The implications of network structure for epidemic dynamics

The contribution of movement to social network structure and spreading dynamics under simple and complex transmission

The structure of social networks fundamentally influences spreading dynamics. In general, the more contact between individuals, the more opportunity there is for the transmission of information or disease to take place. Yet, contact between individuals, and any resulting transmission events, are determined by a combination of spatial (where individuals choose to move) and social rules (who they choose to interact with or learn from). Here, we examine the effect of the social-spatial interface on spreading dynamics using a simulation model. We quantify the relative effects of different movement rules (localized, semi-localized, nomadic and resource-based movement) and social transmission rules (simple transmission, anti-conformity, proportional, conformity and threshold rules) to both the structure of social networks and spread of a novel behaviour. Localized movement created weakly connected sparse networks, nomadic movement created weakly connected dense networks, and resource-based movement generated strongly connected modular networks. The resulting rate of spreading varied with different combinations of movement and transmission rules, but-importantly-the relative rankings of transmission rules changed when running simulations on static versus dynamic representations of networks. Our results emphasize that individual-level social and spatial behaviours influence emergent network structure, and are of particular consequence for the spread of information under complex transmission rules.This article is part of the theme issue 'The spatial-social interface: a theoretical and empirical integration'.

Leveraging artificial intelligence and software engineering methods in epidemiology for the co-creation of decision-support tools based on mechanistic models

Epidemiological modeling is a key lever for infectious disease control and prevention on farms. It makes it possible to understand the spread of pathogens, but also to compare intervention scenarios even in counterfactual situations. However, the actual capability of decision makers to use mechanistic models to support timely interventions is limited. This study demonstrates how artificial intelligence (AI) techniques can make mechanistic epidemiological models more accessible to farmers and veterinarians, and how to transform such models into user-friendly decision-support tools (DST). By leveraging knowledge representation methods, such as the textual formalization of model components through a domain-specific language (DSL), the co-design of mechanistic models and DST becomes more efficient and collaborative. This facilitates the integration of explicit expert knowledge and practical insights into the modeling process. Furthermore, the utilization of AI and software engineering enables the automation of web application generation based on existing mechanistic models. This automation simplifies the development of DST, as tool designers can focus on identifying users' needs and specifying expected features and meaningful presentations of outcomes, instead of wasting time in writing code to wrap models into web apps. To illustrate the practical application of this approach, we consider the example of Bovine Respiratory Disease (BRD), a tough challenge in fattening farms where young beef bulls often develop BRD shortly after being allocated into pens. BRD is a multi-factorial, multi-pathogen disease that is difficult to anticipate and control, often resulting in the massive use of antimicrobials to mitigate its impact on animal health, welfare, and economic losses. The DST developed from an existing mechanistic BRD model empowers users, including farmers and veterinarians, to customize scenarios based on their specific farm conditions. It enables them to anticipate the effects of various pathogens, compare the epidemiological and economic outcomes associated with different farming practices, and decide how to balance the reduction of disease impact and the reduction of antimicrobial usage (AMU). The generic method presented in this article illustrates the potential of artificial intelligence (AI) and software engineering methods to enhance the co-creation of DST based on mechanistic models in veterinary epidemiology. The corresponding pipeline is distributed as an open-source software. By leveraging these advancements, this research aims to bridge the gap between theoretical models and the practical usage of their outcomes on the field.

SIR+ models: accounting for interaction-dependent disease susceptibility in the planning of public health interventions

Avoiding physical contact is regarded as one of the safest and most advisable strategies to follow to reduce pathogen spread. The flip side of this approach is that a lack of social interactions may negatively affect other dimensions of health, like induction of immunosuppressive anxiety and depression or preventing interactions of importance with a diversity of microbes, which may be necessary to train our immune system or to maintain its normal levels of activity. These may in turn negatively affect a population's susceptibility to infection and the incidence of severe disease. We suggest that future pandemic modelling may benefit from relying on 'SIR+ models': epidemiological models extended to account for the benefits of social interactions that affect immune resilience. We develop an SIR+ model and discuss which specific interventions may be more effective in balancing the trade-off between minimizing pathogen spread and maximizing other interaction-dependent health benefits. Our SIR+ model reflects the idea that health is not just the mere absence of disease, but rather a state of physical, mental and social well-being that can also be dependent on the same social connections that allow pathogen spread, and the modelling of public health interventions for future pandemics should account for this multidimensionality.

Static graph approximations of dynamic contact networks for epidemic forecasting

Epidemic modeling is essential in understanding the spread of infectious diseases like COVID-19 and devising effective intervention strategies to control them. Recently, network-based disease models have integrated traditional compartment-based modeling with real-world contact graphs and shown promising results. However, in an ongoing epidemic, future contact network patterns are not observed yet. To address this, we use aggregated static networks to approximate future contacts for disease modeling. The standard method in the literature concatenates all edges from a dynamic graph into one collapsed graph, called the full static graph. However, the full static graph often leads to severe overestimation of key epidemic characteristics. Therefore, we propose two novel static network approximation methods, DegMST and EdgeMST, designed to preserve the sparsity of real world contact network while remaining connected. DegMST and EdgeMST use the frequency of temporal edges and the node degrees respectively to preserve sparsity. Our analysis show that our models more closely resemble the network characteristics of the dynamic graph compared to the full static ones. Moreover, our analysis on seven real-world contact networks suggests EdgeMST yield more accurate estimations of disease dynamics for epidemic forecasting when compared to the standard full static method.

Nonrandom foraging and resource distributions affect the relationships between host density, contact rates and parasite transmission

Nonrandom foraging can cause animals to aggregate in resource dense areas, increasing host density, contact rates and pathogen transmission, but when should nonrandom foraging and resource distributions also have density-independent effects? Here, we used a factorial experiment with constant resource and host densities to quantify host contact rates across seven resource distributions. We also used an agent-based model to compare pathogen transmission when host movement was based on random foraging, optimal foraging or something between those states. Nonrandom foraging strongly depressed contact rates and transmission relative to the classic random movement assumptions used in most epidemiological models. Given nonrandom foraging in the agent-based model and experiment, contact rates and transmission increased with resource aggregation and average distance to resource patches due to increased host movement in search of resources. Overall, we describe three density-independent mechanisms by which host behaviour and resource distributions alter contact rate functions and pathogen transmission.

Probabilistic activity driven model of temporal simplicial networks and its application on higher-order dynamics

Network modeling characterizes the underlying principles of structural properties and is of vital significance for simulating dynamical processes in real world. However, bridging structure and dynamics is always challenging due to the multiple complexities in real systems. Here, through introducing the individual's activity rate and the possibility of group interaction, we propose a probabilistic activity-driven (PAD) model that could generate temporal higher-order networks with both power-law and high-clustering characteristics, which successfully links the two most critical structural features and a basic dynamical pattern in extensive complex systems. Surprisingly, the power-law exponents and the clustering coefficients of the aggregated PAD network could be tuned in a wide range by altering a set of model parameters. We further provide an approximation algorithm to select the proper parameters that can generate networks with given structural properties, the effectiveness of which is verified by fitting various real-world networks. Finally, we construct the co-evolution framework of the PAD model and higher-order contagion dynamics and derive the critical conditions for phase transition and bistable phenomenon using theoretical and numerical methods. Results show that tendency of participating in higher-order interactions can promote the emergence of bistability but delay the outbreak under heterogeneous activity rates. Our model provides a basic tool to reproduce complex structural properties and to study the widespread higher-order dynamics, which has great potential for applications across fields.

