Estimation in time-delay modeling of insecticide-induced mortality

Banks, Harvey Thomas; Banks, John E.; Joyner, Sarah Lynn

doi:10.1515/jiip.2009.012

Cited by 5 publications

(7 citation statements)

References 23 publications

(51 reference statements)

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“…Iatrogenic effects on mortality and survivorship refer to negative and positive medical effects on mortality and survivorship [80,81]; such effects include, for example, iatrogenic effects of surgery [82], pharmacologic medication (e.g., antibiotics [83]), or public health campaigns [84][85][86]; iatrogenic medical effects on mortality and survivorship provide suggestive evidence of medical-specific mortacauses and vitacauses that negatively and positively affect mortality and survivorship. Similarly, nonlinear or varying respective effects of radiation [60,64,87,88], insecticides [89], and food intake [90] on mortality and survivorship provide suggestive evidence of respective radiation-specific, insecticides-specific, and food-intakespecific mortacauses and vitacauses that negatively and positively affect mortality and survivorship. Additionally, Strehler-Mildvan correlations [66,78,[91][92][93][94][95], compensations [66,67,88,95], decelerations [64,[95][96][97][98][99][100][101][102][103][104][105][106][107][108], and hysteresis or delays [89,109,…”

Section: Suggestive Evidence Of Tetraeffective Causes Of Mortality Anmentioning

confidence: 97%

“…Similarly, nonlinear or varying respective effects of radiation [60,64,87,88], insecticides [89], and food intake [90] on mortality and survivorship provide suggestive evidence of respective radiation-specific, insecticides-specific, and food-intakespecific mortacauses and vitacauses that negatively and positively affect mortality and survivorship. Additionally, Strehler-Mildvan correlations [66,78,[91][92][93][94][95], compensations [66,67,88,95], decelerations [64,[95][96][97][98][99][100][101][102][103][104][105][106][107][108], and hysteresis or delays [89,109,110] in effects of age on mortality and survivorship provide suggestive evidence of age-specific mortacauses and vitacauses that negatively and positively affect mortality and survivorship. Moreover, there is ample evidence of nonlinear or varying effects of socioeconomic causes on mortality and survivorship; such socioeconomic effects include, for example, effects of educational attainment, race, gender, income, and economic development [15,[84][85][86][111][112]…”

Section: Suggestive Evidence Of Tetraeffective Causes Of Mortality Anmentioning

confidence: 97%

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Tetraeffective causes, mortacauses, and vitacauses of mortality and survivorship

Epelbaum¹

2016

Preprint

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Any cause that negatively affects mortality, positively affects mortality, negatively affects survivorship, and positively affects survivorship is tetraeffective (i.e., having four kinds of effects). However, until now, tetraeffective causes of mortality and survivorship have been undescribed, unidentified, unnamed, unrecognized, unclear, misconceived, unspecified, and unexplained. Here I describe, identify, name, recognize, elucidate, conceptualize, specify, and explain tetraeffective causes of mortality and survivorship. I show that every tetraeffective cause of mortality and survivorship combines corresponding at least one mortacause and at least one vitacause; "mortacause" refers here to a cause that positively affects mortality and negatively affects survivorship, and "vitacause" refers to a cause that positively affects survivorship and negatively affects mortality. I present strong rationales that suggest that every cause of mortality and survivorship is tetraeffective, and I present references to considerable previous evidence that I interpret to be suggestive evidence of tetraeffective causes of mortality and survivorship. Moreover, rigorous and thorough multivariable analyses of mortality and survivorship of humans and medflies provide here direct evidence of tetraeffective causes of mortality and survivorship, revealing best-fitting specifications dY/d(X p ) = a + bX p such that sign(a) = -sign(bX p ), where: Y indicates mortality or survivorship; X indicates age, lifespan, contemporary aggregate size, lifespan aggregate size, or historical time; dY/d(X p ) indicates composite effects of X p on Y; a indicates an Xspecific mortacause or vitacause; bX p indicates the corresponding opposite X-specific mortacause or vitacause; and coefficients a, b, and p denote respective X-specific and entityspecific constants. Thus description, identification, naming, recognition, elucidation, conception, specification, explanation, and demonstration of tetraeffective causes of mortality and survivorship usher a new paradigm of causes of mortality and survivorship and enable and promote further scientific research and practical applications. Figure 3. A causal structure of a tetraeffective cause of mortality and survivorship. X denotes a cause of mortality M and survivorship S, Xm denotes an X-specific mortacause, Xs denotes an X-specific vitacause, double dotted lines denote that Xm and Xv are X-specific, arrow → denotes positive effects, and arrow ----> denotes negative effects. Xm M Xv S X

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Section: Suggestive Evidence Of Tetraeffective Causes Of Mortality Anmentioning

confidence: 97%

Section: Suggestive Evidence Of Tetraeffective Causes Of Mortality Anmentioning

confidence: 97%

Tetraeffective causes, mortacauses, and vitacauses of mortality and survivorship

Epelbaum¹

2016

Preprint

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“…Example 1: Insect/Insecticide models. We describe here a nonautonomous delay system arising in insect/insecticide investigations [BBDS2,BBJ]. Mathematical models that are suitable for field data with mixed populations should consider reproductive effects and should also account for multiple generations, containing neonates (juveniles) and adults and their interconnectedness.…”

