Parameter estimation and fractional derivatives of dengue transmission model

Windarto; Muhammad Altaf Khan; Fatmawati; Windarto; Muhammad Altaf Khan; Fatmawati

doi:10.3934/math.2020178

AIMS Mathematics

2020, Volume 5, Issue 3: 2758-2779. doi: 10.3934/math.2020178

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Research article Special Issues

Parameter estimation and fractional derivatives of dengue transmission model

1.
Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia
2.
Faculty of Natural and Agricultural Sciences, University of the Free state, South Africa

Received: 05 November 2019 Accepted: 12 March 2020 Published: 17 March 2020
MSC : 34A08, 92B05

In this paper, we propose a parameter estimation of dengue fever transmission model using a particle swarm optimization method. This method is applied to estimate the parameters of the host-vector and SIR type dengue transmission models by using cumulative data of dengue patient in East Java province, Indonesia. Based on the parameter values, the basic reproduction number of both models are greater than one and obtained their value for SIR is $\mathcal{R}_0 = 1.4159$ and for vector host is $\mathcal{R}_0 = 1.1474$. We then formulate the models in fractional Atangana-Baleanu derivative that possess the property of nonlocal and nonsingular kernel that has been remained effective to many real-life problems. A numerical procedure for the solution of the model SIR model is shown. Some specific numerical values are considered to obtain the graphical results for both the SIR and Vector Host model. We show that the model vector host provide good results for data fitting than that of the SIR model.
- dengue model,
- parameter estimation,
- particle swarm optimization method,
- Atangana-Baleanu derivative
Citation: Windarto, Muhammad Altaf Khan, Fatmawati. Parameter estimation and fractional derivatives of dengue transmission model[J]. AIMS Mathematics, 2020, 5(3): 2758-2779. doi: 10.3934/math.2020178

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Abstract

In this paper, we propose a parameter estimation of dengue fever transmission model using a particle swarm optimization method. This method is applied to estimate the parameters of the host-vector and SIR type dengue transmission models by using cumulative data of dengue patient in East Java province, Indonesia. Based on the parameter values, the basic reproduction number of both models are greater than one and obtained their value for SIR is $\mathcal{R}_0 = 1.4159$ and for vector host is $\mathcal{R}_0 = 1.1474$. We then formulate the models in fractional Atangana-Baleanu derivative that possess the property of nonlocal and nonsingular kernel that has been remained effective to many real-life problems. A numerical procedure for the solution of the model SIR model is shown. Some specific numerical values are considered to obtain the graphical results for both the SIR and Vector Host model. We show that the model vector host provide good results for data fitting than that of the SIR model.

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