arXiv subjects

Leah B. Shaw

Publications and source records attributed to Leah B. Shaw.

At least 19 recordsLinked to original sources

arXiv2023

Stability and Fluctuations in Complex Ecological Systems

From 08-12 August, 2022, 32 individuals participated in a workshop, Stability and Fluctuations in Complex Ecological Systems, at the Lorentz Center, located in Leiden, The Netherlands. An interdisciplinary dialogue between ecologists, mathematicians, and physicists provided a foundation of important problems to consider over the next 5-10 years. This paper outlines eight areas including (1) improving our understanding of the effect of scale, both temporal and spatial, for both deterministic and stochastic problems; (2) clarifying the different terminologies and definitions used in different scientific fields; (3) developing a comprehensive set of data analysis techniques arising from different fields but which can be used together to improve our understanding of existing data sets; (4) having theoreticians/computational scientists collaborate closely with empirical ecologists to determine what new data should be collected; (5) improving our knowledge of how to protect and/or restore ecosystems; (6) incorporating socio-economic effects into models of ecosystems; (7) improving our understanding of the role of deterministic and stochastic fluctuations; (8) studying the current state of biodiversity at the functional level, taxa level and genome level.

q-bio.PE↗

arXiv2020

Impacts of density-dependent predation, cannibalism and fishing in a stage-structured population model of the blue crab in Chesapeake Bay

The blue crab (Callinectes sapidus) is a dominant ecological species of high commercial value. Spawning stock and recruitment of the Chesapeake Bay population declined by 80% in the 1990s. After severe management actions were implemented in 2008, female abundance rebounded to pre-1994 levels and stabilized. The stepwise decline in the early 1990s, followed by a consistently low level of abundance for 15 y and a jump to high abundance after 2008, suggested the existence of alternative stable states. Alternatively, high fishing pressure combined with low recruitment in 1992 could have triggered a proportional decline in the population, followed by a population increase in 2008 due to rigorous management actions that reduced fishing. We evaluated these alternatives with a stage-structured dynamic population model using ordinary differential equations. In addition, stock assessment models assume that fishing and mortality are independent of density. Hence, we also investigated the role of density-dependent predation, cannibalism and fishing in blue crab population dynamics. We conclude that for the blue crab population in Chesapeake Bay: (1) bistable positive states are not likely with biologically realistic parameter values; (2) hyperbolic (depensatory) fishing will not produce extinction at the range of population densities observed in the bay; and (3) crabs can survive a higher fishing rate under the more realistic assumption of sigmoidal (density-dependent) predation and cannibalism than under constant (density-independent) predation and cannibalism. These collectively indicate that the blue crab population in Chesapeake Bay is resilient to a range of biotic and abiotic disturbances.

q-bio.PE↗

arXiv2018

Intervention Strategies for Epidemics: Does Ignoring Time Delay Lead to Incorrect Predictions?

Our paper investigates distributions of exposed and infectious time periods in an epidemic model and how applying a disease control strategy affects the model's accuracy. While ordinary differential equations are widely used for their simplicity, they incorporate an exponential distribution for time spent exposed or infectious. This allows for a high probability of unrealistically short exposed and infectious time periods. We propose that caution must be taken when applying intervention methods to basic models in order to avoid inaccurate predictions. Delay differential equations, which use a delta distribution for exposed and infectious periods, can provide better realism but are more difficult to use and analyze. We introduce a multi-infected compartment model to interpolate between an ODE model with exponential distributions and a DDE model with delta distributions in order to investigate the effect these distributions have on the dynamics of the system when an intervention method is also included. Using steady state stability and bifurcation analysis, this paper considers when simpler infectious disease models can be used versus when more realistic time periods must be incorporated. We find that the placement of control measures on subpopulations and the length of the time delay impacts the accuracy of the simpler models.

q-bio.PE↗

arXiv2018

Enhancement of large fluctuations to extinction in adaptive networks

During an epidemic, individual nodes in a network may adapt their connections to reduce the chance of infection. A common form of adaption is avoidance rewiring, where a noninfected node breaks a connection to an infected neighbor and forms a new connection to another noninfected node. Here we explore the effects of such adaptivity on stochastic fluctuations in the susceptible-infected-susceptible model, focusing on the largest fluctuations that result in extinction of infection. Using techniques from large-deviation theory, combined with a measurement of heterogeneity in the susceptible degree distribution at the endemic state, we are able to predict and analyze large fluctuations and extinction in adaptive networks. We find that in the limit of small rewiring there is a sharp exponential reduction in mean extinction times compared to the case of zero adaption. Furthermore, we find an exponential enhancement in the probability of large fluctuations with increased rewiring rate, even when holding the average number of infected nodes constant.

