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Mathematical Modelling of Dengue Transmission with Intervention Strategies Using Fractional Derivatives

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Abstract

This paper deals with a deterministic mathematical model of dengue based on a system of fractional-order differential equations (FODEs). In this study, we consider dengue control strategies that are relevant to the current situation in Malaysia. They are the use of adulticides, larvicides, destruction of the breeding sites, and individual protection. The global stability of the disease-free equilibrium and the endemic equilibrium is constructed using the Lyapunov function theory. The relations between the order of the operator and control parameters are briefly analysed. Numerical simulations are performed to verify theoretical results and examine the significance of each intervention strategy in controlling the spread of dengue in the community. The model shows that vector control tools are the most efficient method to combat the spread of the dengue virus, and when combined with individual protection, make it more effective. In fact, the massive use of personal protection alone can significantly reduce the number of dengue cases. Inversely, mechanical control alone cannot suppress the excessive number of infections in the population, although it can reduce the Aedes mosquito population. The result of the real-data fitting revealed that the FODE model slightly outperformed the integer-order model. Thus, we suggest that the FODE approach is worth to be considered in modelling an infectious disease like dengue.

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Acknowledgements

The authors are very grateful for partial financial support by the Universiti Putra Malaysia providing Putra Grant GP-IPS/2018/9625000. The authors also thank the Ministry of Education Malaysia and the Universiti Teknologi Mara (UiTM), and special appreciation to the School of Mathematical Sciences, College of Computing, Informatics and Media, Universiti Teknologi MARA. The authors would like to extend sincere gratitude for the constructive comments and suggestions in improving the manuscript by the reviewers.

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Correspondence to Nur ’Izzati Hamdan.

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Hamdan, N.’., Kilicman, A. Mathematical Modelling of Dengue Transmission with Intervention Strategies Using Fractional Derivatives. Bull Math Biol 84, 138 (2022). https://doi.org/10.1007/s11538-022-01096-2

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