Modeling the effects of farming practices on bovine respiratory disease in a multi-batch cattle fattening farm

Bovine Respiratory Disease (BRD) affects young bulls, causing animal welfare and health concerns as well as economical costs. BRD is caused by an array of viruses and bacteria and also by environmental and abiotic factors. How farming practices influence the spread of these causal pathogens remains unclear. Our goal was to assess the impact of zootechnical practices on the spread of three causal agents of BRD, namely the bovine respiratory syncytial virus (BRSV), Mannheimia haemolytica and Mycoplasma bovis. In that extent, we used an individual based stochastic mechanistic model monitoring risk factors, infectious processes, detection and treatment in a farm possibly featuring several batches simultaneously. The model was calibrated with three sets of parameters relative to each of the three pathogens using data extracted from literature. Separated batches were found to be more effective than a unique large one for reducing the spread of pathogens, especially for BRSV and M.bovis. Moreover, it was found that allocating high risk and low risk individuals into separated batches participated in reducing cumulative incidence, epidemic peaks and antimicrobial usage, especially for M. bovis. Theses findings rise interrogations on the optimal farming practices in order to limit BRD occurrence and pave the way to models featuring coinfections and collective treatments p { line-height: 115%; margin-bottom: 0.25 cm; background: transparent}a:link { color: #000080; text-decoration: underline}a.cjk:link { so-language: zxx}a.ctl:link { solanguage: zxx}.

Estimating contact network properties by integrating multiple data sources associated with infectious diseases

To effectively mitigate the spread of communicable diseases, it is necessary to understand the interactions that enable disease transmission among individuals in a population; we refer to the set of these interactions as a contact network. The structure of the contact network can have profound effects on both the spread of infectious diseases and the effectiveness of control programs. Therefore, understanding the contact network permits more efficient use of resources. Measuring the structure of the network, however, is a challenging problem. We present a Bayesian approach to integrate multiple data sources associated with the transmission of infectious diseases to more precisely and accurately estimate important properties of the contact network. An important aspect of the approach is the use of the congruence class models for networks. We conduct simulation studies modeling pathogens resembling SARS-CoV-2 and HIV to assess the method; subsequently, we apply our approach to HIV data from the University of California San Diego Primary Infection Resource Consortium. Based on simulation studies, we demonstrate that the integration of epidemiological and viral genetic data with risk behavior survey data can lead to large decreases in mean squared error (MSE) in contact network estimates compared to estimates based strictly on risk behavior information. This decrease in MSE is present even in settings where the risk behavior surveys contain measurement error. Through these simulations, we also highlight certain settings where the approach does not improve MSE.

The 2013 Chikungunya outbreak in the Caribbean was structured by the network of cultural relationships among islands

In 2013, the Caribbean underwent an unprecedented epidemic of Chikungunya that affected 29 islands and mainland territories throughout the Caribbean in the first six months. Analysing the spread of the epidemic among the Caribbean islands, we show that the initial patterns of the epidemic can be explained by a network model based on the flight connections among islands. The network does not follow a random graph model and its topology is likely the product of geo-political relationships that generate increased connectedness among locations sharing the same language. Therefore, the infection propagated preferentially among islands that belong to the same cultural domain, irrespective of their human and vector population densities. Importantly, the flight network topology was also a more important determinant of the disease dynamics than the actual volume of traffic. Finally, the severity of the epidemic was found to depend, in the first instance, on which island was initially infected. This investigation shows how a simple epidemic model coupled with an appropriate human mobility model can reproduce the observed epidemiological dynamics. Also, it sheds light on the design of interventions in the face of the emergence of infections in similar settings of naive subpopulations loosely interconnected by host movement. This study delves into the feasibility of developing models to anticipate the emergence of vector-borne infections, showing the importance of network topology, bringing valuable methods for public health officials when planning control policies. Significance statement: The study shows how a simple epidemic model associated with an appropriate human mobility model can reproduce the observed epidemiological dynamics of the 2014 Chikungunya epidemic in the Caribbean region. This model sheds light on the design of interventions in the face of the emergence of infections in similar settings of naive subpopulations loosely interconnected by the host.

A practical guide to mathematical methods for estimating infectious disease outbreak risks

Mathematical models are increasingly used throughout infectious disease outbreaks to guide control measures. In this review article, we focus on the initial stages of an outbreak, when a pathogen has just been observed in a new location (e.g., a town, region or country). We provide a beginner's guide to two methods for estimating the risk that introduced cases lead to sustained local transmission (i.e., the probability of a major outbreak), as opposed to the outbreak fading out with only a small number of cases. We discuss how these simple methods can be extended for epidemiological models with any level of complexity, facilitating their wider use, and describe how estimates of the probability of a major outbreak can be used to guide pathogen surveillance and control strategies. We also give an overview of previous applications of these approaches. This guide is intended to help quantitative researchers develop their own epidemiological models and use them to estimate the risks associated with pathogens arriving in new host populations. The development of these models is crucial for future outbreak preparedness. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Epidemic Diffusion Network of Spain: A Mobility Model to Characterize the Transmission Routes of Disease

Human mobility drives the geographical diffusion of infectious diseases at different scales, but few studies focus on mobility itself. Using publicly available data from Spain, we define a Mobility Matrix that captures constant flows between provinces by using a distance-like measure of effective distance to build a network model with the 52 provinces and 135 relevant edges. Madrid, Valladolid and Araba/Álaba are the most relevant nodes in terms of degree and strength. The shortest routes (most likely path between two points) between all provinces are calculated. A total of 7 mobility communities were found with a modularity of 63%, and a relationship was established with a cumulative incidence of COVID-19 in 14 days (CI14) during the study period. In conclusion, mobility patterns in Spain are governed by a small number of high-flow connections that remain constant in time and seem unaffected by seasonality or restrictions. Most of the travels happen within communities that do not completely represent political borders, and a wave-like spreading pattern with occasional long-distance jumps (small-world properties) can be identified. This information can be incorporated into preparedness and response plans targeting locations that are at risk of contagion preventively, underscoring the importance of coordination between administrations when addressing health emergencies.

COVID-safe behaviour before, during and after a youth mass gathering event: a longitudinal cohort study

OBJECTIVE

As mass gathering events resume in the wake of the COVID-19 pandemic, there is a pressing need to understand (a) engagement in COVID-safe behaviour at these events and (b) how attending a mass gathering impacts subsequent behaviours. This study examined anticipated COVID-safe behaviour before, during, and after a youth mass gathering event.

DESIGN

Longitudinal cohort study.

SETTING

Self-report data were collected online at five timepoints from secondary-school graduates participating in celebrations linked to an annual week-long youth mass gathering event in Australia.