nlin.AO↗

arXiv2014

Rare Event Extinction on Stochastic Networks

We consider the problem of extinction processes on random networks with a given structure. For sufficiently large well-mixed populations, the process of extinction of one or more state variable components occurs in the tail of the quasi-stationary probability distribution, thereby making it a rare event. Here we show how to extend the theory of large deviations to random networks to predict extinction times. In particular, we use the theory to find the most probable path leading to extinction. We apply the methodology to epidemic models and discover how mean extinction times scale with epidemiological and network parameters in Erdos-Renyi networks. The results are shown to compare quite well with Monte Carlo simulations of the network in predicting both the most probable paths to extinction and mean extinction times.

q-bio.PE↗

arXiv2014

Inferring unobserved multistrain epidemic sub-populations using synchronization dynamics

A new method is proposed to infer unobserved epidemic sub-populations by exploiting the synchronization properties of multistrain epidemic models. A model for dengue fever is driven by simulated data from secondary infective populations. Primary infective populations in the driven system synchronize to the correct values from the driver system. Most hospital cases of dengue are secondary infections, so this method provides a way to deduce unobserved primary infection levels. We derive center manifold equations that relate the driven system to the driver system and thus motivate the use of synchronization to predict unobserved primary infectives. Synchronization stability between primary and secondary infections is demonstrated through numerical measurements of conditional Lyapunov exponents and through time series simulations.

nlin.CD↗

arXiv2013

Asymptotically inspired moment-closure approximation for adaptive networks

Adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a new approach to moment closure based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.

cond-mat.stat-mech↗

arXiv2012

Effects of community structure on epidemic spread in an adaptive network

When an epidemic spreads in a population, individuals may adaptively change the structure of their social contact network to reduce risk of infection. Here we study the spread of an epidemic on an adaptive network with community structure. We model the effect of two communities with different average degrees. The disease model is susceptible-infected-susceptible (SIS), and adaptation is rewiring of links between susceptibles and infectives. The bifurcation structure is obtained, and a mean field model is developed that accurately predicts the steady state behavior of the system. We show that an epidemic can alter the community structure.

q-bio.PE↗

arXiv2012

Recruitment dynamics in adaptive social networks

We model recruitment in adaptive social networks in the presence of birth and death processes. Recruitment is characterized by nodes changing their status to that of the recruiting class as a result of contact with recruiting nodes. Only a susceptible subset of nodes can be recruited. The recruiting individuals may adapt their connections in order to improve recruitment capabilities, thus changing the network structure adaptively. We derive a mean field theory to predict the dependence of the growth threshold of the recruiting class on the adaptation parameter. Furthermore, we investigate the effect of adaptation on the recruitment level, as well as on network topology. The theoretical predictions are compared with direct simulations of the full system. We identify two parameter regimes with qualitatively different bifurcation diagrams depending on whether nodes become susceptible frequently (multiple times in their lifetime) or rarely (much less than once per lifetime).

q-bio.PE↗

arXiv2011

Converging towards the optimal path to extinction

Extinction appears ubiquitously in many fields, including chemical reactions, population biology, evolution, and epidemiology. Even though extinction as a random process is a rare event, its occurrence is observed in large finite populations. Extinction occurs when fluctuations due to random transitions act as an effective force which drives one or more components or species to vanish. Although there are many random paths to an extinct state, there is an optimal path that maximizes the probability to extinction. In this article, we show that the optimal path is associated with the dynamical systems idea of having maximum sensitive dependence to initial conditions. Using the equivalence between the sensitive dependence and the path to extinction, we show that the dynamical systems picture of extinction evolves naturally toward the optimal path in several stochastic models of epidemics.

q-bio.PE↗

arXiv2011

Bistability in a differential equation model of oyster reef height and sediment accumulation

Native oyster populations in Chesapeake Bay have been the focus of three decades of restoration attempts, which have generally failed to rebuild the populations and oyster reef structure. Recent restoration successes and field experiments suggest that high-relief reefs offset heavy sedimentation and promote oyster survival, disease resistance and growth, in contrast to low-relief reefs which degrade in just a few years. These findings suggest the existence of alternative stable states in oyster reef populations. We developed a mathematical model consisting of three differential equations that represent volumes of live oysters, dead oyster shells (= accreting reef), and sediment. Bifurcation analysis and numerical simulations demonstrated that multiple nonnegative equilibria can exist for live oyster, accreting reef and sediment volume at an ecologically reasonable range of parameter values; the initial height of oyster reefs determined which equilibrium was reached. This investigation thus provides a conceptual framework for alternative stable states in native oyster populations, and can be used as a tool to improve the likelihood of success in restoration efforts.

q-bio.PE↗

arXiv2010

Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.

