Models for Miridae, a cocoa insect pest. Application in control strategies

Cocoa mirid, Sahlbergella singularis, is one of the major pests of cocoa in West Africa. It is responsible of several damages in plots. In this paper, we study the dynamics of this pest. Based on biological and ecological partial knowledge, we develop 2 cooperative mathematical models that aim to describe the time dynamics of the cocoa mirids. We first develop a cooperative stage‐structured model, derived some qualitative results, and a sensitivity analysis study in order to determine the most important parameters. Assuming that all parameters are or not periodic, we obtain conditions that allow the persistence or not of the population. We highlight the influence of cocoa pods variation along the year on the time evolution of the population. Then, we derive a 2‐stage cooperative time‐delay model, with 2 delays, that takes into account the eggs' development time and the females' maturation time. We illustrate our theoretical results with some simulations and show that the delayed system provides the best results compared with real observations. Finally, we focus on chemical control that is commonly used in Cameroon and compare it to a new biological control, mixing mating disrupting and trapping. We discuss the results and provide future perspectives based on this work.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  P. Hatcher,et al.  Knowledge and perception of Ghanaian cocoa farmers on mirid control and their willingness to use forecasting systems , 2016 .

[3]  D. Guest.  Black pod: diverse pathogens with a global impact on cocoa yield. , 2007, Phytopathology.

[4]  N. Röling,et al.  Assessing the effectiveness of a Local Agricultural Research Committee in diffusing sustainable cocoa production practices: the case of capsid control in Ghana , 2007 .

[5]  Edmond Dounias,et al.  Les agroforêts Mvae et Yassa du cameroun littoral : fonctions socioculturelles, structure et composition floristique , 1996 .

[6]  J. Anikwe,et al.  The population dynamics of the brown cocoa mirid, Sahlbergella singularis haglund in Ibadan, Nigeria , 2010 .

[7]  A. Adesina,et al.  Diversity of plants in cocoa agroforests in the humid forest zone of Southern Cameroon , 2007, Biodiversity and Conservation.

[8]  Hal L. Smith.  Cooperative systems of differential equations with concave nonlinearities , 1986 .

[9]  J. Jiggins,et al.  The cocoa mirid (Hemiptera: Miridae) problem: evidence to support new recommendations on the timing of insecticide application on cocoa in Ghana , 2014 .

[10]  W. Marsden.  I and J , 2012 .

[11]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[12]  Roumen Anguelov,et al.  On nonstandard finite difference schemes in biosciences , 2012, AIP conference proceedings.

[13]  Jiang Jifa.  THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES , 1993 .

[14]  R. Kumar,et al.  Biology, immature stages and rearing of cocoa-capsids (Miridae: Heteroptera) , 1974 .

[15]  Roumen Anguelov,et al.  Mathematical modeling of sterile insect technology for control of anopheles mosquito , 2011, Comput. Math. Appl..

[16]  Nn Kouame,et al.  Variations saisonnières des populations de mirides du cacaoyer dans la région de l’Indénié-Djuablin en Côte d’Ivoire , 2015 .

[17]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[18]  C. Cilas,et al.  True Bug (Heteroptera) Impact on Cocoa Fruit Mortality and Productivity , 2012, Journal of economic entomology.

[19]  D. Alemagi,et al.  Pathways for sustainable intensification and diversification of cocoa agroforestry landscapes in Cameroon , 2015 .

[20]  Régis Babin,et al.  Rearing method and life‐table data for the cocoa mirid bug Sahlbergella singularis Haglund (Hemiptera: Miridae) , 2008 .

[21]  A. I.,et al.  Neural Field Continuum Limits and the Structure–Function Partitioning of Cognitive–Emotional Brain Networks , 2023, Biology.

[22]  S. Vidal,et al.  Dispersion Models and Sampling of Cacao Mirid Bug Sahlbergella singularis (Hemiptera: Miridae) on Theobroma cacao in Southern Cameroon , 2011, Environmental entomology.

[23]  S. Laird,et al.  Cocoa farms in the Mount Cameroon region: biological and cultural diversity in local livelihoods , 2007, Biodiversity and Conservation.

[24]  S. Ribeiro,et al.  Influence of breeding site availability on the oviposition behaviour of Aedes aegypti , 2015, Memorias do Instituto Oswaldo Cruz.

[25]  D. Kirschner,et al.  A methodology for performing global uncertainty and sensitivity analysis in systems biology. , 2008, Journal of theoretical biology.

[26]  Y. Dumont,et al.  Mathematical model for pest-insect control using mating disruption and trapping , 2016, 1608.04880.

[27]  Roumen Anguelov,et al.  Simulations and parameter estimation of a trap-insect model using a finite element approach , 2017, Math. Comput. Simul..

[28]  P. Entwistle,et al.  Pests of cocoa. , 1972 .

[29]  Yves Dumont,et al.  Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control , 2013, Comput. Math. Appl..

[30]  G. Awudzi,et al.  Optimizing mirid control on cocoa farms through complementary monitoring systems , 2017 .

[31]  D. Hall,et al.  Design and placement of synthetic sex pheromone traps for cacao mirids in Ghana , 2018 .

[32]  Régis Babin,et al.  Field evaluation of synthetic sex pheromone traps for the cocoa mirid Sahlbergella singularis (Hemiptera: Miridae). , 2011, Pest management science.

[33]  G. Matthews,et al.  A survey of pesticide application in Cameroon , 2003 .

[34]  Régis Babin,et al.  Contribution à l'amélioration de la lutte contre le miride du cacaoyer Sahlbergella singularis Hagl. (Hemiptera : Miridae). Influence des facteurs agro-écologiques sur la dynamique des populations du ravageur , 2009 .

[35]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[36]  J. Mbang,et al.  Effect of genotype of cocoa (Theobroma cacao) on attractiveness to the mirid Sahlbergella singularis (Hemiptera: Miridae) in the laboratory. , 2008, Pest management science.

[37]  D. Kline,et al.  The Effects of Larval Habitat Quality on Aedes albopictus Skip Oviposition. , 2015, Journal of the American Mosquito Control Association.

[38]  J. C. Anikwe,et al.  Effects of cocoa tree phenology and canopy microclimate on the performance of the mirid bug Sahlbergella singularis , 2011 .

[39]  G. Williams.  Field Observations on the Cacao Mirids, Sahlbergella singularis Hagl. and Distantiella theobroma (Dist.), in the Gold Coast , 1953 .

[40]  Régis Babin,et al.  Isolation and Characterization of Twelve Polymorphic Microsatellite Loci for the Cocoa Mirid Bug Sahlbergella Singularis , 2012, International journal of molecular sciences.

[41]  M. Hirsch,et al.  4. Monotone Dynamical Systems , 2005 .

[42]  J. Lumaret,et al.  Impact of shade on the spatial distribution of Sahlbergella singularis in traditional cocoa agroforests , 2010 .