Analysis of the sensitivity properties of a model of vector-borne bubonic plague

Buzby, Megan; Neckels, David; Antolin, Michael F.; Estep, Donald

doi:10.1098/rsif.2007.1339

Cited by 9 publications

(9 citation statements)

References 12 publications

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“…Applications of sensitivity analysis to continuous-time models has been mostly restricted to specific applications (but see Buzby et al 2008;Tavener et al 2011), notably to study properties of equilibria, such as their stability (Gurney and Nisbet 1998), their sensitivity to parameter change (Levins 1974;Justus 2006), or their reactivity (Verdy and Caswell 2008). The insight that sensitivity analysis can yield for understanding model behavior is, however, potentially as large as their discrete-time cousins, and ecological and evolutionary theory would certainly benefit from a more widespread application of sensitivity analyses.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis of continuous-time models for ecological and evolutionary theories

2015

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National audienceSensitivity analyses are of paramount importance in ecological and evolutionary theories, but their application to continuous time models has been virtually ignored from these fields. We present a simple and general method that makes this analysis possible for any model specified by a system of ordinary differential equations, using the direct method from mathematical theory. The resulting analysis may be used to study the effect of parameter perturbation on the whole trajectories of the state variables as well as for deriving the sensitivity of composite metrics such as the population growth rate. We also present methods for analyzing the sensitivity of discrete events within a continuous-time framework, such as the age at maturation, where timing may be affected by the perturbation. These methods are applied to a model for the energetics of individual growth, reproduction, and mortality. The method is versatile and can be applied to study transient as well as asymptotic dynamics, and its application may benefit many fields of ecology and evolution

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Section: Introductionmentioning

confidence: 99%

Sensitivity analysis of continuous-time models for ecological and evolutionary theories

2015

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“…It should be recognized that nonlinear models may have multiple equilibria, and sensitivity with respect to parameters may differ in different regions of parameter space. Buzby et al. (2008) present an adjoint‐based approach to examine sensitivity for ODEs over entire regions of parameter space by systematically examining sensitivities in the vicinity of reference values of the parameters and adaptively constructing a piecewise linear approximation to the sensitivity surface.…”

Section: Discussionmentioning

confidence: 99%

“…The standard forward sensitivity analysis approach (in contrast to an adjoint‐based approach; see Buzby et al. 2008) is to differentiate with respect to the k th parameter p k providing an expression for the sensitivities of all variables with respect to all parameters, …”

Section: Parametrized Nonlinear Mapsmentioning

confidence: 99%

Transient sensitivity analysis for nonlinear population models

et al. 2011

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Summary1. Performing sensitivity analyses for deterministic multi-stage, multi-parameter population models that include nonlinearity presents a significant computational challenge. 2. We implement a standard forward sensitivity analysis to evaluate partial derivatives of population state variables with respect to parameters at all times for which the solution is known. We present a hybrid Matlab/Maple software package, sensai, which automates the steps required to calculate sensitivities and elasticities. We focus on sensitivities of transient states of populations. Our analysis therefore differs from the more common analysis of linear systems where sensitivities are computed for the asymptotic stable-stage distribution assuming unbounded population growth. The method generalizes the matrix calculus methods for nonlinear, stage-structured matrix models previously developed by Caswell (2009, Journal of Difference Equations and Applications, 15, 349-369). 3. We present an example of a nonlinear, discrete-time population model in the form of a stagestructured Lefkovitch matrix, and another multi-stage, continuous-time SIR disease model in the form of a system of ordinary differential equations. In addition, we extend the framework for composite nonlinear maps of population demography to include single-locus genetics with natural selection discriminating among genotypes. 4. SENSAI allows for the analysis of a quantity of interest (an arbitrary function of variables and parameters, e.g. the proportion of infected individuals in a disease model), and sensitivity to combinations of model parameters. For example, we can compute sensitivities with respect to parameters and initial conditions at all times during an outbreak in a disease model, before a steady state of disease prevalence is attained. Similarly, in population genetic models, we can compute sensitivity of a response to natural selection (e.g. the change in allele frequencies) in relation to fitness differences among genotypes. 5. We illustrate the capabilities of sensai through a series of canonical models with relatively few variables and parameters. However, sensai has the capability to analyse significantly more complex models.

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“…The stability and local transient dynamics of equilibria (and other fixed points) defined by the system of equations is determined by the eigenspectrum of the Jacobian matrix. See Keeling and Gilligan (2000) and Buzby et al (2008) for a general discussion, with application to analysis of a vector-transmitted disease system. Analysis of the equilibrium condition(s) often provide qualitative insights to the conditions necessary for an Fig.…”

Section: Classical Sir Models: Deterministic Continuous Timementioning

confidence: 99%

Disease dynamics in wild populations: modeling and estimation: a review

et al. 2010

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Models of infectious disease dynamics focus on describing the temporal and spatial variations in disease prevalence, and on understanding the factors that affect how many cases will occur in each time period and which individuals are likely to become infected. Classical methods for selecting and fitting models, mostly motivated by human diseases, are almost always based solely on raw counts of infected and uninfected individuals. We begin by reviewing the main classical approaches to parameter estimation, and some of their applications. We then review recently developed methods which enable representation of component processes such as infection and recovery, with observation models that acknowledge the complexities of the sampling and detection processes. We demonstrate the need to account for detectability in modeling disease dynamics, and explore a number of mark-recapture and occupancy study designs for estimating disease parameters while simultaneously accounting for variation in detectability. We highlight the utility of different modeling approaches and also consider the typically strong assumptions that may actually serve to limit their utility in general application to the study of disease dynamics (e.g., assignment of individuals to discrete disease states when underlying state space is more generally continuous; transitions assumed to be simple firstorder Markov; temporal separation of hazard and transition events).

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Analysis of the sensitivity properties of a model of vector-borne bubonic plague

Cited by 9 publications

References 12 publications

Sensitivity analysis of continuous-time models for ecological and evolutionary theories

Sensitivity analysis of continuous-time models for ecological and evolutionary theories

Transient sensitivity analysis for nonlinear population models

Disease dynamics in wild populations: modeling and estimation: a review

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