physics.bio-ph↗

arXiv2009

Enhanced vaccine control of epidemics in adaptive networks

We study vaccine control for disease spread on an adaptive network modeling disease avoidance behavior. Control is implemented by adding Poisson distributed vaccination of susceptibles. We show that vaccine control is much more effective in adaptive networks than in static networks due to an interaction between the adaptive network rewiring and the vaccine application. Disease extinction rates using vaccination are computed, and orders of magnitude less vaccine application is needed to drive the disease to extinction in an adaptive network than in a static one.

q-bio.PE↗

arXiv2009

Asymmetry in the presence of migration stabilizes multistrain disease outbreaks

We study the effect of migration between coupled populations, or patches, on the stability properties of multistrain disease dynamics. The epidemic model used in this work displays a Hopf bifurcation to oscillations in a single well mixed population. It is shown numerically that migration between two non-identical patches stabilizes the endemic steady state, delaying the onset of large amplitude outbreaks and reducing the total number of infections. This result is motivated by analyzing generic Hopf bifurcations with different frequencies and with diffusive coupling between them. Stabilization of the steady state is again seen, indicating that our observation in the full multistrain model is based on qualitative characteristics of the dynamics rather than on details of the disease model.

q-bio.PE↗

arXiv2009

Epidemics with Multistrain Interactions: The Interplay Between Cross Immunity and Antibody-Dependent Enhancement

This paper examines the interplay of the effect of cross immunity and antibody-dependent enhancement (ADE) in mutistrain diseases. Motivated by dengue fever, we study a model for the spreading of epidemics in a population with multistrain interactions mediated by both partial temporary cross immunity and ADE. Although ADE models have previously been observed to cause chaotic outbreaks, we show analytically that weak cross immunity has a stabilizing effect on the system. That is, the onset of disease fluctuations requires a larger value of ADE with small cross immunity than without. However, strong cross immunity is shown numerically to cause oscillations and chaotic outbreaks even for low values of ADE.

q-bio.PE↗

arXiv2008

Noise induced dynamics in adaptive networks with applications to epidemiology

Recent work in modeling the coupling between disease dynamics and dynamic social network geometry has led to the examination of how human interactions force a rewiring of connections in a population. Rewiring of the network may be considered an adaptive response to social forces due to disease spread, which in turn feeds back to the disease dynamics. Such epidemic models, called adaptive networks, have led to new dynamical instabilities along with the creation of multiple attracting states. The co-existence of several attractors is sensitive to internal and external fluctuations, and leads to enhanced stochastic oscillatory outbreaks and disease extinction. The aim of this paper is to explore the bifurcations of adaptive network models in the presence of fluctuations and to review some of the new fluctuation phenomena induced in adaptive networks.

cond-mat.stat-mech↗

arXiv2008

Fluctuating epidemics on adaptive networks

A model for epidemics on an adaptive network is considered. Nodes follow an SIRS (susceptible-infective-recovered-susceptible) pattern. Connections are rewired to break links from non-infected nodes to infected nodes and are reformed to connect to other non-infected nodes, as the nodes that are not infected try to avoid the infection. Monte Carlo simulation and numerical solution of a mean field model are employed. The introduction of rewiring affects both the network structure and the epidemic dynamics. Degree distributions are altered, and the average distance from a node to the nearest infective increases. The rewiring leads to regions of bistability where either an endemic or a disease-free steady state can exist. Fluctuations around the endemic state and the lifetime of the endemic state are considered. The fluctuations are found to exhibit power law behavior.

q-bio.PE↗

arXiv2007

Zero Lag Synchronization of Mutually Coupled Lasers in the Presence of Delays

We consider a line of three mutually coupled lasers with time delays and study chaotic synchronization of the outer lasers. Two different systems are presented: optoelectronically coupled semiconductor lasers and optically coupled fiber lasers. While the dynamics of the two systems are very different, robust synchronization of end lasers is obtained in both cases over a range of parameters. Here, we present analysis and numerical simulation to explain some of the observed synchronization phenomena. First, we introduce the system of three coupled semiconductor lasers and discuss the onset of oscillations that occurs via a bifurcation as the coupling strength increases. Next, we analyze the synchronization of the end lasers by examining the dynamics transverse to synchronized state. We prove that chaotic synchronization of the outer semiconductor lasers will occur for sufficiently long delays, and we make a comparison to generalized synchronization in driven dissipative systems. It is shown that the stability of synchronous state (as indicated by negative Lyupunov exponents transverse to the synchronization manifold) depends on the internal dissipation of the outer lasers. We next present numerical simulations for three coupled fiber lasers, highlighting some of the differences between the semiconductor and fiber laser systems. Due to the large number of coupled modes in fiber lasers, this is a good system for investigating spatio-temporal chaos. Stochastic noise is included in the fiber laser model, and synchrony of the outer lasers is observed even at very small coupling strengths.

nlin.CD↗