Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing

In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic SIR epidemic models on undirected contact networks. We then show how the same theory can be used to analyze stochastic SIR models with random and proportionate mixing. The epidemic percolation networks for these models are purely directed because undirected edges disappear in the limit of a large population. In a series of simulations, we show that epidemic percolation networks accurately predict the mean outbreak size and probability and final size of an epidemic for a variety of epidemic models in homogeneous and heterogeneous populations. Finally, we show that epidemic percolation networks can be used to re-derive classical results from several different areas of infectious disease epidemiology. In an appendix, we show that an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model in a closed population and prove that the distribution of outbreak sizes given the infection of any given node in the SIR model is identical to the distribution of its out-component sizes in the corresponding probability space of epidemic percolation networks. We conclude that the theory of percolation on semi-directed networks provides a very general framework for the analysis of stochastic SIR models in closed populations.Comment: 40 pages, 9 figure

Generation interval contraction and epidemic data analysis

The generation interval is the time between the infection time of an infected person and the infection time of his or her infector. Probability density functions for generation intervals have been an important input for epidemic models and epidemic data analysis. In this paper, we specify a general stochastic SIR epidemic model and prove that the mean generation interval decreases when susceptible persons are at risk of infectious contact from multiple sources. The intuition behind this is that when a susceptible person has multiple potential infectors, there is a ``race'' to infect him or her in which only the first infectious contact leads to infection. In an epidemic, the mean generation interval contracts as the prevalence of infection increases. We call this global competition among potential infectors. When there is rapid transmission within clusters of contacts, generation interval contraction can be caused by a high local prevalence of infection even when the global prevalence is low. We call this local competition among potential infectors. Using simulations, we illustrate both types of competition. Finally, we show that hazards of infectious contact can be used instead of generation intervals to estimate the time course of the effective reproductive number in an epidemic. This approach leads naturally to partial likelihoods for epidemic data that are very similar to those that arise in survival analysis, opening a promising avenue of methodological research in infectious disease epidemiology.Comment: 20 pages, 5 figures; to appear in Mathematical Bioscience

Molecular Infectious Disease Epidemiology: Survival Analysis and Algorithms Linking Phylogenies to Transmission Trees

Recent work has attempted to use whole-genome sequence data from pathogens to reconstruct the transmission trees linking infectors and infectees in outbreaks. However, transmission trees from one outbreak do not generalize to future outbreaks. Reconstruction of transmission trees is most useful to public health if it leads to generalizable scientific insights about disease transmission. In a survival analysis framework, estimation of transmission parameters is based on sums or averages over the possible transmission trees. A phylogeny can increase the precision of these estimates by providing partial information about who infected whom. The leaves of the phylogeny represent sampled pathogens, which have known hosts. The interior nodes represent common ancestors of sampled pathogens, which have unknown hosts. Starting from assumptions about disease biology and epidemiologic study design, we prove that there is a one-to-one correspondence between the possible assignments of interior node hosts and the transmission trees simultaneously consistent with the phylogeny and the epidemiologic data on person, place, and time. We develop algorithms to enumerate these transmission trees and show these can be used to calculate likelihoods that incorporate both epidemiologic data and a phylogeny. A simulation study confirms that this leads to more efficient estimates of hazard ratios for infectiousness and baseline hazards of infectious contact, and we use these methods to analyze data from a foot-and-mouth disease virus outbreak in the United Kingdom in 2001. These results demonstrate the importance of data on individuals who escape infection, which is often overlooked. The combination of survival analysis and algorithms linking phylogenies to transmission trees is a rigorous but flexible statistical foundation for molecular infectious disease epidemiology.Comment: 28 pages, 11 figures, 3 table

Perspective review of what is needed for molecular-specific fluorescence-guided surgery

Molecular image-guided surgery has the potential for translating the tools of molecular pathology to real-time guidance in surgery. As a whole, there are incredibly positive indicators of growth, including the first United States Food and Drug Administration clearance of an enzyme-biosynthetic-activated probe for surgery guidance, and a growing number of companies producing agents and imaging systems. The strengths and opportunities must be continued but are hampered by important weaknesses and threats within the field. A key issue to solve is the inability of macroscopic imaging tools to resolve microscopic biological disease heterogeneity and the limitations in microscopic systems matching surgery workflow. A related issue is that parsing out true molecular-specific uptake from simple-enhanced permeability and retention is hard and requires extensive pathologic analysis or multiple in vivo tests, comparing fluorescence accumulation with standard histopathology and immunohistochemistry. A related concern in the field is the over-reliance on a finite number of chosen preclinical models, leading to early clinical translation when the probe might not be optimized for high intertumor variation or intratumor heterogeneity. The ultimate potential may require multiple probes, as are used in molecular pathology, and a combination with ultrahigh-resolution imaging and image recognition systems, which capture the data at a finer granularity than is possible by the surgeon. Alternatively, one might choose a more generalized approach by developing the tracer based on generic hallmarks of cancer to create a more "one-size-fits-all" concept, similar to metabolic aberrations as exploited in fluorodeoxyglucose-positron emission tomography (FDG-PET) (i.e., Warburg effect) or tumor acidity. Finally, methods to approach the problem of production cost minimization and regulatory approvals in a manner consistent with the potential revenue of the field will be important. In this area, some solid steps have been demonstrated in the use of fluorescent labeling commercial antibodies and separately in microdosing studies with small molecules. (C) The Authors

