Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis

Tchiekre Michel Henri Daugny; Aguemon Wiwegnon Uriel-Longin; Kambire Diopina Gnowille; Akahoua David Vincent Brou; Adou Kablan Jerome

doi:doi:10.11648/j.ijssam.20261101.11

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Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis

Tchiekre Michel Henri Daugny^*

, Aguemon Wiwegnon Uriel-Longin, Kambire Diopina Gnowille, Akahoua David Vincent Brou, Adou Kablan Jerome

Published in International Journal of Systems Science and Applied Mathematics (Volume 11, Issue 1)

Received: 7 September 2025 Accepted: 9 October 2025 Published: 4 February 2026

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Abstract

This work presents a rigorous mathematical study of a vegetation fire propagation model specifically adapted to the Ivorian environmental context, where climatic conditions and vegetation types significantly influence fire dynamics. The model aims to describe the thermal behavior of vegetation during combustion and the spatial spread of fire fronts. We first analyze a nonlinear ordinary differential equation (ODE) governing the temporal evolution of temperature, which captures the essential mechanisms of heat production and dissipation during combustion. Using classical results from the theory of differential equations, we establish the existence and uniqueness of solutions under suitable assumptions on the model parameters and initial conditions. The study is then extended to a transport-reaction partial differential equation (PDE) that incorporates spatial effects and allows the description of fire propagation in a heterogeneous domain. This PDE model accounts for both the advective transport of heat and the local reaction terms associated with combustion processes. The analysis relies on tools from functional analysis, including appropriate function spaces and a priori estimates, combined with the method of characteristics to handle the transport component of the equation. Under physically relevant assumptions, we prove the existence and uniqueness of weak solutions to the PDE model. The proposed mathematical framework provides a solid theoretical foundation for vegetation fire modeling in West African environments. Beyond its theoretical interest, this work contributes to a better understanding of fire dynamics and offers a basis for future numerical simulations and risk assessment tools aimed at improving fire prevention and management strategies in Côte d'Ivoire and similar regions.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 11, Issue 1)
DOI	10.11648/j.ijssam.20261101.11
Page(s)	1-5
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Fire, Mathematical, Model, Ordinary Differential Equation, Partial Differential Equation

References

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[2]	P. A. Santoni, J. H. Balbi, J. L. Dupuy, “Dynamic modelling of upslope fire growth”, International Journal of Wildland Fire, vol. 9, pp. 285–292, 1999.
[3]	F. Morandini, P. A. Santoni, J. H. Balbi, “Analogy between wind and slope effects on fire spread across a fuel bed – Modelling and validations”, in: Proceedings of the 3rd International Seminar on Fire and Explosion Hazards, 2000.
[4]	B. Porterie, N. Zekri, J.-P. Clerc, J.-C. Loraud, “Un reseau de petit monde local à sites ponderes pour les feux de forêts”, Comptes Rendus Physique, vol. 6, pp. 151–157, 2005.
[5]	J. K. Adou, Y. Billaud, D. A. Brou, J.-P. Clerc, J.-L. Consalvi, A. Fuentes, A. Kaiss, F. Nmira, B. Porterie,
[6]	L. Zekri, “Simulating wildfire patterns using a small-world network model”, Ecological Modelling, vol. 221, pp. 1463–1471, 2010.
[7]	G. F. Carrier, F. E. Fendell, M. F. Wolff, “Wind-aided firespread across arrays of discrete fuel elements. I. Theory”, Combustion Science and Technology, vol. 75, pp. 31–51, 1991.
[8]	R. R. Linn; P. Cunningham “Numerical simulations of grass fires using a coupled atmosphere-fire model: Basic fire behavior and dependence on wind speed”, J. Geophys. Res., Volume 110 (2005), D13107.
[9]	E. Koo; P. Pagni; S. Stephens; J. Huff; J. Woycheese; D. Weise “A simple physical model for forest fire spread rate”, Fire Saf Sci., Volume 8 (2005), pp. 851-862.
[10]	N. Cheney; J. Gould; W. Catchpole “Prediction of fire spread in grasslands, Int. J. Wildland Fire”, Volume 8 (1998), pp. 1-13
[11]	D. R. Weise; G. S. Biging “A qualitative comparison of fire spread models incorporating wind and slope effects”, For. Sci., Volume 43 (1997), pp. 170-180.
[12]	D. R. Weise; G. S. Biging Effects of wind velocity and slope on fire behavior, Fire Saf. Sci. - Proc. Fourth Int. Symp., Volume 4 (1994), pp. 1041-1051.

