Mathematical modelling for sustainable crop protection

Suzanne Touzeau

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Suzanne Touzeau. Mathematical modelling for sustainable crop protection. DSABNS 2024 - 15th International Conference on Dynamical Systems Applied to Biology and Natural Sciences, Feb 2024, Caparica, Portugal. hal-04452000

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Submitted on 12 Feb 2024

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Distributed under a Creative Commons Attribution 4.0 International License
Mathematical modelling for sustainable crop protection

Suzanne Touzeau

► To cite this version:

Suzanne Touzeau. Mathematical modelling for sustainable crop protection. DSABNS 2024 - 15th International Conference on Dynamical Systems Applied to Biology and Natural Sciences, Feb 2024, Caparica, Portugal. hal-04452000

HAL Id: hal-04452000

https://hal.inrae.fr/hal-04452000v1

Submitted on 12 Feb 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
MATHEMATICAL MODELLING FOR SUSTAINABLE CROP PROTECTION

Suzanne Touzeau*<fnref n="1" />,<fnref n="2" />

suzanne.touzeau@inrae.fr (*presenter)

Crop pests, pathogens and weeds have a major economic impact and threaten food security. Their control still heavily relies on chemical pesticides, which are harmful to both the environment and public health, and which induce pest resistance, hence the need for eco-friendly sustainable alternatives. The aim of this talk is to present modelling studies which implement alternative control methods, in particular resistant crops and biocontrol agents. These studies focus on how “best” to deploy such control methods, to limit damages cost-efficiently or in seeking some sort of bioeconomic optimum by means of a yield proxy. The models are dynamical systems derived from classical epidemiological models, adapted to the pathosystem considered. Optimisation or optimal control methods are used to determine appropriate deployment strategies.

To efficiently control the disease and avoid resistance breakdown, susceptible and resistant crops can be alternated in space or time, depending on the pathosystem under study. An example of optimal resistance deployment in time will be given to control root-knot nematodes in horticultural crops [3]. Optimising cropping practices, as in the case of banana burrowing nematode management [4], is another example of alternatives to chemical pesticides. Several biocontrol methods can be implemented, which will be illustrated for coffee crop pests: fungus-based biopesticides to control coffee berry borers [2], or predators to control coffee leaf rust [1].

Finally, several general issues, such as “small data”, and perspectives will be discussed.

**Acknowledgements**

Results detailed in this presentation were obtained as part of the PhD theses of Samuel Nilusmas, Israël Tankam Chedjou, Yves Fotso Fotso and Clotilde Djuikem, as well as co-authors cited in the associated references. EPITAG, and Inria associate team with universities in Cameroon, supported part of their research (https://team.inria.fr/epitag/).

**References**

[1] Djuikem, C., Grognard, F., Touzeau, S. (2023). Impulsive modelling of rust dynamics and predator releases for biocontrol. *Mathematical Biosciences* 356: 108968. https://doi.org/10.1016/j.mbs.2023.108968

[2] Fotso Fotso, Y., Touzeau, S., Tsanou, B., Bowong, S., Grognard, F. (2021). Modelling and optimal strategy to control coffee berry borer. *Mathematical Methods in the Applied Sciences* 44(18): 14569–14592. https://doi.org/10.1002/mma.7726

<footnote n="1">¹Université Côté d'Azur, INRAE, ISA, Sophia Antipolis, France</footnote>

<footnote n="2">²Université Côté d'Azur, Inria, INRAE, CNRS, MACBES, Sophia Antipolis, France</footnote>
MATHEMATICAL MODELLING FOR SUSTAINABLE CROP PROTECTION

Suzanne Touzeau*¹,²

¹Université Côté d'Azur, INRAE, ISA, Sophia Antipolis, France

²Université Côté d'Azur, Inria, INRAE, CNRS, MACBES, Sophia Antipolis, France

suzanne.touzeau@inrae.fr (*presenter)

Crop pests, pathogens and weeds have a major economic impact and threaten food security. Their control still heavily relies on chemical pesticides, which are harmful to both the environment and public health, and which induce pest resistance, hence the need for eco-friendly sustainable alternatives. The aim of this talk is to present modelling studies which implement alternative control methods, in particular resistant crops and biocontrol agents. These studies focus on how “best” to deploy such control methods, to limit damages cost-efficiently or in seeking some sort of bioeconomic optimum by means of a yield proxy. The models are dynamical systems derived from classical epidemiological models, adapted to the pathosystem considered. Optimisation or optimal control methods are used to determine appropriate deployment strategies.

To efficiently control the disease and avoid resistance breakdown, susceptible and resistant crops can be alternated in space or time, depending on the pathosystem under study. An example of optimal resistance deployment in time will be given to control root-knot nematodes in horticultural crops [3]. Optimising cropping practices, as in the case of banana burrowing nematode management [4], is another example of alternatives to chemical pesticides. Several biocontrol methods can be implemented, which will be illustrated for coffee crop pests: fungus-based biopesticides to control coffee berry borers [2], or predators to control coffee leaf rust [1].

Finally, several general issues, such as “small data”, and perspectives will be discussed.

**Acknowledgements**

Results detailed in this presentation were obtained as part of the PhD theses of Samuel Nilusmas, Israël Tankam Chedjou, Yves Fotso Fotso and Clotilde Djuikem, as well as co-authors cited in the associated references. EPITAG, and Inria associate team with universities in Cameroon, supported part of their research (https://team.inria.fr/epitag/).

**References**

[1] Djuikem, C., Grognard, F., Touzeau, S. (2023). Impulsive modelling of rust dynamics and predator releases for biocontrol. *Mathematical Biosciences* 356: 108968. https://doi.org/10.1016/j.mbs.2023.108968

[2] Fotso Fotso, Y., Touzeau, S., Tsanou, B., Bowong, S., Grognard, F. (2021). Modelling and optimal strategy to control coffee berry borer. *Mathematical Methods in the Applied Sciences* 44(18): 14569–14592. https://doi.org/10.1002/mma.7726
[3] Nilusmas, S., Mercat, M., Perrot, T., Djian-Caporalino, C., Castagnone-Sereno, P., Touzeau, S., Calcagno, V., Mailleret, L. (2020). Multi-seasonal modelling of plant-nematode interactions reveals efficient plant resistance deployment strategies. *Evolutionary Applications* 13(9): 2206–2221. https://doi.org/10.1111/eva.12989

[4] Tankam Chedjou, I., Grognard, F., Tewa, J. J., Touzeau, S. (2021). Optimal and sustainable management of a soil-borne banana pest. *Applied Mathematics and Computation* 397: 125883. https://doi.org/10.1016/j.amc.2020.125883
[3] Nilusmas, S., Mercat, M., Perrot, T., Djian-Caporalino, C., Castagnone-Sereno, P., Touzeau, S., Calcagno, V., Mailleret, L. (2020). Multi-seasonal modelling of plant-nematode interactions reveals efficient plant resistance deployment strategies. *Evolutionary Applications* 13(9): 2206–2221. https://doi.org/10.1111/eva.12989

[4] Tankam Chedjou, I., Grognard, F., Tewa, J. J., Touzeau, S. (2021). Optimal and sustainable management of a soil-borne banana pest. *Applied Mathematics and Computation* 397: 125883. https://doi.org/10.1016/j.amc.2020.125883