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Correctly modeling plant-insect-herbivore-pesticide interactions as aggregate data

1 Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, 27695, USA
2 Undergraduate Research Opportunities Center (UROC), California State University, Monterey Bay, Seaside, CA 93955, USA
3 The Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA
4 Department of Mathematics & Statistics, East Tennessee State University, Johnson City, TN 37614, USA
5 Department of Entomology, Washington State University, Puyallup, WA 98371, USA

Special Issues: Mathematical Modeling with Measures

We consider a population dynamics model in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). The experimental data is clearly aggregate in nature. In previous efforts [1], the aggregate nature of the data was ignored. In this paper, we embrace this aspect of the experiment and correctly model the data as aggregate data, comparing the results to the previous approach. We discuss cases in which the approach may provide similar results as well as cases in which there is a clear difference in the resulting fit to the data.
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8. H. T. Banks, J. E. Banks, N. Murad, J. A Rosenheim, K. Tillman, Modelling pesticide treatment effects on Lygus hesperus in cotton fields, Proceedings, 27 th IFIP TC7 Conference 2015 on System Modelling and Optimization, L. Bociu et al (Eds.) CSMO 2015 IFIP AICT 494, p.1-12, 2017, Springer.

9. H. T. Banks, J. Catenacci, Aggregate data and the Prohorov Metric Framework: Efficient gradient computation, CRSC-TR15-13, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, November, 2015; Appl. Math. Lett., 56 (2016), 1-9.

10. H. T. Banks, Jared Catenacci and Shuhua Hu, Asymptotic properties of probability measure estimators in a nonparametric model, CRSC TR14-05, N. C. State University, Raleigh, NC, May, 2014; SIAM/ASA J. Uncertain., 3 (2015), 417-433.

11. H. T. Banks, K. B. Flores, I. G. Rosen, E. M. Rutter, M. Sirlanci, W. C. Thompson, The Prohorov Metric Framework and aggregate data inverse problems for random PDEs, Commun. Appl. Anal., 22 (2018), 415-446.

12. H. T. Banks, W. C. Thompson, Least squares estimation of probability measures in the Prohorov Metric Framework, CRSC-TR12-21, N. C. State University, Raleigh, NC, November, 2012.

13. H. T. Banks, W. C. Thompson, Existence and consistency of a nonparametric estimator of probability measures in the Prohorov metric framework, Int. J. Pure Appl. Math., 103 (2015), 819-843.

14. H. T. Banks, W. C. Thompson, Random delay differential equations and inverse problems for aggregate data problems, Eurasian J. Math. Computer Appl., 6 (2018), 4-16.

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16. H. T. Banks, K. L. Bihari, Modeling and estimating uncertainty in parameter estimation, Inverse Probl., 17 (2001), 95-111.

17. L. K. Potter, Physiologically based pharmacokinetic models for the systemic transport of trichloroethylene, Ph. D. thesis, North Carolina State University, 2001, www.lib.ncsu.edu.

18. H. T. Banks, D. M. Bortz, G. A. Pinter, L. K. Potter, Modeling and imaging techniques with potential for application in bioterrorism, Chapter 6 in Bioterrorism: Mathematical Modeling Applications in Homeland Security, (H.T. Banks and C. Castillo-Chavez, eds.), Frontiers in Applied Math, FR28, SIAM, 2003, Philadelphia, PA, 129-154.

19. H. T. Banks, J. L. Davis, A comparison of approximation methods for the estimation of probability distributions on parameters, Appl. Numer. Math., 57 (2007), 753-777.

20. H. T. Banks, J. L. Davis, Quantifying uncertainty in the estimation of probability distributions, Math. Biosci. Eng., 5, (2008), 647-667.

21. H. T. Banks, B. G. Fitzpatrick, Estimation of growth rate distributions in size-structured population models, Q. Appl. Math., 49 (1991), 215-235.

22. H. T. Banks, B. G. Fitzpatrick, L. K. Potter, Y. Zhang, Estimation of probability distributions for individual parameters using aggregate population data, In Stochastic Analysis, Control, Optimization and Applications, (W. McEneaney, G. Yin and Q. Zhang, eds.), Birkhauser, 1989, Boston.

23. P. Billingsley, Convergence of Probability Measures, Wiley, New York,1968.

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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