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Bifurcation analysis and transient spatiotemporal dynamics for a diffusive plantherbivore system with Dirichlet boundary conditions
Mathematical probit and logistic mortality models of the Khapra beetle fumigated with plant essential oils
1.  Department of Mathematics, Najran University, Najran,1988, Saudi Arabia 
2.  Zoology Department, Faculty of Science, Kafrelsheikh University, Kafr El sheikh3516, Egypt, Egypt 
References:
[1] 
A. Agresti, An Introduction to Categorical Data Analysis,, $2^{nd}$ edition, (2007). doi: 10.1002/0470114754. 
[2] 
C. H. Bell and S. M. Wilson, Phosphine tolerance and resistance in Trogoderma granarium Everts (Coleoptera: Dermestidae),, J. Stored Prod. Res., 31 (1995), 199. doi: 10.1016/0022474X(95)00012V. 
[3] 
A. Ben and T. Greville, Generalized Inverses: Theory and Applications,, Springer press, (2003). 
[4] 
C. I. Bliss, The relation between exposure time, concentration and toxicity in experiments on insecticides,, Ann. Entomol. Soc. Am., 33 (1940), 721. doi: 10.1093/aesa/33.4.721. 
[5] 
E. J. Bond, Manual of Fumigation for Insect Control,, in: FAO Plant Production and Protection Paper, (1984). 
[6] 
S. Boyer, H. Zhang and G. Lempérière, A review of control methods and resistance mechanisms in storedproduct insects,, B. Entomol. Res., 102 (2012), 213. doi: 10.1017/S0007485311000654. 
[7] 
M. Q. Chaudhry, A review of the mechanisms involved in the action of phosphine as an insecticide and phosphine resistance in storedproduct insects,, Pestic Sci., 49 (1997), 213. doi: 10.1002/(SICI)10969063(199703)49:3<213::AIDPS516>3.3.CO;2R. 
[8] 
P. J. Collins, G. Daglish, H. Pavic and R. Kopittke, Response of mixedage cultures of phosphineresistant and susceptible strains of lesser grain borer, Rhyzopertha dominica to phosphine at a range of concentrations and exposure periods,, J. Stored Prod. Res., 41 (2005), 373. doi: 10.1016/j.jspr.2004.05.002. 
[9] 
P. Eliopoulos, New approaches for tackling Khapra beetle,, CAB Rev., 8 (2013), 1. 
[10]  
[11] 
W. Hermawan, S. Nakajima, R. Tsukuda, K. Fujisaki and F. Nakasuji, Isolation of an antifeedant compound from Andrographis paniculata (Acanthaceae) against the diamond back, Plutella xylostella (Lepidoptera: Yponomeutidae),, Appl. Entomol. Zool, 32 (1997), 551. 
[12] 
M. B. Isman, Botanical insecticides, deterrents, and repellents in modern agriculture and an increasingly regulated world,, Annu. Rev. Entomol., 51 (2006), 45. doi: 10.1146/annurev.ento.51.110104.151146. 
[13] 
M. B. Isman, C. Machial, S. Miresmailli and L. Bainard, Essential oilbased pesticides: New insights from old chemistry,, in Pesticide Chemistry (WileyVCH, (2007), 201. doi: 10.1002/9783527611249.ch21. 
[14] 
K. Lilford, G. Fulford, D. Schlipalius and A. Ridley, Fumigation of storedgrain insectsa two locus model of phosphine resistance,, in The 18th World IMACS Congress and MODSIM09, (2009). 
[15] 
S. Lowe, M. Browne, S. Boudjelas and M. de Poorter, 100 of the world's worst invasive alien species, The global invasive species database,, in: World Conservation Union, (2000). 
[16] 
G. Nenaah, Toxic and antifeedant activities of potato glycoalkaloids against Trogoderma granarium (Coleoptera: Dermestidae),, J. Stored Prod. Res., 47 (2011), 185. doi: 10.1016/j.jspr.2010.11.003. 
[17] 
G. Nenaah, Chemical composition, insecticidal and repellence activities of essential oils of three Achillea species against the Khapra beetle (Coleoptera: Dermestidae),, J. Pest Sci., 87 (2014), 273. doi: 10.1007/s1034001305471. 
[18] 
G. Nenaah, Chemical composition, toxicity and growth inhibitory activities of essential oils of three Achillea species and their nanoemulsions against Tribolium castaneum (Herbst),, Ind. Crop Prod., 53 (2014), 252. 
