NUMERICAL ANALYSIS OF A FOUR-STAGE AGE-STRUCTURED POPULATION DYNAMICS MODEL WITH SPATIAL DIFFUSION FOR DESERT LOCUSTS
Keywords:
numerical solutions, desert locusts, convergence, finite differencesDOI:
https://doi.org/10.17654/0975045226001Abstract
Consider a linear system of a locust population dynamics model structured on age, space with non-local boundary conditions. The behavior of the terms of the numerical solutions of this model is studied using the finite difference method, as well as the convergence (consistency and stability) of the method. Numerical illustrations of the schemes are proposed.
Received: June 2, 2025
Revised: July 18, 2025
Accepted: July 30, 2025
References
[1] O. Angulo, J. C. López-Marcos, M. A. López Marcos and F. A. Milner, A numerical method for nonlinear age-structured population models with finite maximum age, Journal of Mathematical Analysis and Applications 361(1) (2010), 150-160.
[2] R. Courant, K. Friedrichs and H. Lewy, Über die partiellen differenzengleichungen der mathematischen physic, Mathematische Annalen 100(1) (1928), 32-74.
[3] R. Courant, K. Friedrichs and H. Lewy, On the partial difference equations of mathematical physics, IBM Journal of Research and Development 11(2) (1967), 215-234.
[4] R. Courant, E. Isaacson and M. Rees, On the solution of nonlinear hyperbolic differential equations by finite differences, Communications on Pure and Applied Mathematics 5(3) (1952), 243-255.
[5] K. Cressman, Desert locust, Biological and Environmental Hazards, Risks, and Disasters (2016), 87-105.
[6] E. Fernandez-Cara, R. Morales and D. A. Souza, Numerical null controllability of parabolic PDEs using Lagrangian methods. arXiv preprint arXiv:2411.14031, 2024.
[7] G. Gilioli, S. Pasquali and E. Marchesini, A modelling framework for pest population dynamics and management: An application to the grape berry moth, Ecological Modelling 320 (2016), 348-357.
[8] J. Guan, M. Li, X. Ju, J. Lin, J. Wu and J. Zheng. The potential habitat of desert locusts is contracting: predictions under climate change scenarios, Peer J. 9 (2021), e12311.
[9] M. Y. Kim and E. J. Park, An upwind scheme for a nonlinear model in age-structured population dynamics, Computers Mathematics with Applications 30(8) (1995), 5-17.
[10] E. Kimathi, H. E. Z. Tonnang, S. Subramanian, K. Cressman, E. M. Abdel-Rahman, M. Tesfayohannes, S. Niassy, B. Torto, T. Dubois, C. M. Tanga, M. Kassie, S. Ekesi, D. Mwangi and S. Kelemu, Prediction of breeding regions for the desert locust Schistocerca gregaria in east Africa, Scientific Reports 10(1) (2020), 11937.
[11] E. Lanzarone, S. Pasquali, G. Gilioli and E. Marchesini, A Bayesian estimation approach for the mortality in a stage-structured demographic model, Journal of Mathematical Biology 75(3) (2017), 759-779.
[12] P. D. Lax and R. D. Richtmyer, Survey of the stability of linear finite difference equations, In Selected Papers Volume I, Springer, 2005, pp. 125-151.
[13] S. Mechhoud, E. Witrant, L. Dugard and D. Moreau, Estimation de la diffusion thermique dans les plasmas de tokamak, In CIFA 2012-7ème Conférence Internationale Francophone d’Automatique, 2012.
[14] G. G. O’Brien, M. A. Hyman and S. Kaplan, A study of the numerical solution of partial differential equations, Journal of Mathematics and Physics 29(1-4) (1950), 223-251.
[15] S. Pasquali, C. Soresina and G. Gilioli, The effects of fecundity, mortality and distribution of the initial condition in phenological models, Ecological Modelling 402 (2019), 45-58.
[16] D. Picart and B. Ainseba, Parameter identification in multistage population dynamics model, Nonlinear Analysis: Real World Applications 12(6) (2011), 3315-3328.
[17] N. Ramdé, A. Traoré, Y. Simporé and O. Nakoulima, Existence and uniqueness of a solution for a four-stage age-structured population dynamics model with spatial diffusion for desert locusts, International Journal of Mathematics and Mathematical Sciences 2024(1) (2024), 8421625.
[18] K. Ren, L. Zhang and Y. Zhou, An energy-based discontinuous Galerkin method for the nonlinear Schrödinger equation with wave operator, SIAM Journal on Numerical Analysis 62(6) (2024), 2459-2483.
[19] A. T. Showler, Desert locust, Schistocerca gregaria forskål (orthoptera: Acrididae): plagues, Encyclopedia of Entomology (2008), pages 1181-1186.
[20] Y. Simporé, Null controllability of size-age dependent population dynamics models. arXiv preprint arXiv:2408.05291, 2024.
[21] Y. Simporé, Null controllability of a nonlinear population dynamics with age structuring and spatial diffusion, In Nonlinear Analysis, Geometry and Applications: Proceedings of the First NLAGA-BIRS Symposium, Dakar, Senegal, June 24-28, 2019, pages 1–33. Springer, 2020.
[22] Y. Simpore and A. Tambue, Null controllability and numerical method for crocco equation with incomplete data based on an exponential integrator and finite difference-finite element method, Computers and Mathematics with Applications 74(5) (2017), 1043-1058.
[23] P. M. Symmons and K. Cressman, Desert Locust Guidelines: Biology and Behaviour, FAO, Rome, 2001, pp. 1-42.
[24] A. Traoré, B. Ainseba and O. Traoré, Null controllability of a four stage and age-structured population dynamics model, Journal of Mathematics 2021(1) (2021), 5546150.
[25] A. Traore, B. Ainseba and O. Traore, On the existence of solution of a four-stage and age-structured population dynamics model, Journal of Mathematical Analysis and Applications 495(1) (2021), 124699.
[26] A. Traoré, O. S. Sougué, Y. Simporé and O. Traoré, Null Controllability of a Nonlinear Age Structured Model for a Two-sex Population, In Abstract and Applied Analysis, Vol. 2021, Wiley Online Library, 2021, p. 6666942.
[27] P. Y. Lagrée, Résolution numérique des équations de saint-venant, mise en oeuvre en volumes fnis par un solveur de riemann bien balance, Institut Jean Le Rond D’Alembert, 2020.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

This work is licensed under a Creative Commons Attribution 4.0 International License.
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pushpa Publishing House for more info or permissions.



Publication count:
Google h-index: