A Fractional-Order Model for Zika Virus Infection with Multiple Delays

Time delays and fractional order play a vital role in biological systems with memory. In this paper, we propose an epidemic model for Zika virus infection using delay differential equations with fractional order. Multiple time delays are incorporated in the model to consider the latency of the infec...

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Main Authors: R. Rakkiyappan, V. Preethi Latha, Fathalla A. Rihan
Format: Article
Language:English
Published: Wiley 2019-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2019/4178073
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author R. Rakkiyappan
V. Preethi Latha
Fathalla A. Rihan
author_facet R. Rakkiyappan
V. Preethi Latha
Fathalla A. Rihan
author_sort R. Rakkiyappan
collection DOAJ
description Time delays and fractional order play a vital role in biological systems with memory. In this paper, we propose an epidemic model for Zika virus infection using delay differential equations with fractional order. Multiple time delays are incorporated in the model to consider the latency of the infection in a vector and the latency of the infection in the infected host. We investigate the necessary and sufficient conditions for stability of the steady states and Hopf bifurcation with respect to three time delays τ1, τ2, and τ3. The model undergoes a Hopf bifurcation at the threshold parameters τ1∗, τ2∗, and τ3∗. Some numerical simulations are given to show the effectiveness of obtained results. The numerical simulations confirm that combination of fractional order and time delays in the epidemic model effectively enriches the dynamics and strengthens the stability condition of the model.
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institution Kabale University
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language English
publishDate 2019-01-01
publisher Wiley
record_format Article
series Complexity
spelling doaj-art-4e866a2943694a65a5352b9d33bbfa152025-08-20T03:26:25ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/41780734178073A Fractional-Order Model for Zika Virus Infection with Multiple DelaysR. Rakkiyappan0V. Preethi Latha1Fathalla A. Rihan2Department of Mathematics, Bharathiar University, Coimbatore-641 046, Tamil Nadu, IndiaDepartment of Mathematics, Bharathiar University, Coimbatore-641 046, Tamil Nadu, IndiaDepartment of Mathematical Sciences, College of Science, UAE University, Al Ain 15551, UAETime delays and fractional order play a vital role in biological systems with memory. In this paper, we propose an epidemic model for Zika virus infection using delay differential equations with fractional order. Multiple time delays are incorporated in the model to consider the latency of the infection in a vector and the latency of the infection in the infected host. We investigate the necessary and sufficient conditions for stability of the steady states and Hopf bifurcation with respect to three time delays τ1, τ2, and τ3. The model undergoes a Hopf bifurcation at the threshold parameters τ1∗, τ2∗, and τ3∗. Some numerical simulations are given to show the effectiveness of obtained results. The numerical simulations confirm that combination of fractional order and time delays in the epidemic model effectively enriches the dynamics and strengthens the stability condition of the model.http://dx.doi.org/10.1155/2019/4178073
spellingShingle R. Rakkiyappan
V. Preethi Latha
Fathalla A. Rihan
A Fractional-Order Model for Zika Virus Infection with Multiple Delays
Complexity
title A Fractional-Order Model for Zika Virus Infection with Multiple Delays
title_full A Fractional-Order Model for Zika Virus Infection with Multiple Delays
title_fullStr A Fractional-Order Model for Zika Virus Infection with Multiple Delays
title_full_unstemmed A Fractional-Order Model for Zika Virus Infection with Multiple Delays
title_short A Fractional-Order Model for Zika Virus Infection with Multiple Delays
title_sort fractional order model for zika virus infection with multiple delays
url http://dx.doi.org/10.1155/2019/4178073
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