Publications (81) View all
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Article: Breaking the symmetry: Immune enhancement increases persistence of dengue viruses in the presence of asymmetric transmission rates.
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ABSTRACT: The dengue viruses exist as four antigenically distinct serotypes. These four serotypes co-circulate and interact with each other through multiple immune-mediated mechanisms. Though the majority of previous efforts to understand the transmission dynamics of dengue have assumed identical characteristics for these four serotypes, empirical data suggests that they differ from one another in important ways. Here, we examine dynamics and persistence in models that do not assume symmetry between the dengue viruses. We find that for serotype transmission rates that are only slightly asymmetric, increased transmissibility of secondary infections through immune enhancement increases the persistence of all dengue viruses in opposition to findings in symmetric models. We identify an optimal magnitude of immune enhancement that maximizes the probability of persistence of all four serotypes. In contrast to other pathogen systems where heterogeneity between serotypes in transmissibility facilitates competitive exclusion (Bremmermann and Thieme, 1989), here we find that in the presence of Antibody Dependent Enhancement (ADE) heterogeneity can increase the persistence of multiple serotypes of dengue.Journal of Theoretical Biology 05/2013; · 2.21 Impact Factor -
Article: Distributed allocation of mobile sensing swarms in gyre flows
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ABSTRACT: We address the synthesis of distributed control policies to enable a swarm of homogeneous mobile sensors to maintain a desired spatial distribution in a geophysical flow environment, or workspace. In this article, we assume the mobile sensors (or robots) have a "map" of the environment denoting the locations of the Lagrangian coherent structures or LCS boundaries. Based on this information, we design agent-level hybrid control policies that leverage the surrounding fluid dynamics and inherent environmental noise to enable the team to maintain a desired distribution in the workspace. We establish the stability properties of the ensemble dynamics of the distributed control policies. Since realistic quasi-geostrophic ocean models predict double-gyre flow solutions, we use a wind-driven multi-gyre flow model to verify the feasibility of the proposed distributed control strategy and compare the proposed control strategy with a baseline deterministic allocation strategy. Lastly, we validate the control strategy using actual flow data obtained by our coherent structure experimental testbed.03/2013; -
Article: Statistical multimoment bifurcations in random-delay coupled swarms.
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ABSTRACT: We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments.Physical Review E 11/2012; 86(5-2):056202. · 2.26 Impact Factor -
Article: An iterative action minimizing method for computing optimal paths in stochastic dynamical systems
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ABSTRACT: We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by minimizing the effective action in a corresponding deterministic Hamiltonian system. The numerical method presented here involves using an iterative scheme for solving a two-point boundary value problem for the Hamiltonian system. We validate our method by applying it to both continuous stochastic systems, such as nonlinear oscillators governed by the Duffing equation, and finite discrete systems, such as epidemic problems, which are governed by a set of master equations. Furthermore, we demonstrate that this method is capable of dealing with stochastic systems of delay differential equations.10/2012; -
Article: Noise Induced Switching in Delayed Systems
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ABSTRACT: We consider the problem of switching in stochastic systems with delayed feedback. A general variational formulation is derived for the switching rate in a stochastic differential delay equation where the noise source is of general form. The resulting equations of motion and boundary conditions describe the optimal escape path which maximizes the probability of escape. Analyzing the dynamics along the optimal path yields exponents of the distribution in terms of delay time, dissipation, and noise intensity. Theoretical predictions compare very well with numerical simulations in both additive and multiplicative noise cases, even outside of regions where the delay is assumed to be small. Manuscript approved07/2012;
