arXiv subjects

Joshua S. Weitz

Publications and source records attributed to Joshua S. Weitz.

At least 19 recordsLinked to original sources

arXiv2020

Heterogeneity in susceptibility dictates the order of epidemiological models

The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but do not incorporate population-level heterogeneity in infection susceptibility. We show that variation strongly influences the rate of infection, while the infection process simultaneously sculpts the susceptibility distribution. These joint dynamics influence the force of infection and are, in turn, influenced by the shape of the initial variability. Intriguingly, we find that certain susceptibility distributions (the exponential and the gamma) are unchanged through the course of the outbreak, and lead naturally to power-law behavior in the force of infection; other distributions often tend towards these "eigen-distributions" through the process of contagion. The power-law behavior fundamentally alters predictions of the long-term infection rate, and suggests that first-order epidemic models that are parameterized in the exponential-like phase may systematically and significantly over-estimate the final severity of the outbreak.

q-bio.PE↗

arXiv2019

Spatial interactions and oscillatory tragedies of the commons

A tragedy of the commons (TOC) occurs when individuals acting in their own self-interest deplete commonly-held resources, leading to a worse outcome than had they cooperated. Over time, the depletion of resources can change incentives for subsequent actions. Here, we investigate long-term feedback between game and environment across a continuum of incentives in an individual-based framework. We identify payoff-dependent transition rules that lead to oscillatory TOC-s in stochastic simulations and the mean field limit. Further extending the stochastic model, we find that spatially explicit interactions can lead to emergent, localized dynamics, including the propagation of cooperative wave fronts and cluster formation of both social context and resources. These dynamics suggest new mechanisms underlying how TOCs arise and how they might be averted.

q-bio.PE↗

arXiv2018

Optimal control policies for evolutionary dynamics with environmental feedback

We study a dynamical model of a population of cooperators and defectors whose actions have long-term consequences on environmental "commons" - what we term the "resource". Cooperators contribute to restoring the resource whereas defectors degrade it. The population dynamics evolve according to a replicator equation coupled with an environmental state. Our goal is to identify methods of influencing the population with the objective to maximize accumulation of the resource. In particular, we consider strategies that modify individual-level incentives. We then extend the model to incorporate a public opinion state that imperfectly tracks the true environmental state, and study strategies that influence opinion. We formulate optimal control problems and solve them using numerical techniques to characterize locally optimal control policies for three problem formulations: 1) control of incentives, and control of opinions through 2) propaganda-like strategies and 3) awareness campaigns. We show numerically that the resulting controllers in all formulations achieve the objective, albeit with an unintended consequence. The resulting dynamics include cycles between low and high resource states - a dynamical regime termed an "oscillating tragedy of the commons". This outcome may have desirable average properties, but includes risks to resource depletion. Our findings suggest the need for new approaches to controlling coupled population-environment dynamics.

eess.SY↗

arXiv2016

Networked SIS Epidemics with Awareness

We study an SIS epidemic process over a static contact network where the nodes have partial information about the epidemic state. They react by limiting their interactions with their neighbors when they believe the epidemic is currently prevalent. A node's awareness is weighted by the fraction of infected neighbors in their social network, and a global broadcast of the fraction of infected nodes in the entire network. The dynamics of the benchmark (no awareness) and awareness models are described by discrete-time Markov chains, from which mean-field approximations (MFA) are derived. The states of the MFA are interpreted as the nodes' probabilities of being infected. We show a sufficient condition for existence of a "metastable", or endemic, state of the awareness model coincides with that of the benchmark model. Furthermore, we use a coupling technique to give a full stochastic comparison analysis between the two chains, which serves as a probabilistic analogue to the MFA analysis. In particular, we show that adding awareness reduces the expectation of any epidemic metric on the space of sample paths, e.g. eradication time or total infections. We characterize the reduction in expectations in terms of the coupling distribution. In simulations, we evaluate the effect social distancing has on contact networks from different random graph families (geometric, Erdős-Renyi, and scale-free random networks).

cs.SI↗

arXiv2016

Disease dynamics on a network game: a little empathy goes a long way

Individuals change their behavior during an epidemic in response to whether they and/or those they interact with are healthy or sick. Healthy individuals are concerned about contracting a disease from their sick contacts and may utilize protective measures. Sick individuals may be concerned with spreading the disease to their healthy contacts and adopt preemptive measures. Yet, in practice both protective and preemptive changes in behavior come with costs. This paper proposes a stochastic network disease game model that captures the self-interests of individuals during the spread of a susceptible-infected-susceptible (SIS) disease where individuals react to current risk of disease spread, and their reactions together with the current state of the disease stochastically determine the next stage of the disease. We show that there is a critical level of concern, i.e., empathy, by the sick individuals above which disease is eradicated fast. Furthermore, we find that if the network and disease parameters are above the epidemic threshold, the risk averse behavior by the healthy individuals cannot eradicate the disease without the preemptive measures of the sick individuals. This imbalance in the role played by the response of the infected versus the susceptible individuals in disease eradication affords critical policy insights.

