International Journal of Numerical Methods and Applications

The International Journal of Numerical Methods and Applications publishes research articles on numerical methods and their applications in various fields, including differential equations, fluid dynamics, and bioinformatics. It also welcomes survey articles on new methods in numerical analysis.

Submit Article

NUMERICAL ANALYSIS OF A FOUR-STAGE AGE-STRUCTURED POPULATION DYNAMICS MODEL WITH SPATIAL DIFFUSION FOR DESERT LOCUSTS

Authors

  • Nestor RAMDE
  • Amidou TRAORE
  • Seydou SORE
  • Yacouba SIMPORE
  • Ousseynou NAKOULIMA

Keywords:

numerical solutions, desert locusts, convergence, finite differences

DOI:

https://doi.org/10.17654/0975045226001

Abstract

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.

Published

2025-09-01

Issue

Section

Articles

How to Cite

NUMERICAL ANALYSIS OF A FOUR-STAGE AGE-STRUCTURED POPULATION DYNAMICS MODEL WITH SPATIAL DIFFUSION FOR DESERT LOCUSTS. (2025). International Journal of Numerical Methods and Applications, 26(1), 1-38. https://doi.org/10.17654/0975045226001

Similar Articles

21-30 of 36

You may also start an advanced similarity search for this article.