Forest model dynamics analysis and optimal control based on disease and fire interactions

Xiaoxiao Liu; Chunrui Zhang; Xiaoxiao Liu; Chunrui Zhang

doi:10.3934/math.2024154

AIMS Mathematics

2024, Volume 9, Issue 2: 3174-3194. doi: 10.3934/math.2024154

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Research article

Forest model dynamics analysis and optimal control based on disease and fire interactions

Xiaoxiao Liu ¹,
Chunrui Zhang ^{2
,
,}

1.
College of Computer and Control Engineering, Northeast Forestry University, Harbin 150040, China
2.
College of Science, Northeast Forestry University, Harbin 150040, China

Received: 08 November 2023 Revised: 24 December 2023 Accepted: 27 December 2023 Published: 03 January 2024
MSC : 34C23, 35K57

Three models for the propagation of forest disease are revisited to include the effect of forest fires and disease spread. We study the global stability of the forest-disease model in the absence of forest fires and the spread of disease. When forest fires caused by grass cover are considered, we show that the equilibrium points are locally asymptotically stable. If both forest fires and the spread of disease exist in the second model, then Turing instability can occur. In this case, the system exhibits complex dynamic behavior. To determine the effect of fire on the forest disease model, we obtain the optimal control expression of the key parameter fire factor, and carry out sensitivity analysis. Finally, we use forest biomass data of some provinces in China from 2002 to 2018 for numerical simulation, and the results are in agreement with the theoretical analysis.
- Forest-Disease model,
- forest fire,
- stability,
- optimal control,
- sensitivity analysis
Citation: Xiaoxiao Liu, Chunrui Zhang. Forest model dynamics analysis and optimal control based on disease and fire interactions[J]. AIMS Mathematics, 2024, 9(2): 3174-3194. doi: 10.3934/math.2024154

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Abstract

Three models for the propagation of forest disease are revisited to include the effect of forest fires and disease spread. We study the global stability of the forest-disease model in the absence of forest fires and the spread of disease. When forest fires caused by grass cover are considered, we show that the equilibrium points are locally asymptotically stable. If both forest fires and the spread of disease exist in the second model, then Turing instability can occur. In this case, the system exhibits complex dynamic behavior. To determine the effect of fire on the forest disease model, we obtain the optimal control expression of the key parameter fire factor, and carry out sensitivity analysis. Finally, we use forest biomass data of some provinces in China from 2002 to 2018 for numerical simulation, and the results are in agreement with the theoretical analysis.

References

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