cs.SI↗

arXiv2016

Conflicting attachment and the growth of bipartite networks

Simple growth mechanisms have been proposed to explain the emergence of seemingly universal network structures. The widely-studied model of preferential attachment assumes that new nodes are more likely to connect to highly connected nodes. Preferential attachment explains the emergence of scale-free degree distributions within complex networks. Yet, it is incompatible with many network systems, particularly bipartite systems in which two distinct types of agents interact. For example, the addition of new links in a host-parasite system corresponds to the infection of hosts by parasites. Increasing connectivity is beneficial to a parasite and detrimental to a host. Therefore, the overall network connectivity is subject to conflicting pressures. Here, we propose a stochastic network growth model of conflicting attachment, inspired by a particular kind of parasite-host interactions: that of viruses interacting with microbial hosts. The mechanism of network growth includes conflicting preferences to network density as well as costs involved in modifying the network connectivity according to these preferences. We find that the resulting networks exhibit realistic patterns commonly observed in empirical data, including the emergence of nestedness, modularity, and nested-modular structures that exhibit both properties. We study the role of conflicting interests in shaping network structure and assess opportunities to incorporate greater realism in linking growth process to pattern in systems governed by antagonistic and mutualistic interactions.

physics.soc-ph↗

arXiv2015

A Touch of Sleep: Biophysical Model of Contact-mediated Dormancy of Archaea by Viruses

The canonical view of the interactions between viruses and their microbial hosts presumes that changes in host and virus fate require the initiation of infection of a host by a virus. That is, first virus particles diffuse randomly outside of host cells, then the virus genome enters the target host cell, and only then do intracellular dynamics and regulation of virus and host cell fate unfold. Intracellular dynamics may lead to the death of the host cell and release of viruses, to the elimination of the virus genome through cellular defense mechanisms, or the integration of the virus genome with the host as a chromosomal or extra-chromosomal element. Here we revisit this canonical view, inspired by recent experimental findings of Bautista and colleagues (mBio, 2015) in which the majority of target host cells can be induced into a dormant state when exposed to either active or de-activated viruses, even when viruses are present at low relative titer. We propose that both the qualitative phenomena and the quantitative time-scales of dormancy induction can be reconciled given the hypothesis that cellular physiology can be altered by contact on the surface of host cells rather than strictly by infection. We develop a biophysical model of contact-mediated dynamics involving virus particles and target cells. We show how in this model virus particles can catalyze - extracellularly - cellular transformations amongst many cells, even if they ultimately infect only one (or none). We discuss implications of the present biophysical model relevant to the study of virus-microbe interactions more generally.

q-bio.PE↗

arXiv2014

Post-death Transmission of Ebola: Challenges for Inference and Opportunities for Control

Multiple epidemiological models have been proposed to predict the spread of Ebola in West Africa. These models include consideration of counter-measures meant to slow and, eventually, stop the spread of the disease. Here, we examine one component of Ebola dynamics that is of growing concern -- the transmission of Ebola from the dead to the living. We do so by applying the toolkit of mathematical epidemiology to analyze the consequences of post-death transmission. We show that underlying disease parameters cannot be inferred with confidence from early-stage incidence data (that is, they are not "identifiable") because different parameter combinations can produce virtually the same epidemic trajectory. Despite this identifiability problem, we find robustly that inferences that don't account for post-death transmission tend to underestimate the basic reproductive number -- thus, given the observed rate of epidemic growth, larger amounts of post-death transmission imply larger reproductive numbers. From a control perspective, we explain how improvements in reducing post-death transmission of Ebola may reduce the overall epidemic spread and scope substantially. Increased attention to the proportion of post-death transmission has the potential to aid both in projecting the course of the epidemic and in evaluating a portfolio of control strategies.

q-bio.PE↗

arXiv2014

BiMAT: a MATLAB(R) package to facilitate the analysis and visualization of bipartite networks

