Simulations and fractional modeling of dengue transmission in Bangladesh

Saima Akter; Zhen Jin; Saima Akter; Zhen Jin

doi:10.3934/mbe.2023434

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 9891-9922. doi: 10.3934/mbe.2023434

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Research article

Simulations and fractional modeling of dengue transmission in Bangladesh

Saima Akter ^1,2,
Zhen Jin ^{1,2
,
,}

1.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
2.
Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan 030006, China

Academic Editor: Ulf Schmitz

Received: 15 January 2023 Revised: 17 February 2023 Accepted: 06 March 2023 Published: 27 March 2023

Dengue is one of the most infectious diseases in the world. In Bangladesh, dengue occurs nationally and has been endemic for more than a decade. Therefore, it is crucial that we model dengue transmission in order to better understand how the illness behaves. This paper presents and analyzes a novel fractional model for the dengue transmission utilizing the non-integer Caputo derivative (CD) and are analysed using q-homotopy analysis transform method (q-HATM). By using the next generation method, we derive the fundamental reproduction number $ R_0 $ and show the findings based on it. The global stability of the endemic equilibrium (EE) and the disease-free equilibrium (DFE) is calculated using the Lyapunov function. For the proposed fractional model, numerical simulations and dynamical attitude are seen. Moreover, A sensitivity analysis of the model is performed to determine the relative importance of the model parameters to the transmission.
- fractional model,
- q-Homotopy analysis method,
- stability analysis,
- basic reproduction number,
- sensitivity analysis,
- numerical simulations
Citation: Saima Akter, Zhen Jin. Simulations and fractional modeling of dengue transmission in Bangladesh[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 9891-9922. doi: 10.3934/mbe.2023434

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Abstract

Dengue is one of the most infectious diseases in the world. In Bangladesh, dengue occurs nationally and has been endemic for more than a decade. Therefore, it is crucial that we model dengue transmission in order to better understand how the illness behaves. This paper presents and analyzes a novel fractional model for the dengue transmission utilizing the non-integer Caputo derivative (CD) and are analysed using q-homotopy analysis transform method (q-HATM). By using the next generation method, we derive the fundamental reproduction number $ R_0 $ and show the findings based on it. The global stability of the endemic equilibrium (EE) and the disease-free equilibrium (DFE) is calculated using the Lyapunov function. For the proposed fractional model, numerical simulations and dynamical attitude are seen. Moreover, A sensitivity analysis of the model is performed to determine the relative importance of the model parameters to the transmission.

References

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