PARTICIPANTS

Australian secondary-school graduates completed surveys before the event (N=397), on days 1 (N=183), 3 (N=158) and 5 (N=163) of the event, and 3 weeks after the event (N=140). Of those who completed the first survey, 72 indicated they would attend a primary mass gathering site where the largest mass gathering of graduates in Australia occurs in a typical (non-pandemic) year; 325 indicated they would be celebrating at other locations (ie, secondary sites).

PRIMARY OUTCOME MEASURES

Anticipated COVID-safe behaviour: physical distancing from friends and strangers and additional protective behaviours (hand hygiene and mask wearing).

RESULTS

At all timepoints, participants anticipated maintaining appropriate (>1.5 m) physical distance from strangers, but not from friends (<0.5 m). Attendees at the primary site reported less physical distancing from friends over time throughout the mass gathering, χ2(4)=16.89, p=0.002. Physical distancing from strangers, χ2(4)=26.93, p<0.001, and additional protective behaviours, χ2(4)=221.23, p<0.001, also declined across the mass gathering among both groups. These reductions in COVID-safe behaviour were significant and enduring, with all declines persisting at follow-up.

CONCLUSION

It is critical that public health messaging and interventions emphasise the risks of disease transmission arising from other attendees who are known to us during mass gathering events, and that such messaging is sustained during and following the event to combat reductions in COVID-safe behaviour.

When might host heterogeneity drive the evolution of asymptomatic, pandemic coronaviruses?

Controlling many infectious diseases, including SARS-Coronavirus-2 (SARS-CoV-2), requires surveillance followed by isolation, contact-tracing and quarantining. These interventions often begin by identifying symptomatic individuals. However, actively removing pathogen strains causing symptomatic infections may inadvertently select for strains less likely to cause symptomatic infections. Moreover, a pathogen's fitness landscape is structured around a heterogeneous host pool; uneven surveillance efforts and distinct transmission risks across host classes can meaningfully alter selection pressures. Here, we explore this interplay between evolution caused by disease control efforts and the evolutionary consequences of host heterogeneity. Using an evolutionary epidemiology model parameterized for coronaviruses, we show that intense symptoms-driven disease control selects for asymptomatic strains, particularly when these efforts are applied unevenly across host groups. Under these conditions, increasing quarantine efforts have diverging effects. If isolation alone cannot eradicate, intensive quarantine efforts combined with uneven detections of asymptomatic infections (e.g., via neglect of some host classes) can favor the evolution of asymptomatic strains. We further show how, when intervention intensity depends on the prevalence of symptomatic infections, higher removal efforts (and isolating symptomatic cases in particular) more readily select for asymptomatic strains than when these efforts do not depend on prevalence. The selection pressures on pathogens caused by isolation and quarantining likely lie between the extremes of no intervention and thoroughly successful eradication. Thus, analyzing how different public health responses can select for asymptomatic pathogen strains is critical for identifying disease suppression efforts that can effectively manage emerging infectious diseases.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11071-022-07548-7.

Dropping mortality by increasing connectivity in plant epidemics

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

Spatial distancing by fungus-exposed Myrmica ants is prompted by sickness rather than contagiousness

The ecological success of ants relies on their high level of sociality and cooperation between genetically related nestmates. However, these group-living insects suffer from elevated risks of disease outbreak in the whole nest. To face this sanitary challenge, social and spatial distancing of pathogen-exposed individuals from susceptible nestmates appear to be simple, although efficient, ways to limit the propagation of contact-transmitted pathogens. Here we question whether spatial distancing in Myrmica rubra ants is an active response of diseased individuals that correlates with their level of infectiousness. We contaminated foragers with spores of Metarhizium brunneum entomopathogenic fungus. We daily tracked the location of these pathogen-exposed individuals and we analyzed their movement patterns until their death on the 5th day post-contamination. Quite unexpectedly, we found that contagious individuals, whose body was covered with infectious spores, did not reduce their mobility nor stayed far away from larvae in order to limit pathogen transmission to healthy nestmates. Spatial distancing occurred later when diseased individuals were no longer contagious because spores had penetrated their body. These sick ants mainly stayed outside the nest, were less mobile and showed a shift from a superdiffusive to subdiffusive walking pattern. Furthermore, these diseased ants did not actively head towards directions that were opposite to the nest entrance. This study found no evidence for early spatial distancing by contaminated M.rubra workers that would fit to the actual risk of colony-wide contagion. Coupled to a lower mobility and area-reduced walking patterns, the late distancing of moribund individuals appears to be a symptom of sickness resulting from fungus-induced physical and physiological dysfunctions. Besides questioning the truly altruistic nature of death in isolation in this system (and potentially others), we discuss about the ecological and physiological constraints that explain the absence of early distancing when some ant species are exposed to pathogens.

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.

Commuting in metapopulation epidemic modeling

The COVID-19 pandemic led authorities all over the world to imposing travel restrictions both on a national and on an international scale. Understanding the effect of such restrictions requires analysis of the role of commuting and calls for a metapopulation modeling that incorporates both local, intra-community infection and population exchange between different locations. Standard metapopulation models are formulated as markovian processes, and as such they do not label individuals according to their original location. However, commuting from home to work and backwards (reverse commuting) is the main pattern of transportation. Thus, it is important to be able to accurately model the effect of commuting on epidemic spreading. In this study we develop a methodology for modeling bidirectional commuting of individuals, without keeping track of each individual separately and with no need of proliferation of number of compartments beyond those defined by the epidemiologic model. We demonstrate the method using a city map of the state of Israel. The presented algorithm does not require any special computation resources and it may serve as a basis for intervention strategy examination in various levels of complication and resolution. We show how to incorporate an epidemiological model into a metapopulation commuting scheme while preserving the internal logic of the epidemiological modeling. The method is general and independent on the details of the epidemiological model under consideration.

A novel geo-hierarchical population mobility model for spatial spreading of resurgent epidemics

Computational models for large, resurgent epidemics are recognized as a crucial tool for predicting the spread of infectious diseases. It is widely agreed, that such models can be augmented with realistic multiscale population models and by incorporating human mobility patterns. Nevertheless, a large proportion of recent studies, aimed at better understanding global epidemics, like influenza, measles, H1N1, SARS, and COVID-19, underestimate the role of heterogeneous mixing in populations, characterized by strong social structures and geography. Motivated by the reduced tractability of studies employing homogeneous mixing, which make conclusions hard to deduce, we propose a new, very fine-grained model incorporating the spatial distribution of population into geographical settlements, with a hierarchical organization down to the level of households (inside which we assume homogeneous mixing). In addition, population is organized heterogeneously outside households, and we model the movement of individuals using travel distance and frequency parameters for inter- and intra-settlement movement. Discrete event simulation, employing an adapted SIR model with relapse, reproduces important qualitative characteristics of real epidemics, like high variation in size and temporal heterogeneity (e.g., waves), that are challenging to reproduce and to quantify with existing measures. Our results pinpoint an important aspect, that epidemic size is more sensitive to the increase in distance of travel, rather that the frequency of travel. Finally, we discuss implications for the control of epidemics by integrating human mobility restrictions, as well as progressive vaccination of individuals.

