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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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| 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. |
| format | Article |
| id | doaj-art-4e866a2943694a65a5352b9d33bbfa15 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| 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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