Section: Theorem 4 Assume That (H1) Holds and Letmentioning

confidence: 99%

Inverse Problems for Nonlinear Delay Systems

Banks¹,

Rehm²,

Sutton³

2010

Methods and Applications of Analysis

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Abstract. We consider inverse or parameter estimation problems for general nonlinear nonautonomous dynamical systems with delays. The parameters may be from a Euclidean set as usual, may be time dependent coefficients or may be probability distributions across a population as arise in aggregate data problems. Theoretical convergence results for finite dimensional approximations to the systems are given. Several examples are used to illustrate the ideas and computational results that demonstrate efficacy of the approximations are presented.Key words. Nonlinear delay systems, inverse problems, uncertainty, computational methods.AMS subject classifications. 34C55, 34K06, 34K28, 34K29, 34G20, 93C10.1. Introduction. Delay differential equations have been a topic of much interest in the mathematical research literature for more than 50 years. Contributions range from classical applications and theoretical and computational methodologies [Ba79, Ba82, BBu1, BBu2, BKap, BellCook, Cushing, Diekmann, Driver, Gorecki, JKH1, JKH2, JKH3, Kap82, KapSal87, KapSal89, KapSch, Kuang, Minorsky, Webb, Wright] to modern applications in biology [BBJ, BBH, MSNP, NMiP, NMuP, NP]. In this paper we return to a topic that has become increasingly relevant in current research: a theoretical and computational approach for inverse problems involving nonlinear delay systems. One approach that is by now classical dates back to the 1970's [Ba79, BBu1, BBu2, BKap]. In this approach one approximates solutions to the infinite dimensional state systems such as (1) below by first converting them to an abstract evolution equation in a functional analytic state space setting. One can approximate solutions in finite dimensional subspaces spanned by pre-chosen basis elements (e.g., piece-wise linear or cubic splines) in a Galerkin approach which is equivalent to a finite element approximation framework (as is classically used for partial differential equations). One is then able to numerically calculate the generalized Fourier coefficients of approximate solutions relative to the splines, and with these coefficients, recover an approximation to the solutions of delay systems (1).Here we turn to the mathematical aspects of these nonlinear FDE systems and present an outline of the necessary mathematical and numerical analysis foundations. Thus we provide an extension (to treat time dependent coefficients and general parameters including probability measures) of arguments for approximation and convergence in inverse problems found in [Ba82].For nonlinear delay systems such as those discussed here, approximation in the context of a linear semigroup framework as presented [BBu1, BBu2, BKap] is not direct. However one can use the ideas of that theory as a basis for a wide class of nonlinear delay system approximations. Details in this direction can be found in the early work [Ba79, Kap82] which is a direct extension of the results of [BBu1, BBu2, BKap] to nonlinear delay systems. The new theoretical results presented here are extensions of these earlier ideas t...

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“…The solutions to the system (1) can be simulated using an algorithm developed by Banks and Kappel [14] and extended for nonlinear systems [5,6,28] (see also [7,8] for applications of this algorithm). The idea behind the algorithm is to first represent the system as an infinite dimensional abstract evolution equation (AEE) and then consider approximations in a space spanned by piecewise linear splines.…”

Section: Numerical Implementationmentioning

confidence: 99%

“…Successful examples of such endeavors are given in [15,Chapter V,Sec. 6,7] and more recently in [10].…”

Section: Introductionmentioning

confidence: 99%

A discrete events delay differential system model for transmission of Vancomycin-resistant enterococcus (VRE) in hospitals

Ortíz

Banks

Castillo‐Chavez

et al. 2010

Jiip

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Surveillance data from an oncology hospital unit on Vancomycin-resistant enterococcus (VRE), one of the most prevalent and dangerous pathogens involved in hospital infections, is used to motivate possibilities of modeling nosocomial infection dynamics. This is done in the context of hospital monitoring and isolation procedures as a prelude to the evaluation and improved design of control measures. A discrete event delay differential equation model in conjunction with statistical computational methods is formulated to estimate key population-level nosocomial transmission parameters and isolation procedures. This framework is used to test the surveillance data's usefulness in model validation. In the process of model calibration we discovered significant irregularities in the available surveillance data; these irregularities are most likely the result of the data observational recording-process as well as those in the isolation procedures. Efforts to fit data within our highly flexible dynamic-modeling framework suggest that clinical-trial level surveillance data is needed if one is to successfully develop quantitative models for disease transmission and intervention. It is concluded that typical "cold" data sets typically encountered in biological/sociological quantitative modeling efforts may be inadequate for support of serious model development.

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Estimation in time-delay modeling of insecticide-induced mortality

Abstract: We present a mathematical and statistical computational framework for inverse problems involving delay or hysteretic differential equations. We demonstrate efficacy of the methodology in the context of models for insect maturation and mortality due to insecticide exposure.

Cited by 5 publications

References 23 publications

Tetraeffective causes, mortacauses, and vitacauses of mortality and survivorship

Tetraeffective causes, mortacauses, and vitacauses of mortality and survivorship

Inverse Problems for Nonlinear Delay Systems

A discrete events delay differential system model for transmission of Vancomycin-resistant enterococcus (VRE) in hospitals

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