Scalable Estimation of Epidemic Thresholds via Node Sampling

Infectious or contagious diseases can be transmitted from one person to another through social contact networks. In today's interconnected global society, such contagion processes can cause global public health hazards, as exemplified by the ongoing Covid-19 pandemic. It is therefore of great practical relevance to investigate the network transmission of contagious diseases from the perspective of statistical inference. An important and widely studied boundary condition for contagion processes over networks is the so-called epidemic threshold. The epidemic threshold plays a key role in determining whether a pathogen introduced into a social contact network will cause an epidemic or die out. In this paper, we investigate epidemic thresholds from the perspective of statistical network inference. We identify two major challenges that are caused by high computational and sampling complexity of the epidemic threshold. We develop two statistically accurate and computationally efficient approximation techniques to address these issues under the Chung-Lu modeling framework. The second approximation, which is based on random walk sampling, further enjoys the advantage of requiring data on a vanishingly small fraction of nodes. We establish theoretical guarantees for both methods and demonstrate their empirical superiority.

Thinking clearly about social aspects of infectious disease transmission

Social and cultural forces shape almost every aspect of infectious disease transmission in human populations, as well as our ability to measure, understand, and respond to epidemics. For directly transmitted infections, pathogen transmission relies on human-to-human contact, with kinship, household, and societal structures shaping contact patterns that in turn determine epidemic dynamics. Social, economic, and cultural forces also shape patterns of exposure, health-seeking behaviour, infection outcomes, the likelihood of diagnosis and reporting of cases, and the uptake of interventions. Although these social aspects of epidemiology are hard to quantify and have limited the generalizability of modelling frameworks in a policy context, new sources of data on relevant aspects of human behaviour are increasingly available. Researchers have begun to embrace data from mobile devices and other technologies as useful proxies for behavioural drivers of disease transmission, but there is much work to be done to measure and validate these approaches, particularly for policy-making. Here we discuss how integrating local knowledge in the design of model frameworks and the interpretation of new data streams offers the possibility of policy-relevant models for public health decision-making as well as the development of robust, generalizable theories about human behaviour in relation to infectious diseases.

Individual-based model for the control of Bovine Viral Diarrhea spread in livestock trade networks

Bovine Viral Diarrhea (BVD) is a cattle disease that causes substantial financial losses, in particular to the dairy industry. Hence, several countries including Germany introduced compulsory disease control programs. For the case of Germany in particular, all animals had to be tested and persistently infected animals (PI animals) were removed from the population. The program was successful in reducing the number of PI animals, but was overtly expensive. Alternative approaches were therefore discussed to eliminate the remaining PI animals and alter the testing system in order to reduce costs. Contributing to these efforts, we developed an agent-based model that aimed to cover all relevant aspects of the disease biology and would allow to evaluate different control strategies. For the biological part of the infection spread, the model includes horizontal and vertical transmission, transient and persistent infections. Moreover, several control strategies including import of animals, trade restrictions, vaccination, as well as various testing schemes were included. The model was furthermore defined to be stochastic, event-driven and hierarchical, with cattle movements as the main route of spreading between farms. For the spread within farms, we included susceptible-infected-recovered (SIR) dynamics with an additional permanently infectious class. The interaction between the farms was described by a supply and demand farm manager mechanism governing the network structure and dynamics. Additionally, we carried out a sensitivity analysis of the input parameters to study the impact of extreme values on the model. Since the population size in the model is limited, we tested the influence of the initial population size on the model results. Our results showed that the model could accurately describe the dynamics of the disease in the presence and absence of disease control. Although we developed the model for the spread of BVD, it may be adapted to similar diseases of cattle and swine.

The role of habitat configuration in shaping animal population processes: a framework to generate quantitative predictions

By shaping where individuals move, habitat configuration can fundamentally structure animal populations. Yet, we currently lack a framework for generating quantitative predictions about the role of habitat configuration in modulating population outcomes. To address this gap, we propose a modelling framework inspired by studies using networks to characterize habitat connectivity. We first define animal habitat networks, explain how they can integrate information about the different configurational features of animal habitats, and highlight the need for a bottom–up generative model that can depict realistic variations in habitat potential connectivity. Second, we describe a model for simulating animal habitat networks (available in the R package AnimalHabitatNetwork), and demonstrate its ability to generate alternative habitat configurations based on empirical data, which forms the basis for exploring the consequences of alternative habitat structures. Finally, we lay out three key research questions and demonstrate how our framework can address them. By simulating the spread of a pathogen within a population, we show how transmission properties can be impacted by both local potential connectivity and landscape-level characteristics of habitats. Our study highlights the importance of considering the underlying habitat configuration in studies linking social structure with population-level outcomes.

Small-world effects in a modified epidemiological model with mutation and permanent immune mechanism

Pandemic with mutation and permanent immune spreading in a small-world network described is studied by a modified SIR model, with consideration of mutation-immune mechanism. First, a novel mutation-immune model is proposed to modify the classical SIR model to simulate the transmission of mutable viruses that can be permanently immunized in small-world networks. Then, the influences of the size, coordination number and disorder parameter of the small-world network on the spread of the epidemic are analyzed in detail. Finally, the influences of mutation cycle and infection rate on epidemic transmission in small-world network are investigated further. The results show that the structure of the small-world network and the virus mutation cycle have an important impact on the spread of the epidemic. For viruses that can be permanently immunized, virus mutation is equivalent to making the immune cycle of human beings from infinite to finite. The dynamical behavior of the modified SIR epidemic model changes from an irregular, low-amplitude evolution at small disorder parameter to a spontaneous state of wide amplitude oscillations at large disorder parameter. Moreover, similar transition can also be found in increasing mutation cycle parameter. The maximum valid variation mutation decreases with the increase of disorder parameter and coordination number, but increase with respect to system size. In addition above, as the infection rate increases, the fraction of the infected increases and then decreases. As the mutation cycle increases, the time-average fraction of the infected and the infection rate corresponding to the maximum time-average fraction of the infected also decrease. As one conclusion, the results could give a deep understanding Pandemic with mutation and permanent immune spreading, from viewpoint of small-world network.

Network models and the interpretation of prolonged infection plateaus in the COVID19 pandemic

Non-pharmaceutical intervention measures, such as social distancing, have so far been the only means to slow the spread of SARS-CoV-2. In the United States, strict social distancing during the first wave of virus spread has resulted in different types of infection dynamics. In some states, such as New York, extensive infection spread was followed by a pronounced decline of infection levels. In other states, such as California, less infection spread occurred before strict social distancing, and a different pattern was observed. Instead of a pronounced infection decline, a long-lasting plateau is evident, characterized by similar daily new infection levels. Here we show that network models, in which individuals and their social contacts are explicitly tracked, can reproduce the plateau if network connections are cut due to social distancing measures. The reason is that in networks characterized by a 2D spatial structure, infection tends to spread quadratically with time, but as edges are randomly removed, the infection spreads along nearly one-dimensional infection “corridors”, resulting in plateau dynamics. Further, we show that plateau dynamics are observed only if interventions start sufficiently early; late intervention leads to a “peak and decay” pattern. Interestingly, the plateau dynamics are predicted to eventually transition into an infection decline phase without any further increase in social distancing measures. Additionally, the models suggest that a second wave becomes significantly less pronounced if social distancing is only relaxed once the dynamics have transitioned to the decline phase. The network models analyzed here allow us to interpret and reconcile different infection dynamics during social distancing observed in various US states.

