Math. Model. Nat. Phenom.
Volume 18, 2023
|Number of page(s)||34|
|Section||Population dynamics and epidemiology|
|Published online||17 October 2023|
Mathematical modelling and optimal control of production losses caused by Miridae
Department of Mathematics and Computer Science, Faculty of Science, The University of Douala, PO Box 24157 Douala - Cameroon
2 IRD, Sorbonne University, UMMISCO, F-93143 Bondy, France
3 Faculty of Economics Science and Applied Management, The University of Douala, PO Box 17273, Douala, Cameroon
* Corresponding author: firstname.lastname@example.orgemail@example.com
Accepted: 19 August 2023
Cocoa mirid, Sahlbergella singulars, is the major pest of cocoa (Theobroma cacao) responsible of several damage in plots in West Africa and particularly in Cameroon. Occasional damage accounts for 30 40% of pod losses. However, when miridae affect the foliage, gradual wilting occurs and eventually, tree death. A few studies have focused on describing the time evolution of Miridae in the plot in Cameroon, yet numerous questions remain. The aim of this paper is to estimate and control the losses of production caused by the bites of miridea. To do this, we will formulate and study a mathematical model for the dynamics of pods that takes into account the feeding and egg-laying of adults miridae on pods. We present the theoretical analysis of the model. More precisely, we compute equilibria and derive a threshold parameter that determines the presence or not of miridae in the plot. Throughout numerical simulations, we found that miridae can cause approximately 39.21% of production losses (which represents approximatively USD 1276.8 revenue losses) when initially, one has 1200 plants in the plot. After, we aim to increase cocoa production through optimal control. Optimal control consists in reducing density the number of nymphs and adults miridae in the plot. We studied the controlled model and we found that losses with control shrink to 20.58% which corresponds to USD670.32 income revenue.
Mathematics Subject Classification: 35K57 / 93D05 / 65M06 / 92D30
Key words: Sahlbergella singularis / Cocoa / mathematical models / stability / optimal control
© The authors. Published by EDP Sciences, 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.