Inferring network of infectious disease spread


Figure: Spread of upper respiratory tract disease in a desert tortoise population. Nodes are animals and edges represent asynchronous burrow use of tortoises. Orange nodes are the animals that were reported infected, green are the ones reported healthy, and purple nodes are the individuals with unknown health status.

Infectious disease spread is a fundamental process that takes place through host contact networks. Constructing network models of disease spread, however, requires knowledge of the transmission mode of a pathogen. While it has been possible to characterize contact networks of several human infectious diseases based on our understanding of how pathogens transmit (e.g., sexual contacts for HIV, physical proximity for measles), limited knowledge about how pathogens transmits and high costs of data collection makes network modeling of infectious diseases in several other systems particularly difficult.

We have developed a new tool, INoDS, that utilizes Bayesian inference to infer contact networks of disease transmission in human or animal populations, as well as disease transmission higher spatial scales. INoDS (Inferring Networks of infectious Disease Spread) uses time-stamped disease and network data to provide evidence supporting contact networks that represent competing hypotheses about transmission modes. We have evaluated this tool on synthetic network disease data, and shown that INoDS accurately identifies the underlying contact network even when the networks are partially sampled and information on disease spread is incomplete. We are currently using the tool to explain transmission mechanisms of infectious disease spread in three real animal populations (bumble bees, Australian sleepy lizards the desert tortoises). INoDS therefore provides a novel network inference tool which extends the potential of network modelling in disease ecology and provides insights towards biological mechanisms of pathogen spread which would take years to resolve through traditional laboratory techniques.

Disease implications of animal social organization and network structure


Figure: Phylogenetic distribution of animal species represented in the interaction network dataset used in this study. Numbers next to the inner ring denote the total networks available for the particular species. The inner and the middle ring is color coded according to the taxonomic class and the social system of the species. The colors in the outer ring indicates the type of interaction represented in the network

Past studies examining the disease costs of sociality have generally explored hypotheses that link larger group size to higher rates of infection transmission. However, beyond a simple dependence on group size, infection spread is largely influenced by the organization of infection­spreading interactions between individuals. Network analysis tools have allowed for rapid advances in our understanding of the disease consequences of sociality at an individual scale, but studies on species level sociality are still lacking. Here we conduct a comparative analysis of 666 interaction networks across 47 species to investigate the relationship between network complexity and the costs of disease transmission for four social systems – solitary, fission­fusion, social and socially hierarchical. Specifically, we use phylogenetically­controlled Bayesian MCMC modelling and in­silico disease simulations to identify the relative costs of disease transmission for each social system as mediated by their network structure.

We find that solitary, fission­fusion, and higher social organizations can be distinguished from each other based on (a) degree of variation among social partners, (b) the extent to which the interaction network is fragmented and (c) the proportion of individuals that occupy socially central positions within the interaction networks. In particular, individuals of solitary species demonstrate the highest variation in the number of social partners, while the interaction networks of fission­fusion species are the most fragmented. The results of disease simulations show that the structure of interaction networks can alleviate the disease costs of group living for social, but not socially hierarchical species. Our findings, therefore, offer new perspectives on the debate about the disease costs of group living by evaluating how social organization strategies mediate pathogen pressures

Unraveling the disease consequences and mechanisms of modular structure in animal social networks


Figure 3 of Sah et al. (2017): Overall disease implications of modular subdivisions. (A) Average outbreak size, measured as the percentage of infected individuals, over increasing subdivided social networks and pathogen transmissibility. Outbreak size values have been normalized to the maximum observed outbreak. The solid line indicates epidemic threshold, viz., the threshold value of pathogen contagiousness below which there is no risk of a large outbreak ( > 10% outbreak size). (B) Epidemic robustnessof networks with increasing value of relative modularity, measured as the percentage reduction in outbreak size as compared to outbreak size experienced by homogeneous ( Qrel = 0 ) networks. The solid line indicates modularity threshold where networks experience at least a 10% reduction in outbreak size. (C) Infection transmission events, expressed as the percentage of total outbreak size, within subgroups (local) and between subgroups (global), pathogen transmissibility = 0.18; (D) Disease implications of modular subdivisions as a function of subgroup cohesion and network fragmentation (measured as the lognumber of subgroups present in the network).