[19] 
G. Nenaah and S. Ibrahim, Chemical composition and the insecticidal activity of certain plants applied as powders and essential oils against two storedproducts coleopteran beetles,, J. Pest Sci., 84 (2011), 393. doi: 10.1007/s1034001103545. 
[20] 
P. PretheepKumar, S. Mohan and P. Balasubramanian, Insecticide Resistancestoredproduct,, mechanism and management strategies, (2010). 
[21] 
S. Rajendran, Postharvest pest losses. New York in: Pimentel,, in D. (Ed), (2002). 
[22] 
S. Rajendran and V. Sriranjini, Plant products as fumigants for storedproduct insect control,, J. Stored Prod. Res., 44 (2008), 126. doi: 10.1016/j.jspr.2007.08.003. 
[23] 
C. RegnaultRoger, C. Vincent and J. T. Arnason, Essential oils in insect control: Lowrisk products in a highstakes world,, Annu. Rev. Entomol., 57 (2012), 405. doi: 10.1146/annurevento120710100554. 
[24] 
M. Shi, P. Collins, J. Smith and M. Renton, Individualbased modelling of the efficacy of fumigation tactics to control lesser grain borer (Rhyzopertha dominica) in stored grain,, J. Stored Prod. Res., 51 (2012), 23. doi: 10.1016/j.jspr.2012.06.003. 
[25] 
M. Shi and M. Renton, Modelling mortality of a stored grain insect pest with fumigation: Probit, logistic or Cauchy model?,, Math. Biosci., 243 (2013), 137. doi: 10.1016/j.mbs.2013.02.005. 
[26] 
M. Shi and M. Renton, Numerical algorithms for estimation and calculation of parameters in modelling pest population dynamics and evolution of resistance in modelling pest population dynamics and evolution of resistance,, Math. Biosci., 233 (2011), 77. doi: 10.1016/j.mbs.2011.06.005. 
[27] 
M. Shi, M. Renton, J. RidsdillSmith and P. J. Collins, Constructing a new individualbased model of phosphine resistance in lesser grain borer (Rhyzopertha dominica): do we need to include two loci rather than one?,, J. Pest Sci., 85 (2012), 451. doi: 10.1007/s1034001204216. 
[28] 
R. G. Winks, The toxicity of phosphine to adults of Tribolium castaneum (Herbst): phosphineinduced narcosis,, J. Stored Prod. Res., 21 (1985), 25. doi: 10.1016/0022474X(85)900566. 
[29] 
J. R. Wolberg, Data analysis using the method of least squares,, Extracting the Most Information From Experiments, (2005). 
show all references
References:
[1] 
A. Agresti, An Introduction to Categorical Data Analysis,, $2^{nd}$ edition, (2007). doi: 10.1002/0470114754. 
[2] 
C. H. Bell and S. M. Wilson, Phosphine tolerance and resistance in Trogoderma granarium Everts (Coleoptera: Dermestidae),, J. Stored Prod. Res., 31 (1995), 199. doi: 10.1016/0022474X(95)00012V. 
[3] 
A. Ben and T. Greville, Generalized Inverses: Theory and Applications,, Springer press, (2003). 
[4] 
C. I. Bliss, The relation between exposure time, concentration and toxicity in experiments on insecticides,, Ann. Entomol. Soc. Am., 33 (1940), 721. doi: 10.1093/aesa/33.4.721. 
[5] 
E. J. Bond, Manual of Fumigation for Insect Control,, in: FAO Plant Production and Protection Paper, (1984). 
[6] 
S. Boyer, H. Zhang and G. Lempérière, A review of control methods and resistance mechanisms in storedproduct insects,, B. Entomol. Res., 102 (2012), 213. doi: 10.1017/S0007485311000654. 
[7] 
M. Q. Chaudhry, A review of the mechanisms involved in the action of phosphine as an insecticide and phosphine resistance in storedproduct insects,, Pestic Sci., 49 (1997), 213. doi: 10.1002/(SICI)10969063(199703)49:3<213::AIDPS516>3.3.CO;2R. 
[8] 
P. J. Collins, G. Daglish, H. Pavic and R. Kopittke, Response of mixedage cultures of phosphineresistant and susceptible strains of lesser grain borer, Rhyzopertha dominica to phosphine at a range of concentrations and exposure periods,, J. Stored Prod. Res., 41 (2005), 373. doi: 10.1016/j.jspr.2004.05.002. 
