An eco-epidemic model for assessing the application of integrated pest management strategies

Wenjie Qin; Yue Xia; Yi Yang; Wenjie Qin; Yue Xia; Yi Yang

doi:10.3934/mbe.2023736

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 9: 16506-16527. doi: 10.3934/mbe.2023736

Previous Article Next Article

Research article Special Issues

An eco-epidemic model for assessing the application of integrated pest management strategies

Wenjie Qin ^{1
,
,},
Yue Xia ¹,
Yi Yang ^{2
,
,}

1.
Department of Mathematics, Yunnan Minzu University, Kunming 650500, China
2.
College of Computer Science and Engineering, Chongqing Three Gorges University, Chongqing 404100, China

Academic Editor: Xiang-Sheng Wang

Received: 23 April 2023 Revised: 26 July 2023 Accepted: 30 July 2023 Published: 16 August 2023

Mathematical models have become indispensable tools for analyzing pest control strategies. However, in the realm of pest control studies, the consideration of a plant population being affected by a model that incorporates pests, natural enemies and disease in the pest population has been relatively limited. Therefore, this paper aims to formulate and investigate a hybrid impulsive eco-epidemic model that incorporates disease in the pest population. Initially, we examine the existence and stability of the pest-eradication periodic solution. Subsequently, to explore the impact of chemical and biological control methods, we propose an updated eco-epidemic model that incorporates varying frequencies of pesticide sprays and the release of both infected pests and natural enemies for pest control. We establish threshold values for the susceptible pest eradication periodic solution under different scenarios, illustrating the global attractiveness of this solution. Finally, we discuss the obtained results and suggest potential avenues for future research in this field.
- eco-epidemic model,
- intermittent control strategy,
- susceptible and infective pests,
- integrated pest management
Citation: Wenjie Qin, Yue Xia, Yi Yang. An eco-epidemic model for assessing the application of integrated pest management strategies[J]. Mathematical Biosciences and Engineering, 2023, 20(9): 16506-16527. doi: 10.3934/mbe.2023736

Related Papers:

Abstract

Mathematical models have become indispensable tools for analyzing pest control strategies. However, in the realm of pest control studies, the consideration of a plant population being affected by a model that incorporates pests, natural enemies and disease in the pest population has been relatively limited. Therefore, this paper aims to formulate and investigate a hybrid impulsive eco-epidemic model that incorporates disease in the pest population. Initially, we examine the existence and stability of the pest-eradication periodic solution. Subsequently, to explore the impact of chemical and biological control methods, we propose an updated eco-epidemic model that incorporates varying frequencies of pesticide sprays and the release of both infected pests and natural enemies for pest control. We establish threshold values for the susceptible pest eradication periodic solution under different scenarios, illustrating the global attractiveness of this solution. Finally, we discuss the obtained results and suggest potential avenues for future research in this field.