Second look at the spread of epidemics on networks

In an important paper, M.E.J. Newman claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor. In this paper, we show that this isomorphism is incorrect and define a semi-directed random network we call the epidemic percolation network that is exactly isomorphic to the SIR epidemic model in any finite population. In the limit of a large population, (i) the distribution of (self-limited) outbreak sizes is identical to the size distribution of (small) out-components, (ii) the epidemic threshold corresponds to the phase transition where a giant strongly-connected component appears, (iii) the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in-component, and (iv) the relative final size of an epidemic is equal to the proportion of the network contained in the giant out-component. For the SIR model considered by Newman, we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold, the same epidemic threshold, and the same final size of an epidemic as the bond percolation model. However, the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution. We confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations. In an appendix, we show that an isomorphism to an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model.Comment: 29 pages, 5 figure

Mixed Ancestry and Admixture in Kauai\u27s Feral Chickens: Invasion of Domestic Genes into Ancient Red Junglefowl Reservoirs

A major goal of invasion genetics is to determine how establishment histories shape non‐native organisms\u27 genotypes and phenotypes. While domesticated species commonly escape cultivation to invade feral habitats, few studies have examined how this process shapes feral gene pools and traits. We collected genomic and phenotypic data from feral chickens (Gallus gallus) on the Hawaiian island of Kauai to (i) ascertain their origins and (ii) measure standing variation in feral genomes, morphology and behaviour. Mitochondrial phylogenies (D‐loop & whole Mt genome) revealed two divergent clades within our samples. The rare clade also contains sequences from Red Junglefowl (the domestic chicken\u27s progenitor) and ancient DNA sequences from Kauai that predate European contact. This lineage appears to have been dispersed into the east Pacific by ancient Polynesian colonists. The more prevalent MtDNA clade occurs worldwide and includes domesticated breeds developed recently in Europe that are farmed within Hawaii. We hypothesize this lineage originates from recently feralized livestock and found supporting evidence for increased G. gallus density on Kauai within the last few decades. SNPs obtained from whole‐genome sequencing were consistent with historic admixture between Kauai\u27s divergent (G. gallus) lineages. Additionally, analyses of plumage, skin colour and vocalizations revealed that Kauai birds\u27 behaviours and morphologies overlap with those of domestic chickens and Red Junglefowl, suggesting hybrid origins. Together, our data support the hypotheses that (i) Kauai\u27s feral G. gallus descend from recent invasion(s) of domestic chickens into an ancient Red Junglefowl reservoir and (ii) feral chickens exhibit greater phenotypic diversity than candidate source populations. These findings complicate management objectives for Pacific feral chickens, while highlighting the potential of this and other feral systems for evolutionary studies of invasions

Predation thresholds for reintroduction of native avifauna following suppression of invasive Brown Treesnakes on Guam

The brown treesnake (BTS) (Boiga irregularis) invasion on Guåhan (in English, Guam) led to the extirpation of nearly all native forest birds. In recent years, methods have been developed to reduce BTS abundance on a landscape scale. To help assess the prospects for the successful reintroduction of native birds to Guåhan following BTS suppression, we modeled bird population persistence based on their life history characteristics and relative sensitivity to BTS predation. We constructed individual-based models and simulated BTS predation in hypothetical founding populations for each of seven candidate bird species. We represented BTS predation risk in two steps: risk of being encountered and risk of mortality if encountered. We link encounter risk from the bird’s perspective to snake contact rates at camera traps with live animal lures, the most direct practical means of estimating BTS predation risk. Our simulations support the well-documented fact that Guåhan’s birds cannot persist with an uncontrolled population of BTS but do indicate that bird persistence in Guåhan’s forests is possible with suppression short of total eradication. We estimate threshold BTS contact rates would need to be below 0.0002–0.0006 snake contacts per bird per night for these birds to persist on the landscape, which translates to an annual encounter probability of 0.07–0.20. We simulated the effects of snake-proof nest boxes for Sihek (Todiramphus cinnamominus) and Såli (Aplonis opaca), but the benefits were small relative to the overall variation in contact rate thresholds among species. This variation among focal bird species in sustainable predation levels can be used to prioritize species for reintroduction in a BTS-suppressed landscape, but variation among these species is narrow relative to the required reduction from current BTS levels, which may be four orders of magnitude higher (\u3e0.18). Our modeling indicates that the required predation thresholds may need to be lower than have yet been demonstrated with current BTS management. Our predation threshold metric provides an important management tool to help estimate target BTS suppression levels that can be used to determine when bird reintroduction campaigns might begin and serves as a model for other systems to match predator control with reintroduction efforts