[9] 
P. Eliopoulos, New approaches for tackling Khapra beetle,, CAB Rev., 8 (2013), 1. 
[10]  
[11] 
W. Hermawan, S. Nakajima, R. Tsukuda, K. Fujisaki and F. Nakasuji, Isolation of an antifeedant compound from Andrographis paniculata (Acanthaceae) against the diamond back, Plutella xylostella (Lepidoptera: Yponomeutidae),, Appl. Entomol. Zool, 32 (1997), 551. 
[12] 
M. B. Isman, Botanical insecticides, deterrents, and repellents in modern agriculture and an increasingly regulated world,, Annu. Rev. Entomol., 51 (2006), 45. doi: 10.1146/annurev.ento.51.110104.151146. 
[13] 
M. B. Isman, C. Machial, S. Miresmailli and L. Bainard, Essential oilbased pesticides: New insights from old chemistry,, in Pesticide Chemistry (WileyVCH, (2007), 201. doi: 10.1002/9783527611249.ch21. 
[14] 
K. Lilford, G. Fulford, D. Schlipalius and A. Ridley, Fumigation of storedgrain insectsa two locus model of phosphine resistance,, in The 18th World IMACS Congress and MODSIM09, (2009). 
[15] 
S. Lowe, M. Browne, S. Boudjelas and M. de Poorter, 100 of the world's worst invasive alien species, The global invasive species database,, in: World Conservation Union, (2000). 
[16] 
G. Nenaah, Toxic and antifeedant activities of potato glycoalkaloids against Trogoderma granarium (Coleoptera: Dermestidae),, J. Stored Prod. Res., 47 (2011), 185. doi: 10.1016/j.jspr.2010.11.003. 
[17] 
G. Nenaah, Chemical composition, insecticidal and repellence activities of essential oils of three Achillea species against the Khapra beetle (Coleoptera: Dermestidae),, J. Pest Sci., 87 (2014), 273. doi: 10.1007/s1034001305471. 
[18] 
G. Nenaah, Chemical composition, toxicity and growth inhibitory activities of essential oils of three Achillea species and their nanoemulsions against Tribolium castaneum (Herbst),, Ind. Crop Prod., 53 (2014), 252. 
[19] 
G. Nenaah and S. Ibrahim, Chemical composition and the insecticidal activity of certain plants applied as powders and essential oils against two storedproducts coleopteran beetles,, J. Pest Sci., 84 (2011), 393. doi: 10.1007/s1034001103545. 
[20] 
P. PretheepKumar, S. Mohan and P. Balasubramanian, Insecticide Resistancestoredproduct,, mechanism and management strategies, (2010). 
[21] 
S. Rajendran, Postharvest pest losses. New York in: Pimentel,, in D. (Ed), (2002). 
[22] 
S. Rajendran and V. Sriranjini, Plant products as fumigants for storedproduct insect control,, J. Stored Prod. Res., 44 (2008), 126. doi: 10.1016/j.jspr.2007.08.003. 
[23] 
C. RegnaultRoger, C. Vincent and J. T. Arnason, Essential oils in insect control: Lowrisk products in a highstakes world,, Annu. Rev. Entomol., 57 (2012), 405. doi: 10.1146/annurevento120710100554. 
[24] 
M. Shi, P. Collins, J. Smith and M. Renton, Individualbased modelling of the efficacy of fumigation tactics to control lesser grain borer (Rhyzopertha dominica) in stored grain,, J. Stored Prod. Res., 51 (2012), 23. doi: 10.1016/j.jspr.2012.06.003. 
[25] 
M. Shi and M. Renton, Modelling mortality of a stored grain insect pest with fumigation: Probit, logistic or Cauchy model?,, Math. Biosci., 243 (2013), 137. doi: 10.1016/j.mbs.2013.02.005. 
[26] 
M. Shi and M. Renton, Numerical algorithms for estimation and calculation of parameters in modelling pest population dynamics and evolution of resistance in modelling pest population dynamics and evolution of resistance,, Math. Biosci., 233 (2011), 77. doi: 10.1016/j.mbs.2011.06.005. 
[27] 
M. Shi, M. Renton, J. RidsdillSmith and P. J. Collins, Constructing a new individualbased model of phosphine resistance in lesser grain borer (Rhyzopertha dominica): do we need to include two loci rather than one?,, J. Pest Sci., 85 (2012), 451. doi: 10.1007/s1034001204216. 
[28] 
R. G. Winks, The toxicity of phosphine to adults of Tribolium castaneum (Herbst): phosphineinduced narcosis,, J. Stored Prod. Res., 21 (1985), 25. doi: 10.1016/0022474X(85)900566. 
[29] 
J. R. Wolberg, Data analysis using the method of least squares,, Extracting the Most Information From Experiments, (2005). 
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