Nonlinear stochastic modeling of aphid population growth

Matis, James H.; Kiffe, Thomas R.; Matis, Timothy I.; Stevenson, Douglass E.

doi:10.1016/j.mbs.2005.07.009

Cited by 18 publications

(12 citation statements)

References 10 publications

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“…The structure of this reaction is motivated by the nonlinear population gowth of aphid's (minute plant-feeding insects) [12]. Let x 1 (t) and x 2 (t) denote the populations of species X 1 and X 2 .…”

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confidence: 99%

Lognormal Moment Closures for Biochemical Reactions

Singh

Hespanha

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-In the stochastic formulation of chemical reactions, the dynamics of the the first M -order moments of the species populations generally do not form a closed system of differential equations, in the sense that the time-derivatives of first M -order moments generally depend on moments of order higher thanM . However, for analysis purposes, these dynamics are often made to be closed by approximating the needed derivatives of the first M -order moments by nonlinear functions of the same moments. These functions are called the moment closure functions.Recent results have introduced the technique of derivativematching, where the moment closure functions are obtained by first assuming that they exhibit a certain separable form, and then matching time derivatives of the exact (not closed) moment equations with that of the approximate (closed) equations for some initial time and set of initial conditions. However, for multi-species reactions these results have been restricted to second order truncations, i.e, M = 2. This paper extends these results by providing explicit formulas to construct moment closure functions for any arbitrary order of truncation M . We show that with increasing M the closed moment equations provide more accurate approximations to the exact moment equations. Striking features of these moment closure functions are that they are independent of the reaction parameters (reaction rates and stoichiometry) and moreover the dependence of higher-order moment on lower order ones is consistent with the population being jointly lognormally distributed. To illustrate the applicability of our results we consider a simple bi-molecular reaction. Moment estimates from a third order truncation are compared with estimates obtained from a large number of Monte Carlo simulations.

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confidence: 99%

Lognormal Moment Closures for Biochemical Reactions

Singh

Hespanha

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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“…To counter the model limitations as discussed above, the classically available approaches, such as the ones using continuous‐time Markovian models with finite number of states to describe drug kinetic data as developed from statistical or engineering fields,62–68 cannot be directly adapted to PBPK models because they are oriented with different purposes. To meet the needs, new methodology advancements have been made recently 69,70.…”

Section: Model‐based Drug Development For Biologicsmentioning

confidence: 99%

Application of pharmacokinetics–pharmacodynamics/clinical response modeling and simulation for biologics drug development

Zhao

Shang

Sahajwalla

2012

Journal of Pharmaceutical Sciences

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“…13 The data necessary for producing a phenological model are generally based on individual insect development under laboratory-controlled temperature conditions. 14,15 Aphids are considered to be good insect models and have been used in studies of phenomena related to climate change 16 because of their plasticity, enabling them to respond rapidly to changes in habitat conditions, and because of their thermal tolerance conferred by endosymbiont bacteria. 17,18 However, the relationship between aphid development rate and various temperature regimes is non-linear.…”

Section: Introductionmentioning

confidence: 99%