Mathematical Biosciences and Engineering (MBE)

Mathematical probit and logistic mortality models of the Khapra beetle fumigated with plant essential oils

Pages: 687 - 697, Volume 12, Issue 4, August 2015      doi:10.3934/mbe.2015.12.687

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Alhadi E. Alamir - Department of Mathematics, Najran University, Najran,1988, Saudi Arabia (email)
Gomah E. Nenaah - Zoology Department, Faculty of Science, Kafrelsheikh University, Kafr El sheikh3516, Egypt (email)
Mohamed A. Hafiz - Zoology Department, Faculty of Science, Kafrelsheikh University, Kafr El sheikh3516, Egypt (email)

Abstract: In the current study, probit and logistic models were employed to fit experimental mortality data of the Khapra beetle, Trogoderma granarium (Everts) (Coleoptera: Dermestidae), when fumigated with three plant oils of the gens Achillea. A generalized inverse matrix technique was used to estimate the mortality model parameters instead of the usual statistical iterative maximum likelihood estimation. As this technique needs to perturb the observed mortality proportions if the proportions include 0 or 1, the optimal perturbation in terms of minimum least squares ($L_2$) error was also determined. According to our results, it was better to log-transform concentration and time as explanatory variables in modeling mortality of the test insect. Estimated data using the probit model were more accurate in terms of $L_2$ errors, than the logistic one. Results of the predicted mortality revealed also that extending the fumigation period could be an effective control strategy, even, at lower concentrations. Results could help in using a relatively safe and effective strategy for the control of this serious pest using alternative control strategy to reduce the health and environmental drawbacks resulted from the excessive reliance on the broadly toxic chemical pesticides and in order to contribute safeguard world-wide grain supplies.

Keywords:  Probit model, logistic model, plant oils, Khapra beetle, mortality.
Mathematics Subject Classification:  Primary: 62P10, 92B05; Secondary: 62P12, 92B10.

Received: May 2014;      Accepted: November 2014;      Available Online: April 2015.