The statistical analysis of the structure of bipartite ecological networks has increased in importance in recent years. Yet, both algorithms and software packages for the analysis of network structure focus on properties of unipartite networks. In response, we describe BiMAT, an object-oriented MATLAB package for the study of the structure of bipartite ecological networks. BiMAT can analyze the structure of networks, including features such as modularity and nestedness, using a selection of widely-adopted algorithms. BiMAT also includes a variety of null models for evaluating the statistical significance of network properties. BiMAT is capable of performing multi-scale analysis of structure - a potential (and under-examined) feature of many biological networks. Finally, BiMAT relies on the graphics capabilities of MATLAB to enable the visualization of the statistical structure of bipartite networks in either matrix or graph layout representations. BiMAT is available as an open-source package at http://ecotheory.biology.gatech.edu/cflores.

q-bio.QM↗

arXiv2014

The virus of my virus is my friend: ecological effects of virophage with alternative modes of coinfection

Virophages are viruses that rely on the replication machinery of other viruses to reproduce within eukaryotic hosts. Two different modes of coinfection have been posited based on experimental observation. In one mode, the virophage and virus enter the host independently. In the other mode, the virophage adheres to the virus so both virophage and virus enter the host together. Here we ask: what are the ecological effects of these different modes of coinfection? In particular, what ecological effects are common to both infection modes, and what are the differences particular to each mode? We develop a pair of biophysically motivated ODE models of viral-host population dynamics, corresponding to dynamics arising from each mode of infection. We find both modes of coinfection allow for the coexistence of the virophage, virus, and host either at a stable fixed point or through cyclical dynamics. In both models, virophage tend to be the most abundant population and their presence always reduces the viral abundance and increases the host abundance. However, we do find qualitative differences between models. For example, via extensive sampling of biologically relevant parameter space, we only observe bistability when the virophage and virus enter the host together. We discuss how such differences may be leveraged to help identify modes of infection in natural environments from population level data.

q-bio.PE↗

arXiv2013

The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion

Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modelled as an elongating path or series of segments without taking into account lateral expansion during elongation. Instead, models of growth often introduce an explicit thickness by expanding the area around the completed elongated path. Modelling expansion in this way can lead to contradictions in the physical plausibility of the resulting surface and to uncertainty about how the object reached certain regions of space. Here, we introduce "fiber walks" as a self-avoiding random walk model for tip-driven growth processes that includes lateral expansion. In 2D, the fiber walk takes place on a square lattice and the space occupied by the fiber is modelled as a lateral contraction of the lattice. This contraction influences the possible follow-up steps of the fiber walk. The boundary of the area consumed by the contraction is derived as the dual of the lattice faces adjacent to the fiber. We show that fiber walks generate fibers that have well-defined curvatures, enable the identification of the process underlying the occupancy of physical space. Hence, fiber walks provide a base from which to model both the extension and expansion of physical biological objects with finite thickness.

physics.bio-ph↗

arXiv2013

Let my people go (home) to Spain: a genealogical model of Jewish identities since 1492

The Spanish government recently announced an official fast-track path to citizenship for any individual who is Jewish and whose ancestors were expelled from Spain during the inquisition-related dislocation of Spanish Jews in 1492. It would seem that this policy targets a small subset of the global Jewish population, i.e., restricted to individuals who retain cultural practices associated with ancestral origins in Spain. However, the central contribution of this manuscript is to demonstrate how and why the policy is far more likely to apply to a very large fraction (i.e., the vast majority) of Jews. This claim is supported using a series of genealogical models that include transmissable "identities" and preferential intra-group mating. Model analysis reveals that even when intra-group mating is strong and even if only a small subset of a present-day population retains cultural practices typically associated with that of an ancestral group, it is highly likely that nearly all members of that population have direct geneaological links to that ancestral group, given sufficient number of generations have elapsed. The basis for this conclusion is that not having a link to an ancestral group must be a property of all of an individual's ancestors, the probability of which declines (nearly) superexponentially with each successive generation. These findings highlight unexpected incongruities induced by genealogical dynamics between present-day and ancestral identities.

q-bio.PE↗

arXiv2013

Mechanisms of Multi-strain Coexistence in Host-Phage Systems with Nested Infection Networks