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APA Style

Daugny, T. M. H., Uriel-Longin, A. W., Gnowille, K. D., Brou, A. D. V., Jerome, A. K. (2026). Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis. International Journal of Systems Science and Applied Mathematics, 11(1), 1-5. https://doi.org/10.11648/j.ijssam.20261101.11

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ACS Style

Daugny, T. M. H.; Uriel-Longin, A. W.; Gnowille, K. D.; Brou, A. D. V.; Jerome, A. K. Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis. Int. J. Syst. Sci. Appl. Math. 2026, 11(1), 1-5. doi: 10.11648/j.ijssam.20261101.11

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AMA Style

Daugny TMH, Uriel-Longin AW, Gnowille KD, Brou ADV, Jerome AK. Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis. Int J Syst Sci Appl Math. 2026;11(1):1-5. doi: 10.11648/j.ijssam.20261101.11

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@article{10.11648/j.ijssam.20261101.11,
  author = {Tchiekre Michel Henri Daugny and Aguemon Wiwegnon Uriel-Longin and Kambire Diopina Gnowille and Akahoua David Vincent Brou and Adou Kablan Jerome},
  title = {Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis
},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {11},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ijssam.20261101.11},
  url = {https://doi.org/10.11648/j.ijssam.20261101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20261101.11},
  abstract = {This work presents a rigorous mathematical study of a vegetation fire propagation model specifically adapted to the Ivorian environmental context, where climatic conditions and vegetation types significantly influence fire dynamics. The model aims to describe the thermal behavior of vegetation during combustion and the spatial spread of fire fronts. We first analyze a nonlinear ordinary differential equation (ODE) governing the temporal evolution of temperature, which captures the essential mechanisms of heat production and dissipation during combustion. Using classical results from the theory of differential equations, we establish the existence and uniqueness of solutions under suitable assumptions on the model parameters and initial conditions. The study is then extended to a transport-reaction partial differential equation (PDE) that incorporates spatial effects and allows the description of fire propagation in a heterogeneous domain. This PDE model accounts for both the advective transport of heat and the local reaction terms associated with combustion processes. The analysis relies on tools from functional analysis, including appropriate function spaces and a priori estimates, combined with the method of characteristics to handle the transport component of the equation. Under physically relevant assumptions, we prove the existence and uniqueness of weak solutions to the PDE model. The proposed mathematical framework provides a solid theoretical foundation for vegetation fire modeling in West African environments. Beyond its theoretical interest, this work contributes to a better understanding of fire dynamics and offers a basis for future numerical simulations and risk assessment tools aimed at improving fire prevention and management strategies in Côte d'Ivoire and similar regions.
},
 year = {2026}
}

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TY  - JOUR
T1  - Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis

AU  - Tchiekre Michel Henri Daugny
AU  - Aguemon Wiwegnon Uriel-Longin
AU  - Kambire Diopina Gnowille
AU  - Akahoua David Vincent Brou
AU  - Adou Kablan Jerome
Y1  - 2026/02/04
PY  - 2026
N1  - https://doi.org/10.11648/j.ijssam.20261101.11
DO  - 10.11648/j.ijssam.20261101.11
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20261101.11
AB  - This work presents a rigorous mathematical study of a vegetation fire propagation model specifically adapted to the Ivorian environmental context, where climatic conditions and vegetation types significantly influence fire dynamics. The model aims to describe the thermal behavior of vegetation during combustion and the spatial spread of fire fronts. We first analyze a nonlinear ordinary differential equation (ODE) governing the temporal evolution of temperature, which captures the essential mechanisms of heat production and dissipation during combustion. Using classical results from the theory of differential equations, we establish the existence and uniqueness of solutions under suitable assumptions on the model parameters and initial conditions. The study is then extended to a transport-reaction partial differential equation (PDE) that incorporates spatial effects and allows the description of fire propagation in a heterogeneous domain. This PDE model accounts for both the advective transport of heat and the local reaction terms associated with combustion processes. The analysis relies on tools from functional analysis, including appropriate function spaces and a priori estimates, combined with the method of characteristics to handle the transport component of the equation. Under physically relevant assumptions, we prove the existence and uniqueness of weak solutions to the PDE model. The proposed mathematical framework provides a solid theoretical foundation for vegetation fire modeling in West African environments. Beyond its theoretical interest, this work contributes to a better understanding of fire dynamics and offers a basis for future numerical simulations and risk assessment tools aimed at improving fire prevention and management strategies in Côte d'Ivoire and similar regions.

