system in western Serengeti, Tanzania, to understand fine-scale movements and between-herd contacts, and to identify locations of greatest interaction between herds. We examined contact across spatiotemporal scales relevant to different disease transmission scenarios. Daily cattle movements increased with herd size and rainfall. Generally, contact between herds was greatest away from households, during periods with low rainfall and in locations close to dipping points. We demonstrate how movements and contacts affect the risk of disease spread. For example, transmission risk is relatively sensitive to the survival time of different pathogens in the environment, and less sensitive to transmission distance, at least over the range of the spatiotemporal definitions of contacts that we explored. We identify times and locations of greatest disease transmission potential and that could be targeted through tailored control strategies.

SARS-CoV-2 infection in UK university students: lessons from September-December 2020 and modelling insights for future student return.

In this paper, we present work on SARS-CoV-2 transmission in UK higher education settings using multiple approaches to assess the extent of university outbreaks, how much those outbreaks may have led to spillover in the community, and the expected effects of control measures. Firstly, we found that the distribution of outbreaks in universities in late 2020 was consistent with the expected importation of infection from arriving students. Considering outbreaks at one university, larger halls of residence posed higher risks for transmission. The dynamics of transmission from university outbreaks to wider communities is complex, and while sometimes spillover does occur, occasionally even large outbreaks do not give any detectable signal of spillover to the local population. Secondly, we explored proposed control measures for reopening and keeping open universities. We found the proposal of staggering the return of students to university residence is of limited value in terms of reducing transmission. We show that student adherence to testing and self-isolation is likely to be much more important for reducing transmission during term time. Finally, we explored strategies for testing students in the context of a more transmissible variant and found that frequent testing would be necessary to prevent a major outbreak.

Epidemics on dynamic networks.

In many populations, the patterns of potentially infectious contacts are transients that can be described as a network with dynamic links. The relative timescales of link and contagion dynamics and the characteristics that drive their tempos can lead to important differences to the static case. Here, we propose some essential nomenclature for their analysis, and then review the relevant literature. We describe recent advances in they apply to infection processes, considering all of the methods used to record, measure and analyse them, and their implications for disease transmission. Finally, we outline some key challenges and opportunities in the field.

A fast algorithm for calculating an expected outbreak size on dynamic contagion networks.

Calculation of expected outbreak size of a simple contagion on a known contact network is a common and important epidemiological task, and is typically carried out by computationally intensive simulation. We describe an efficient exact method to calculate the expected outbreak size of a contagion on an outbreak-invariant network that is a directed and acyclic, allowing us to model all dynamically changing networks when contagion can only travel forward in time. We describe our algorithm and its use in pseudocode, as well as showing examples of its use on disease relevant, data-derived networks.

A descriptive analysis of the growth of unrecorded interactions amongst cattle-raising premises in Scotland and their implications for disease spread.

BACKGROUND: Individual animal-level reporting of cattle movements between agricultural holdings is in place in Scotland, and the resulting detailed movement data are used to inform epidemiological models and intervention. However, recent years have seen a rapid increase in the use of registered links that allow Scottish farmers to move cattle between linked holdings without reporting. RESULTS: By analyzing these registered trade links as a number of different networks, we find that the geographical reach of these registered links has increased over time, with many holdings linked indirectly to a large number of holdings, some potentially geographically distant. This increase was not linked to decreases in recorded movements at the holding level. When combining registered links with reported movements, we find that registered links increase the size of a possible outward chain of infection from a Scottish holding. The impact on the maximum size is considerably greater than the impact on the mean. CONCLUSIONS: We outline the magnitude and geographic extent of that increase, and show that this growth both has the potential to substantially increase the size of epidemics driven by livestock movements, and undermines the extensive, invaluable recording within the cattle tracing system in Scotland and, by extension, the rest of Great Britain.

A few bad apples: a model of disease influenced agent behaviour in a heterogeneous contact environment.

For diseases that infect humans or livestock, transmission dynamics are at least partially dependent on human activity and therefore human behaviour. However, the impact of human behaviour on disease transmission is relatively understudied, especially in the context of heterogeneous contact structures such as described by a social network. Here, we use a strategic game, coupled with a simple disease model, to investigate how strategic agent choices impact the spread of disease over a contact network. Using beliefs that are based on disease status and that build up over time, agents choose actions that stochastically determine disease spread on the network. An agent's disease status is therefore a function of both his own and his neighbours actions. The effect of disease on agents is modelled by a heterogeneous payoff structure. We find that the combination of network shape and distribution of payoffs has a non-trivial impact on disease prevalence, even if the mean payoff remains the same. An important scenario occurs when a small percentage (called noncooperators) have little incentive to avoid disease. For diseases that are easily acquired when taking a risk, then even when good behavior can lead to disease eradication, a small increase in the percentage of noncooperators (less than 5%) can yield a large (up to 25%) increase in prevalence.