The dynamics of Zika virus with Caputo fractional derivative

Muhammad Altaf Khan; Saif Ullah; Muhammad Farhan; Muhammad Altaf Khan; Saif Ullah; Muhammad Farhan

doi:10.3934/Math.2019.1.134

AIMS Mathematics

2019, Volume 4, Issue 1: 134-146. doi: 10.3934/Math.2019.1.134

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The dynamics of Zika virus with Caputo fractional derivative

1.
Department of mathematics, City university of Science and Information Technology, Peshawar, KP, Pakistan
2.
Department of mathematics, University of Peshawar, KP, Pakistan
3.
Department of mathematics, Abdul wali khan university, Mardan, KP, Pakistan

Received: 25 November 2018 Accepted: 11 February 2019 Published: 14 February 2019

In the present paper, we investigate a fractional model in Caputo sense to explore the dynamics of the Zika virus. The basic results of the fractional Zika model are presented. The local and global stability analysis of the proposed model is obtained when the basic reproduction reproduction number is less or greater than 1. To show the global stability of the fractional Zika model, we use the Lyapunov function theory in fractional environment. Further, we simulate the fractional Zika model to present the graphical results for different values of fractional order and model parameters.
- Zika virus model,
- stability analysis,
- generalized mean value theorem,
- Lyapunov function,
- Caputo derivative,
- numerical results
Citation: Muhammad Altaf Khan, Saif Ullah, Muhammad Farhan. The dynamics of Zika virus with Caputo fractional derivative[J]. AIMS Mathematics, 2019, 4(1): 134-146. doi: 10.3934/Math.2019.1.134

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Abstract

In the present paper, we investigate a fractional model in Caputo sense to explore the dynamics of the Zika virus. The basic results of the fractional Zika model are presented. The local and global stability analysis of the proposed model is obtained when the basic reproduction reproduction number is less or greater than 1. To show the global stability of the fractional Zika model, we use the Lyapunov function theory in fractional environment. Further, we simulate the fractional Zika model to present the graphical results for different values of fractional order and model parameters.

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