Modular organization in animal social networks is hypothesized to alleviate the cost of disease burden in group living species. However, our analysis of empirical social networks of 43 animal species along with theoretical networks demonstrates that infectious disease spread is largely unaffected by the underlying modular organi- zation except when social networks are extremely subdivided. We show that high fragmentation and high subgroup cohesion, which are both associated with high modularity in social networks, induce structural delay and trapping of infections that spread through these networks, reducing disease burden. We validate our results using real animal social networks, and recommend the use of appropriate null network models when data-limited estimates of epidemic consequences are necessary.

Random modular network generator


Figure 5 of Sah et al. (2014): Visualization of empirical and random graphs of social interaction of dolphins and food-web trophic interactions at the LittleRock Lake in Wisconsin. Figure (a) is the empirical network of Dolphin social network, (b) its modular random graph, and (c) its random graph counterpart with matched degree distribution (Q = 0). Figure (d) is the empirical network for the food-web trophic interaction at Little Rock Lake in Wisconsin, (e) is its modular random graph and (f) its random graph counterpart with matched degree distribution. Modular random graphs have generated to match the overall degree distribution, network mean degree, the level of modularity and the number of modules of the empirical graphs. Random graphs with matched degree distribution are based on the configuration model.

Networks are mathematical representations of the interactions between different components of a system. In network analysis, the interacting components are represented as nodes (also called vertices) and their interactions are represented as edges. It is now well known that most of the networks around us including metabolic networks, neural networks, protein-protein interaction networks and even social networks are not random; some nodes are more closely associated with each other than with the rest of the networks, forming communities or modules in the network. Even though this property is known to be an almost universal structural feature, little is known about its functional role in a network.

In this study we develop a model that generates simple modular random graphs with tunable strength of community structure. The generated graphs are random with respect to other properties of the network, which makes these graphs an important tool to tease apart the role of community structure in complex real-world networks.

Effect of environmental, demographic drivers and the role of stressors on the social structure of the desert tortoise


Figure 5 of Sah et al. (2016): The effect of various predictors on the two models of burrow use patterns in desert tortoises. Error bars indicate 95 % confidence intervals around the estimated coefficient value. For continuous predictors, the vertical dashed line indicates no effect—positive coefficients indicate increase in burrow popularity/switching with increase in predictor value; negative coefficients indicate decrease in burrow popularity/switching with higher values of predictors. For each categorical predictor, the base factor (solid data points) straddles the vertical line at 0 and appears without a 95 % CI. Positive and negative coefficients for categorical predictors denote increase and decrease, respectively, in burrow popularity/switching relative to the base factor.

Adaptive and social behavior that affects fitness is now being increasingly incorporated in the conservation and management of wildlife species. However, direct observations of social interactions in species considered to be solitary are difficult, and therefore integration of behavior in conservation and management decisions in such species has been infrequent. For such species, we propose quantifying refuge use behavior as it can provide insights towards their (hidden) social structure, establish relevant contact patterns of infectious disease spread, and provide early warning signals of population stressors. Our study highlights this approach in a long-lived and threatened species, the desert tortoise. We provide evidence toward the presence of and identify mechanisms behind the social structure in desert tortoises formed by their burrow use preferences. We also show how individuals burrow use behavior responds to the presence of population stressors.

Adaptive limiter control


Figure 2a of Sah et al. (2013): Effect of magnitude of ALC value in an uncoupled Ricker map (A) Simulations over 1000 iterations, taking the Ricker growth rate parameter, r = 3.1 and K = 60. Increasing the value of c decreases the amplitude of population size fluctuation for a single population. FI decreases monotonically with c except for very small values (c = 0.05) where there is a slight increase. Although ALC does not lead to limit cycles beyond c = 0.3, it does cause a reduction in FI, thus enhancing constancy. This highlights that constancy and simpler dynamics do not necessarily correlate, and the values of ALC to be used should depend on the kind of stability desired in the system.

Stabilizing the dynamics of biological populations and metapopulations has been a popular area of among population biologists, conservation biologists and non-linear dynamists. Out of the several theoretical models proposed, few have been empirically tested but have been of limited success. We proposed a novel control strategy called Adaptive Limiter Control (ALC), which reduces both fluctuation in population size as well as extinction probability of (meta)populations. We used this control strategy to successfully stabilize unstable laboratory populations and metapopulations of fruit flies, Drosophila melanogaster, making it the first control method that has been empirically shown to work for biological metapopulations.