References

[1]	T. W. Culliney, Crop losses to arthropods, Integrated Pest Management: Pesticide Problems, Springer, 3 (2014), 201–225. https://doi.org/10.1007/978-94-007-7796-5_8
[2]	R. Drummond, G. Lambert, H. Smalley, C. Terrill, Estimated losses of livestock to pests, in CRC Handbook of Pest Management in Agriculture, CRC Press, 1 (1981).
[3]	A. Fournier-Level, The future of pest control lies within (the pest), Australas. Sci., 38 (2017), 23–24.
[4]	R. L. Metcalf, W. H. Luckmann, Introduction to Insect Pest Management, John Wiley & Sons, 1994.
[5]	J. E. van Lenteren, J. V. Woets, Biological and integrated pest control in greenhouses, Ann. Rev. Entomol., 33 (1988), 239–269. https://doi.org/10.1146/annurev.en.33.010188.001323 doi: 10.1146/annurev.en.33.010188.001323
[6]	M. A. Altieri, J. G. Farrell, S. B. Hecht, M. Liebman, F. Magdoff, B. Murphy, et al., Integrated pest management, in Agroecology, CRC Press, (2018), 267–281. https://doi.org/10.1201/9780429495465-14
[7]	J. L. Apple, R. F. Smith, Integrated Pest Management, Springer, 1976. https://doi.org/10.1007/978-1-4615-7269-5
[8]	G. J. Hallman, D. L. Denlinger, Temperature Sensitivity in Insects and Application in Integrated Pest Management, CRC Press, 2019. https://doi.org/10.1201/9780429308581
[9]	J. E. van Lenteren, Integrated Pest Management in Protected Crops, Chapman Hall, 1995.
[10]	L. P. Pedigo, S. H. Hutchins, L. G. Higley, Economic injury levels in theory and practice, Ann. Rev. Entomol., 31 (1986), 341–368. https://doi.org/10.1146/annurev.en.31.010186.002013 doi: 10.1146/annurev.en.31.010186.002013
[11]	J. Headley, Defining the economic threshold, in Pest Control Strategies for the Future, Washington, DC: National Academy of Sciences, (1972), 100–108.
[12]	J. Fuxa, Ecological considerations for the use of entomopathogens in IPM, Annu. Rev. Entomol., 32 (1987), 225–251. https://doi.org/10.1146/annurev.en.32.010187.001301 doi: 10.1146/annurev.en.32.010187.001301
[13]	M. P. Zalucki, D. Adamson, M. J. Furlong, The future of IPM: whither or wither, Aust. J. Entomol., 48 (2009), 85–96. https://doi.org/10.1111/j.1440-6055.2009.00690.x doi: 10.1111/j.1440-6055.2009.00690.x
[14]	V. Rossi, G. Sperandio, T. Caffi, A. Simonetto, G. Gilioli, Critical success factors for the adoption of decision tools in IPM, Agronomy, 9 (2019), 710. https://doi.org/10.3390/agronomy9110710 doi: 10.3390/agronomy9110710
[15]	W. Qin, X. Tan, X. Shi, M. Tosato, X. Liu, Sliding dynamics and bifurcations in the extended nonsmooth filippov ecosystem, Int. J. Bifurcation Chaos, 31 (2021), 2150119. https://doi.org/10.1142/S0218127421501194 doi: 10.1142/S0218127421501194
[16]	W. O. Kermack, A. G. McKendrick, Contributions to the mathematical theory of epidemics–I, Bull. Math. Biol., 53 (1991), 33–55. https://doi.org/10.1016/S0092-8240(05)80040-0 doi: 10.1016/S0092-8240(05)80040-0
[17]	Y. Xiao, L. Chen, Modeling and analysis of a predator–prey model with disease in the prey, Math. Biosci., 171 (2001), 59–82. https://doi.org/10.1016/S0025-5564(01)00049-9 doi: 10.1016/S0025-5564(01)00049-9
[18]	Y. Xiao, L. Chen, Analysis of a three species eco-epidemiological model, J. Math. Anal. Appl., 258 (2001), 733–754. https://doi.org/10.1006/jmaa.2001.7514 doi: 10.1006/jmaa.2001.7514
[19]	Y. Xiao, F. van den Bosch, The dynamics of an eco-epidemic model with biological control, Ecol. Modell., 168 (2003), 203–214. https://doi.org/10.1016/S0304-3800(03)00197-2 doi: 10.1016/S0304-3800(03)00197-2
[20]	A. Ballesteros, A. Blasco, I. Gutierrez-Sagredo, Hamiltonian structure of compartmental epidemiological models, Physica D, 413 (2020), 132656. https://doi.org/10.1016/j.physd.2020.132656 doi: 10.1016/j.physd.2020.132656
[21]	W. Qian, E. Viennet, K. Glass, D. Harley, Epidemiological models for predicting ross river virus in australia: a systematic review, PLoS Negl. Trop. Dis., 14 (2020), e0008621. https://doi.org/10.1371/journal.pntd.0008621 doi: 10.1371/journal.pntd.0008621
[22]	R. Bhattacharyya, R. Kundu, R. Bhaduri, D. Ray, L. J. Beesley, M. Salvatore, et al., Incorporating false negative tests in epidemiological models for SARS-CoV-2 transmission and reconciling with seroprevalence estimates, Sci. Rep., 11 (2021), 9748. https://doi.org/10.1038/s41598-021-89127-1 doi: 10.1038/s41598-021-89127-1
[23]	S. Gakkhar, R. Naji, On a food web consisting of a specialist and a generalist predator, J. Biol. Syst., 11 (2003), 365–376. https://doi.org/10.1142/S0218339003000956 doi: 10.1142/S0218339003000956
[24]	N. Apreutesei, Necessary optimality conditions for a lotka-volterra three species system, Math. Model. Nat. Phenome., 1 (2006), 120–132. https://doi.org/10.1051/mmnp:2006007 doi: 10.1051/mmnp:2006007
[25]	A. Priyadarshi, S. Gakkhar, Dynamics of leslie–gower type generalist predator in a tri-trophic food web system, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 3202–3218. https://doi.org/10.1016/j.cnsns.2013.03.001 doi: 10.1016/j.cnsns.2013.03.001
[26]	X. Liang, Y. Pei, M. Zhu, Y. Lv, Multiple kinds of optimal impulse control strategies on plant–pest–predator model with eco-epidemiology, Appl. Math. Comput., 287–288 (2016), 1–11. https://doi.org/10.1016/j.amc.2016.04.034 doi: 10.1016/j.amc.2016.04.034
[27]	B. Legaspi, W. Sterling, A. Hartstack, D. Dean, Testing the interactions of pest–predator–plant components of the texcim model, Environ. Entomol., 18 (1989), 157–163. https://doi.org/10.1093/ee/18.1.157 doi: 10.1093/ee/18.1.157
[28]	N. Apreutesei, An optimal control problem for a pest, predator, and plant system, Nonlinear Anal. Real World Appl., 13 (2012), 1391–1400. https://doi.org/10.1016/j.nonrwa.2011.11.004 doi: 10.1016/j.nonrwa.2011.11.004
[29]	W. Sokol, J. Howell, Kinetics of phenol oxidation by washed cells, Biotechnol. Bioeng., 23 (1981), 2039–2049. https://doi.org/10.1002/bit.260230909 doi: 10.1002/bit.260230909
[30]	S. Tang, G. Tang, R. A. Cheke, Optimum timing for integrated pest management: modelling rates of pesticide application and natural enemy releases, J. Theor. Biol., 264 (2010), 623–638. https://doi.org/10.1016/j.jtbi.2010.02.034 doi: 10.1016/j.jtbi.2010.02.034
[31]	Z. Xiang, S. Tang, C. Xiang, J. Wu, On impulsive pest control using integrated intervention strategies, Appl. Math. Comput., 269 (2015), 930–946. https://doi.org/10.1016/j.amc.2015.07.076 doi: 10.1016/j.amc.2015.07.076

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)