Continental-scale dynamics of avian influenza in U.S. waterfowl are driven by demography, migration, and temperature

Emerging diseases of wildlife origin are increasingly spilling over into humans and domestic animals. Surveillance and risk assessments for transmission between these populations are informed by a mechanistic understanding of the pathogens in wildlife reservoirs. For avian influenza viruses (AIV), much observational and experimental work in wildlife has been conducted at local scales, yet fully understanding their spread and distribution requires assessing the mechanisms acting at both local, (e.g., intrinsic epidemic dynamics), and continental scales, (e.g., long-distance migration). Here, we combined a large, continental-scale data set on low pathogenic, Type A AIV in the United States with a novel network-based application of bird banding/recovery data to investigate the migration-based drivers of AIV and their relative importance compared to well-characterized local drivers (e.g., demography, environmental persistence). We compared among regression models reflecting hypothesized ecological processes and evaluated their ability to predict AIV in space and time using within and out-of-sample validation. We found that predictors of AIV were associated with multiple mechanisms at local and continental scales. Hypotheses characterizing local epidemic dynamics were strongly supported, with age, the age-specific aggregation of migratory birds in an area and temperature being the best predictors of infection. Hypotheses defining larger, network-based features of the migration processes, such as clustering or between-cluster mixing explained less variation but were also supported. Therefore, our results support a role for local processes in driving the continental distribution of AIV.

Measles dynamics on network models with optimal control strategies

To investigate the influences of heterogeneity and waning immunity on measles transmission, we formulate a network model with periodic transmission rate, and theoretically examine the threshold dynamics. We numerically find that the waning of immunity can lead to an increase in the basic reproduction number R 0 and the density of infected individuals. Moreover, there exists a critical level for average degree above which R 0 increases quicker in the scale-free network than in the random network. To design the effective control strategies for the subpopulations with different activities, we examine the optimal control problem of the heterogeneous model. Numerical studies suggest us no matter what the network is, we should implement control measures as soon as possible once the outbreak takes off, and particularly, the subpopulation with high connectivity should require high intensity of interventions. However, with delayed initiation of controls, relatively strong control measures should be given to groups with medium degrees. Furthermore, the allocation of costs (or resources) should coincide with their contact patterns.

Evaluation of SARS-CoV-2 transmission mitigation strategies on a university campus using an agent-based network model

Universities are faced with decisions on how to resume campus activities while mitigating SARS-CoV-2 risk. To provide guidance for these decisions, we developed an agent-based network model of SARS-CoV-2 transmission to assess the potential impact of strategies to reduce outbreaks. The model incorporates important features related to risk at the University of California San Diego. We found that structural interventions for housing (singles only) and instructional changes (from in-person to hybrid with class size caps) can substantially reduce R0, but masking and social distancing are required to reduce this to at or below 1. Within a risk mitigation scenario, increased frequency of asymptomatic testing from monthly to twice weekly has minimal impact on average outbreak size (1.1-1.9), but substantially reduces the maximum outbreak size and cumulative number of cases. We conclude that an interdependent approach incorporating risk mitigation, viral detection, and public health intervention is required to mitigate risk.

Follow the Sex: Influence of Network Structure on the Effectiveness and Cost-Effectiveness of Partner Management Strategies for Sexually Transmitted Infection Control

BACKGROUND

It is well established that network structure strongly influences infectious disease dynamics. However, little is known about how the network structure impacts the cost-effectiveness of disease control strategies. We evaluated partner management strategies to address bacterial sexually transmitted infections (STIs) as a case study to explore the influence of the network structure on the optimal disease management strategy.

METHODS

We simulated a hypothetical bacterial STI spread through 4 representative network structures: random, community-structured, scale-free, and empirical. We simulated disease outcomes (prevalence, incidence, total infected person-months) and cost-effectiveness of 4 partner management strategies in each network structure: routine STI screening alone (no partner management), partner notification, expedited partner therapy, and contact tracing. We determined the optimal partner management strategy following a cost-effectiveness framework and varied key compliance parameters of partner management in sensitivity analysis.

RESULTS

For the same average number of contacts and disease parameters in our setting, community-structured networks had the lowest incidence, prevalence, and total infected person-months, whereas scale-free networks had the highest without partner management. The highly connected individuals were more likely to be reinfected in scale-free networks than in the other network structures. The cost-effective partner management strategy depended on the network structures, the compliance in partner management, the willingness-to-pay threshold, and the rate of external force of infection.

CONCLUSIONS

Our findings suggest that contact network structure matters in determining the optimal disease control strategy in infectious diseases. Information on a population's contact network structure may be valuable for informing optimal investment of limited resources.

Analysis of astrovirus transmission pathways in a free-ranging fission-fusion colony of Natterer’s bats (Myotis nattereri)

Abstract

Bats are a diverse and widespread order of mammals. They fulfill critical ecosystem roles but may also act as reservoirs and spreaders for zoonotic agents. Consequently, many recent studies have focused on the potential of bats to spread diseases to other animals and to humans. However, virus transmission networks within bat colonies remain largely unexplored. We studied the detection rate and transmission pathway of astroviruses in a free-ranging Natterer’s bat colony (Myotis nattereri) that exhibits a high fission-fusion dynamic. Based on automatic roost monitoring data of radio-frequency identification tagged bats, we assessed the impact of the strength of an individual’s roosting associations with all other colony members (weighted degree), and the number of roost sites (bat boxes) an individual used—both being proxies for individual exposure risk—on the detected presence of astrovirus-related nucleic acid in individual swab samples. Moreover, we tested to which degree astrovirus sequence types were shared between individuals that frequently roosted together, as proxy for direct transmission risk, and between bats sharing the same roost sites in close temporal succession, as proxy for indirect transmission risk. Neither roosting associations nor the number of different roost sites had an effect on detected virus presence in individual bats. Transmission network data suggest that astroviruses are transmitted both via direct and indirect contact, implying that roost sites pose a risk of astrovirus infection for several days after the bats leave them. Our study offers novel insights in the presence and transmission of viruses within social networks of bat colonies.

Significance statement

Bats provide many ecosystem services but have moved into the focus of virological research as potential carriers of zoonotic disease agents. However, the sparse information available about virus transmission within bat colonies is solely based on simulated transmission data. In this field study, we examined the daily roosting behavior in a wild bat colony in relation to the presence of viruses in individual colony members. Our findings suggest that astroviruses are transmitted by direct contact and via contaminated roost sites. Bats typically defecate in their roost sites, and astroviruses can remain infectious in feces for several days. The here observed virus diversity and roosting behavior suggest that bats can contract astroviruses even if they use contaminated roost sites days after infected individuals have left. This study provides first-time insights in the transmission of astroviruses within bat colonies in the wild.