VL  - 11
IS  - 1
ER  -

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Author Information

Tchiekre Michel Henri Daugny

Departement Mathematiques Physique Chimie, UFR Sciences Biologiques, Universite Peleforo Gon Coulibaly, Korhogo, Côte d’Ivoire

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http://orcid.org/0009-0000-5372-2785
Aguemon Wiwegnon Uriel-Longin

Departement De Mathematiques, Faculte Des Sciences, Universite De Kindia, Kindia, Guinee

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Kambire Diopina Gnowille

Departement de Mathematiques et Informatiques, UFR-SFA, Universite Nangui Abrogoua, Abidjan, Côte d’Ivoire

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Akahoua David Vincent Brou

UFR Environnement, Universite Jean Lorougnon Guede, Daloa, Côte d’Ivoire

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Adou Kablan Jerome

UFR Math. Info, Universite Felix Houphouët-Boigny, Abidjan, Côte d’Ivoire

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Plain Text BibTeX RIS

APA Style

Daugny, T. M. H., Uriel-Longin, A. W., Gnowille, K. D., Brou, A. D. V., Jerome, A. K. (2026). Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis. International Journal of Systems Science and Applied Mathematics, 11(1), 1-5. https://doi.org/10.11648/j.ijssam.20261101.11

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ACS Style

Daugny, T. M. H.; Uriel-Longin, A. W.; Gnowille, K. D.; Brou, A. D. V.; Jerome, A. K. Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis. Int. J. Syst. Sci. Appl. Math. 2026, 11(1), 1-5. doi: 10.11648/j.ijssam.20261101.11

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AMA Style

Daugny TMH, Uriel-Longin AW, Gnowille KD, Brou ADV, Jerome AK. Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis. Int J Syst Sci Appl Math. 2026;11(1):1-5. doi: 10.11648/j.ijssam.20261101.11

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@article{10.11648/j.ijssam.20261101.11,
  author = {Tchiekre Michel Henri Daugny and Aguemon Wiwegnon Uriel-Longin and Kambire Diopina Gnowille and Akahoua David Vincent Brou and Adou Kablan Jerome},
  title = {Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis
},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {11},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ijssam.20261101.11},
  url = {https://doi.org/10.11648/j.ijssam.20261101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20261101.11},
  abstract = {This work presents a rigorous mathematical study of a vegetation fire propagation model specifically adapted to the Ivorian environmental context, where climatic conditions and vegetation types significantly influence fire dynamics. The model aims to describe the thermal behavior of vegetation during combustion and the spatial spread of fire fronts. We first analyze a nonlinear ordinary differential equation (ODE) governing the temporal evolution of temperature, which captures the essential mechanisms of heat production and dissipation during combustion. Using classical results from the theory of differential equations, we establish the existence and uniqueness of solutions under suitable assumptions on the model parameters and initial conditions. The study is then extended to a transport-reaction partial differential equation (PDE) that incorporates spatial effects and allows the description of fire propagation in a heterogeneous domain. This PDE model accounts for both the advective transport of heat and the local reaction terms associated with combustion processes. The analysis relies on tools from functional analysis, including appropriate function spaces and a priori estimates, combined with the method of characteristics to handle the transport component of the equation. Under physically relevant assumptions, we prove the existence and uniqueness of weak solutions to the PDE model. The proposed mathematical framework provides a solid theoretical foundation for vegetation fire modeling in West African environments. Beyond its theoretical interest, this work contributes to a better understanding of fire dynamics and offers a basis for future numerical simulations and risk assessment tools aimed at improving fire prevention and management strategies in Côte d'Ivoire and similar regions.
},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis

AU  - Tchiekre Michel Henri Daugny
AU  - Aguemon Wiwegnon Uriel-Longin
AU  - Kambire Diopina Gnowille
AU  - Akahoua David Vincent Brou
AU  - Adou Kablan Jerome
Y1  - 2026/02/04
PY  - 2026
N1  - https://doi.org/10.11648/j.ijssam.20261101.11
DO  - 10.11648/j.ijssam.20261101.11
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20261101.11
AB  - This work presents a rigorous mathematical study of a vegetation fire propagation model specifically adapted to the Ivorian environmental context, where climatic conditions and vegetation types significantly influence fire dynamics. The model aims to describe the thermal behavior of vegetation during combustion and the spatial spread of fire fronts. We first analyze a nonlinear ordinary differential equation (ODE) governing the temporal evolution of temperature, which captures the essential mechanisms of heat production and dissipation during combustion. Using classical results from the theory of differential equations, we establish the existence and uniqueness of solutions under suitable assumptions on the model parameters and initial conditions. The study is then extended to a transport-reaction partial differential equation (PDE) that incorporates spatial effects and allows the description of fire propagation in a heterogeneous domain. This PDE model accounts for both the advective transport of heat and the local reaction terms associated with combustion processes. The analysis relies on tools from functional analysis, including appropriate function spaces and a priori estimates, combined with the method of characteristics to handle the transport component of the equation. Under physically relevant assumptions, we prove the existence and uniqueness of weak solutions to the PDE model. The proposed mathematical framework provides a solid theoretical foundation for vegetation fire modeling in West African environments. Beyond its theoretical interest, this work contributes to a better understanding of fire dynamics and offers a basis for future numerical simulations and risk assessment tools aimed at improving fire prevention and management strategies in Côte d'Ivoire and similar regions.

VL  - 11
IS  - 1
ER  -

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