Bacteria and their viruses ("bacteriophages") coexist in natural environments forming complex infection networks. Recent empirical findings suggest that phage-bacteria infection networks often possess a nested structure such that there is a hierarchical relationship among who can infect whom. Here we consider how nested infection networks may affect phage and bacteria dynamics using a multi-type Lotka-Volterra framework with cross-infection. Analysis of similar models have, in the past, assumed simpler interaction structures as a first step towards tractability. We solve the proposed model, finding trade-off conditions on the life-history traits of both bacteria and viruses that allow coexistence in communities with nested infection networks. First, we find that bacterial growth rate should decrease with increasing defense against infection. Second, we find that the efficiency of viral infection should decrease with host range. Next, we establish a relationship between relative densities and the curvature of life history trade-offs. We compare and contrast the current findings to the "Kill-the-Winner" model of multi-species phage-bacteria communities. Finally, we discuss a suite of testable hypotheses stemming from the current model concerning relationships between infection range, life history traits and coexistence in complex phage-bacteria communities.

q-bio.PE↗

arXiv2013

Robust estimation of microbial diversity in theory and in practice

Quantifying diversity is of central importance for the study of structure, function and evolution of microbial communities. The estimation of microbial diversity has received renewed attention with the advent of large-scale metagenomic studies. Here, we consider what the diversity observed in a sample tells us about the diversity of the community being sampled. First, we argue that one cannot reliably estimate the absolute and relative number of microbial species present in a community without making unsupported assumptions about species abundance distributions. The reason for this is that sample data do not contain information about the number of rare species in the tail of species abundance distributions. We illustrate the difficulty in comparing species richness estimates by applying Chao's estimator of species richness to a set of in silico communities: they are ranked incorrectly in the presence of large numbers of rare species. Next, we extend our analysis to a general family of diversity metrics ("Hill diversities"), and construct lower and upper estimates of diversity values consistent with the sample data. The theory generalizes Chao's estimator, which we retrieve as the lower estimate of species richness. We show that Shannon and Simpson diversity can be robustly estimated for the in silico communities. We analyze nine metagenomic data sets from a wide range of environments, and show that our findings are relevant for empirically-sampled communities. Hence, we recommend the use of Shannon and Simpson diversity rather than species richness in efforts to quantify and compare microbial diversity.

q-bio.PE↗

arXiv2011

Hierarchical ordering of reticular networks

The structure of hierarchical networks in biological and physical systems has long been characterized using the Horton-Strahler ordering scheme. The scheme assigns an integer order to each edge in the network based on the topology of branching such that the order increases from distal parts of the network (e.g., mountain streams or capillaries) to the "root" of the network (e.g., the river outlet or the aorta). However, Horton-Strahler ordering cannot be applied to networks with loops because they they create a contradiction in the edge ordering in terms of which edge precedes another in the hierarchy. Here, we present a generalization of the Horton-Strahler order to weighted planar reticular networks, where weights are assumed to correlate with the importance of network edges, e.g., weights estimated from edge widths may correlate to flow capacity. Our method assigns hierarchical levels not only to edges of the network, but also to its loops, and classifies the edges into reticular edges, which are responsible for loop formation, and tree edges. In addition, we perform a detailed and rigorous theoretical analysis of the sensitivity of the hierarchical levels to weight perturbations. We discuss applications of this generalized Horton-Strahler ordering to the study of leaf venation and other biological networks.

q-bio.QM↗

arXiv2010

Fluctuation Domains in Adaptive Evolution

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains - parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource.

q-bio.PE↗

arXiv2002

Packing-Limited Growth

We consider growing spheres seeded by random injection in time and space. Growth stops when two spheres meet leading eventually to a jammed state. We study the statistics of growth limited by packing theoretically in d dimensions and via simulation in d=2, 3, and 4. We show how a broad class of such models exhibit distributions of sphere radii with a universal exponent. We construct a scaling theory that relates the fractal structure of these models to the decay of their pore space, a theory that we confirm via numerical simulations. The scaling theory also predicts an upper bound for the universal exponent and is in exact agreement with numerical results for d=4.

cond-mat.soft↗

arXiv2000

Re-examination of the "3/4-law" of Metabolism

We examine the scaling law $B \propto M^α$ which connects organismal metabolic rate $B$ with organismal mass $M$, where $α$ is commonly held to be 3/4. Since simple dimensional analysis suggests $α=2/3$, we consider this to be a null hypothesis testable by empirical studies. We re-analyze data sets for mammals and birds compiled by Heusner, Bennett and Harvey, Bartels, Hemmingsen, Brody, and Kleiber, and find little evidence for rejecting $α=2/3$ in favor of $α=3/4$. For mammals, we find a possible breakdown in scaling for larger masses reflected in a systematic increase in $α$. We also review theoretical justifications of $α=3/4$ based on dimensional analysis, nutrient-supply networks, and four-dimensional biology. We find that present theories for $α=3/4$ require assumptions that render them unconvincing for rejecting the null hypothesis that $α=2/3$.

physics.bio-ph↗