Will an outbreak exceed available resources for control? Estimating the risk from invading pathogens using practical definitions of a severe epidemic

Forecasting whether or not initial reports of disease will be followed by a severe epidemic is an important component of disease management. Standard epidemic risk estimates involve assuming that infections occur according to a branching process and correspond to the probability that the outbreak persists beyond the initial stochastic phase. However, an alternative assessment is to predict whether or not initial cases will lead to a severe epidemic in which available control resources are exceeded. We show how this risk can be estimated by considering three practically relevant potential definitions of a severe epidemic; namely, an outbreak in which: (i) a large number of hosts are infected simultaneously; (ii) a large total number of infections occur; and (iii) the pathogen remains in the population for a long period. We show that the probability of a severe epidemic under these definitions often coincides with the standard branching process estimate for the major epidemic probability. However, these practically relevant risk assessments can also be different from the major epidemic probability, as well as from each other. This holds in different epidemiological systems, highlighting that careful consideration of how to classify a severe epidemic is vital for accurate epidemic risk quantification.

A Framework for Network-Based Epidemiological Modeling of Tuberculosis Dynamics Using Synthetic Datasets

We present a framework for discrete network-based modeling of TB epidemiology in US counties using publicly available synthetic datasets. We explore the dynamics of this modeling framework by simulating the hypothetical spread of disease over 2 years resulting from a single active infection in Washtenaw County, MI. We find that for sufficiently large transmission rates that active transmission outweighs reactivation, disease prevalence is sensitive to the contact weight assigned to transmissions between casual contacts (that is, contacts that do not share a household, workplace, school, or group quarter). Workplace and casual contacts contribute most to active disease transmission, while household, school, and group quarter contacts contribute relatively little. Stochastic features of the model result in significant uncertainty in the predicted number of infections over time, leading to challenges in model calibration and interpretation of model-based predictions. Finally, predicted infections were more localized by household location than would be expected if they were randomly distributed. This modeling framework can be refined in later work to study specific county and multi-county TB epidemics in the USA.

A social identity perspective on COVID-19: Health risk is affected by shared group membership

In the face of a novel infectious disease, changing our collective behaviour is critical to saving lives. One determinant of risk perception and risk behaviour that is often overlooked is the degree to which we share psychological group membership with others. We outline, and summarize supporting evidence for, a theoretical model that articulates the role of shared group membership in attenuating health risk perception and increasing health risk behaviour. We emphasize the importance of attending to these processes in the context of the ongoing response to COVID‐19 and conclude with three recommendations for how group processes can be harnessed to improve this response.

Vaccination and monitoring strategies for epidemic prevention and detection in the Channel Island fox (Urocyon littoralis)

Disease transmission and epidemic prevention are top conservation concerns for wildlife managers, especially for small, isolated populations. Previous studies have shown that the course of an epidemic within a heterogeneous host population is strongly influenced by whether pathogens are introduced to regions of relatively high or low host densities. This raises the question of how disease monitoring and vaccination programs are influenced by spatial heterogeneity in host distributions. We addressed this question by modeling vaccination and monitoring strategies for the Channel Island fox (Urocyon littoralis), which has a history of substantial population decline due to introduced disease. We simulated various strategies to detect and prevent epidemics of rabies and canine distemper using a spatially explicit model, which was parameterized from field studies. Increasing sentinel monitoring frequency, and to a lesser degree, the number of monitored sentinels from 50 to 150 radio collared animals, reduced the time to epidemic detection and percentage of the fox population infected at the time of detection for both pathogens. Fox density at the location of pathogen introduction had little influence on the time to detection, but a large influence on how many foxes had become infected by the detection day, especially when sentinels were monitored relatively infrequently. The efficacy of different vaccination strategies was heavily influenced by local host density at the site of pathogen entry. Generally, creating a vaccine firewall far away from the site of pathogen entry was the least effective strategy. A firewall close to the site of pathogen entry was generally more effective than a random distribution of vaccinated animals when pathogens entered regions of high host density, but not when pathogens entered regions of low host density. These results highlight the importance of considering host densities at likely locations of pathogen invasion when designing disease management plans.

Population mobility induced phase separation in SIS epidemic and social dynamics

Understanding the impact of behavior dependent mobility in the spread of epidemics and social disorders is an outstanding problem in computational epidemiology. We present a modelling approach for the study of mobility that adapts dynamically according to individual state, epidemic/social-contagion state and network topology in accordance with limited data and/or common behavioral models. We demonstrate that even for simple compartmental network processes, our approach leads to complex spatial patterns of infection in the endemic state dependent on individual behavior. Specifically, we characterize the resulting phenomena in terms of phase separation, highlighting phase transitions between distinct spatial states and determining the systems' phase diagram. The existence of such phases implies that small changes in the populations' perceptions could lead to drastic changes in the spatial extent and morphology of the epidemic/social phenomena.

Increased frequency of travel in the presence of cross-immunity may act to decrease the chance of a global pandemic

The high frequency of modern travel has led to concerns about a devastating pandemic since a lethal pathogen strain could spread worldwide quickly. Many historical pandemics have arisen following pathogen evolution to a more virulent form. However, some pathogen strains invoke immune responses that provide partial cross-immunity against infection with related strains. Here, we consider a mathematical model of successive outbreaks of two strains-a low virulence (LV) strain outbreak followed by a high virulence (HV) strain outbreak. Under these circumstances, we investigate the impacts of varying travel rates and cross-immunity on the probability that a major epidemic of the HV strain occurs, and the size of that outbreak. Frequent travel between subpopulations can lead to widespread immunity to the HV strain, driven by exposure to the LV strain. As a result, major epidemics of the HV strain are less likely, and can potentially be smaller, with more connected subpopulations. Cross-immunity may be a factor contributing to the absence of a global pandemic as severe as the 1918 influenza pandemic in the century since. 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'.

Improved susceptible-infectious-susceptible epidemic equations based on uncertainties and autocorrelation functions

Compartmental equations are primary tools in the study of disease spreading processes. They provide accurate predictions for large populations but poor results whenever the integer nature of the number of agents is evident. In the latter instance, uncertainties are relevant factors for pathogen transmission. Starting from the agent-based approach, we investigate the role of uncertainties and autocorrelation functions in the susceptible-infectious-susceptible (SIS) epidemic model, including their relationship with epidemiological variables. We find new differential equations that take uncertainties into account. The findings provide improved equations, offering new insights on disease spreading processes.

Primate Infectious Disease Ecology: Insights and Future Directions at the Human-Macaque Interface

Global population expansion has increased interactions and conflicts between humans and nonhuman primates over shared ecological space and resources. Such ecological overlap, along with our shared evolutionary histories, makes human-nonhuman primate interfaces hot spots for the acquisition and transmission of parasites. In this chapter, we bring to light the importance of human-macaque interfaces in particular as hot spots for infectious disease ecological and epidemiological assessments. We first outline the significance and broader objectives behind research related to the subfield of primate infectious disease ecology and epidemiology. We then reveal how members of the genus Macaca, being among the most socioecologically flexible and invasive of all primate taxa, live under varying degrees of overlap with humans in anthropogenic landscapes. Thus, human-macaque interfaces may favor the bidirectional exchange of parasites. We then review studies that have isolated various types of parasites at human-macaque interfaces, using information from the Global Mammal Parasite Database (GMPD: http://www.mammalparasites.org/). Finally, we elaborate on avenues through which the implementation of both novel conceptual frameworks (e.g., Coupled Systems, One Health) and quantitative network-based approaches (e.g., social and bipartite networks, agent-based modeling) may potentially address some of the critical gaps in our current knowledge of infectious disease ecology at human-primate interfaces.

Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations

Empirical records of epidemics reveal that fluctuations are important factors for the spread and prevalence of infectious diseases. The exact manner in which fluctuations affect spreading dynamics remains poorly known. Recent analytical and numerical studies have demonstrated that improved differential equations for mean and variance of infected individuals reproduce certain regimes of the SIS epidemic model. Here, we show they form a dynamical system that follows Hamilton’s equations, which allow us to understand the role of fluctuations and their effects on epidemics. Our findings show the Hamiltonian is a constant of motion for large population sizes. For small populations, finite size effects break the temporal symmetry and induce a power-law decay of the Hamiltonian near the outbreak onset, with a parameter-free exponent. Away from the onset, the Hamiltonian decays exponentially according to a constant relaxation time, which we propose as a metric when fluctuations cannot be neglected.

Epidemic Spread on One-Way Circular-Coupled Networks

Real epidemic spreading networks are often composed of several kinds of complex networks interconnected with each other, such as Lyme disease, and the interrelated networks may have different topologies and epidemic dynamics. Moreover, most human infectious diseases are derived from animals, and zoonotic infections always spread on directed interconnected networks. So, in this article, we consider the epidemic dynamics of zoonotic infections on a unidirectional circular-coupled network. Here, we construct two unidirectional three-layer circular interactive networks, one model has direct contact between interactive networks, the other model describes diseases transmitted through vectors between interactive networks, which are established by introducing the heterogeneous mean-field approach method. Then we obtain the basic reproduction numbers and stability of equilibria of the two models. Through mathematical analysis and numerical simulations, it is found that basic reproduction numbers of the models depend on the infection rates, infection periods, average degrees, and degree ratios. Numerical simulations illustrate and expand these theoretical results very well.

EMULSION: Transparent and flexible multiscale stochastic models in human, animal and plant epidemiology

Stochastic mechanistic epidemiological models largely contribute to better understand pathogen emergence and spread, and assess control strategies at various scales (from within-host to transnational scale). However, developing realistic models which involve multi-disciplinary knowledge integration faces three major challenges in predictive epidemiology: lack of readability once translated into simulation code, low reproducibility and reusability, and long development time compared to outbreak time scale. We introduce here EMULSION, an artificial intelligence-based software intended to address those issues and help modellers focus on model design rather than programming. EMULSION defines a domain-specific language to make all components of an epidemiological model (structure, processes, parameters…) explicit as a structured text file. This file is readable by scientists from other fields (epidemiologists, biologists, economists), who can contribute to validate or revise assumptions at any stage of model development. It is then automatically processed by EMULSION generic simulation engine, preventing any discrepancy between model description and implementation. The modelling language and simulation architecture both rely on the combination of advanced artificial intelligence methods (knowledge representation and multi-level agent-based simulation), allowing several modelling paradigms (from compartment- to individual-based models) at several scales (up to metapopulation). The flexibility of EMULSION and its capability to support iterative modelling are illustrated here through examples of progressive complexity, including late revisions of core model assumptions. EMULSION is also currently used to model the spread of several diseases in real pathosystems. EMULSION provides a command-line tool for checking models, producing model diagrams, running simulations, and plotting outputs. Written in Python 3, EMULSION runs on Linux, MacOS, and Windows. It is released under Apache-2.0 license. A comprehensive documentation with installation instructions, a tutorial and many examples are available from: https://sourcesup.renater.fr/www/emulsion-public.

Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model

Canine rabies was endemic pre-urbanisation, yet little is known about how it persists in small populations of dogs typically seen in rural and remote regions. By simulating rabies outbreaks in such populations (50-90 dogs) using a network-based model, our objective was to determine if rabies-induced behavioural changes influence disease persistence. Behavioural changes-increased bite frequency and increased number or duration of contacts (disease-induced roaming or paralysis, respectively)-were found to be essential for disease propagation. Spread occurred in approximately 50% of model simulations and in these, very low case rates (2.0-2.6 cases/month) over long durations (95% range 20-473 days) were observed. Consequently, disease detection is a challenge, risking human infection and spread to other communities via dog movements. Even with 70% pre-emptive vaccination, spread occurred in >30% of model simulations (in these, median case rate was 1.5/month with 95% range of 15-275 days duration). We conclude that the social disruption caused by rabies-induced behavioural change is the key to explaining how rabies persists in small populations of dogs. Results suggest that vaccination of substantially greater than the recommended 70% of dog populations is required to prevent rabies emergence in currently free rural areas.

Network structure and risk-based surveillance algorithms for live shrimp movements in Thailand

Live shrimp movements pose a potential route for site-to-site transmission of acute hepatopancreatic necrosis disease (AHPND) and other shrimp diseases. We present the first application of network theory to study shrimp epizootiology, providing quantitative information about the live shrimp movement network of Thailand (LSMN), and supporting practical and policy implementations of disease surveillance and control measures. We examined the LSMN over a 13-month period from March 2013 to March 2014, with data obtained from the Thailand Department of Fisheries. The LSMN had a mixture of characteristics both limiting and facilitating disease spread. Importantly, the LSMN exhibited power-law distributions of in and out degrees with exponents of 2.87 and 2.17, respectively. This characteristic indicates that the LSMN behaves like a scale-free network and suggests that an effective strategy to control disease spread in the Thai shrimp farming sector can be achieved by removing a small number of targeted inter-site connections (arcs between nodes). Specifically, a disease-control algorithm based on betweenness centrality (defined as the number of shortest paths between node pairs that traverse a given arc) is proposed here to prioritize targets for disease surveillance and control measures.

Impacts of Heterogeneous Host Densities and Contact Rates on Pathogen Transmission in the Channel Island Fox (Urocyon littoralis)

Diseases threaten wildlife populations worldwide and have caused severe declines resulting in host species being listed as threatened or endangered. The risk of a widespread epidemic is especially high when pathogens are introduced to naive host populations, often leading to high morbidity and mortality. Prevention and control of these epidemics is based on knowledge of what drives pathogen transmission among hosts. Previous disease outbreaks suggest the spread of directly transmitted pathogens is determined by host contact rates and local host density. While theoretical models of disease spread typically assume a constant host density, most wildlife populations occur at a variety of densities across the landscape. We explored how spatial heterogeneity in host density influences pathogen spread by simulating the introduction and spread of rabies and canine distemper in a spatially heterogeneous population of Channel Island foxes (Urocyon littoralis), coupling fox density and contact rates with probabilities of viral transmission. For both diseases, the outcome of pathogen introductions varied widely among simulation iterations and depended on the density of hosts at the site of pathogen introduction. Introductions into areas of higher fox densities resulted in more rapid pathogen transmission and greater impact on the host population than if the pathogen was introduced at lower densities. Both pathogens were extirpated in a substantial fraction of iterations. Rabies was over five times more likely to go locally extinct when introduced at low host density sites than at high host-density sites, leaving an average of >99% of foxes uninfected. Canine distemper went extinct in >98% of iterations regardless of introduction site, but only after >90% of foxes had become infected. Our results highlight the difficulty in predicting the course of an epidemic, in part due to complex interactions between pathogen biology and host behavior, exacerbated by the spatial variation of most host populations.

BOARD INVITED REVIEW: Prospects for improving management of animal disease introductions using disease-dynamic models

Management and policy decisions are continually made to mitigate disease introductions in animal populations despite often limited surveillance data or knowledge of disease transmission processes. Science-based management is broadly recognized as leading to more effective decisions yet application of models to actively guide disease surveillance and mitigate risks remains limited. Disease-dynamic models are an efficient method of providing information for management decisions because of their ability to integrate and evaluate multiple, complex processes simultaneously while accounting for uncertainty common in animal diseases. Here we review disease introduction pathways and transmission processes crucial for informing disease management and models at the interface of domestic animals and wildlife. We describe how disease transmission models can improve disease management and present a conceptual framework for integrating disease models into the decision process using adaptive management principles. We apply our framework to a case study of African swine fever virus in wild and domestic swine to demonstrate how disease-dynamic models can improve mitigation of introduction risk. We also identify opportunities to improve the application of disease models to support decision-making to manage disease at the interface of domestic and wild animals. First, scientists must focus on objective-driven models providing practical predictions that are useful to those managing disease. In order for practical model predictions to be incorporated into disease management a recognition that modeling is a means to improve management and outcomes is important. This will be most successful when done in a cross-disciplinary environment that includes scientists and decision-makers representing wildlife and domestic animal health. Lastly, including economic principles of value-of-information and cost-benefit analysis in disease-dynamic models can facilitate more efficient management decisions and improve communication of model forecasts. Integration of disease-dynamic models into management and decision-making processes is expected to improve surveillance systems, risk mitigations, outbreak preparedness, and outbreak response activities.

Ebola vaccination in the Democratic Republic of the Congo

Following the April 2018 reemergence of Ebola in a rural region of the Democratic Republic of the Congo (DRC), the virus spread to an urban center by early May. Within 2 wk of the first case confirmation, a vaccination campaign was initiated in which 3,017 doses were administered to contacts of cases and frontline healthcare workers. To evaluate the spatial dynamics of Ebola transmission and quantify the impact of vaccination, we developed a geographically explicit model that incorporates high-resolution data on poverty and population density. We found that while Ebola risk was concentrated around sites initially reporting infections, longer-range dissemination also posed a risk to areas with high population density and poverty. We estimate that the vaccination program contracted the geographical area at risk for Ebola by up to 70.4% and reduced the level of risk within that region by up to 70.1%. The early implementation of vaccination was critical. A delay of even 1 wk would have reduced these effects to 33.3 and 44.8%, respectively. These results underscore the importance of the rapid deployment of Ebola vaccines during emerging outbreaks to containing transmission and preventing global spread. The spatiotemporal framework developed here provides a tool for identifying high-risk regions, in which surveillance can be intensified and preemptive control can be implemented during future outbreaks.

Equilibrium properties of the spatial SIS model as a point pattern dynamics - How is infection distributed over space?

We revisit the classical epidemiological SIS model as a stochastic point pattern dynamics with special focus on its spatial distribution at equilibrium. In this model, each point on a continuous space is either susceptible S or infectious I, and infection occurs with an infection kernel as a function of distance from I to S. This stochastic process has been mathematically described by the hierarchical dynamics of the probabilities that a point, a pair made by two points, and a triplet made by three points, etc., is in a specific configuration of status. Using a simple closure thereby triplet probabilities that appear in the dynamics are approximated, we show that the average singlet probabilities and the pair probabilities that describe spatial distributions of Ss and Is at equilibrium can be explicitly derived using the infection kernel; Is are spatially clustered in the same order of the infection kernel. The results highlight the advantage of point pattern approach to model spatial population dynamics in general ecology where local interactions among individuals likely depend on distance between them.

Dynamics of bed bug infestations and control under disclosure policies

Bed bugs are household pests that bite humans and cause myriad medical, psychological, social, and economic problems. Infestation levels have resurged across the United States in recent decades, and cities and states are debating strategies to deal with them. Here, we introduce a mathematical model to study the spread of bed bugs and predict the costs and benefits of policies aimed at controlling them. In particular, we evaluate disclosure, a policy that requires landlords to notify potential tenants of recent infestations in a unit. While disclosure aims to protect individual tenants, our results suggest that these policies also reduce infestation prevalence market-wide. Disclosure results in some initial cost to landlords but leads to significant savings in the long term.

Bed bugs have reemerged in the United States and worldwide over recent decades, presenting a major challenge to both public health practitioners and housing authorities. A number of municipalities have proposed or initiated policies to stem the bed bug epidemic, but little guidance is available to evaluate them. One contentious policy is disclosure, whereby landlords are obligated to notify potential tenants of current or prior bed bug infestations. Aimed to protect tenants from leasing an infested rental unit, disclosure also creates a kind of quarantine, partially and temporarily removing infested units from the market. Here, we develop a mathematical model for the spread of bed bugs in a generalized rental market, calibrate it to parameters of bed bug dispersion and housing turnover, and use it to evaluate the costs and benefits of disclosure policies to landlords. We find disclosure to be an effective control policy to curb infestation prevalence. Over the short term (within 5 years), disclosure policies result in modest increases in cost to landlords, while over the long term, reductions of infestation prevalence lead, on average, to savings. These results are insensitive to different assumptions regarding the prevalence of infestation, rate of introduction of bed bugs from other municipalities, and the strength of the quarantine effect created by disclosure. Beyond its application to bed bugs, our model offers a framework to evaluate policies to curtail the spread of household pests and is appropriate for systems in which spillover effects result in highly nonlinear cost–benefit relationships.

Comparing the effects of non-homogenous mixing patterns on epidemiological outcomes in equine populations: A mathematical modelling study

Disease transmission models often assume homogenous mixing. This assumption, however, has the potential to misrepresent the disease dynamics for populations in which contact patterns are non-random. A disease transmission model with an SEIR structure was used to compare the effect of weighted and unweighted empirical equine contact networks to weighted and unweighted theoretical networks generated using random mixing. Equine influenza was used as a case study. Incidence curves generated with the unweighted empirical networks were similar in epidemic duration (5-8 days) and peak incidence (30.8-46.4%). In contrast, the weighted empirical networks resulted in a more pronounced difference between the networks in terms of the epidemic duration (8-15 days) and the peak incidence (5-25%). The incidence curves for the empirical networks were bimodal, while the incidence curves for the theoretical networks were unimodal. The incorporation of vaccination and isolation in the model caused a decrease in the cumulative incidence for each network, however, this effect was only seen at high levels of vaccination and isolation for the complete network. This study highlights the importance of using empirical networks to describe contact patterns within populations that are unlikely to exhibit random mixing such as equine populations.