Influence of seasonality on <i>Zika virus</i> transmission

Miled El Hajji; Mohammed Faraj S. Aloufi; Mohammed H. Alharbi; Miled El Hajji; Mohammed Faraj S. Aloufi; Mohammed H. Alharbi

doi:10.3934/math.2024943

AIMS Mathematics

2024, Volume 9, Issue 7: 19361-19384. doi: 10.3934/math.2024943

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Influence of seasonality on Zika virus transmission

1.
Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
2.
ENIT-LAMSIN, BP. 37, 1002 Tunis-Belvédère, Tunis El Manar University, Tunisia

Received: 04 April 2024 Revised: 08 May 2024 Accepted: 28 May 2024 Published: 12 June 2024
MSC : 34C15, 34A34, 34C60, 37C75, 92D30

In order to study the impact of seasonality on Zika virus dynamics, we analyzed a non-autonomous mathematical model for the Zika virus (ZIKV) transmission where we considered time-dependent parameters. We proved that the system admitted a unique bounded positive solution and a global attractor set. The basic reproduction number, $ \mathcal{R}_0 $, was defined using the next generation matrix method for the case of fixed environment and as the spectral radius of a linear integral operator for the case of seasonal environment. We proved that if $ \mathcal{R}_0 $ was smaller than the unity, then a disease-free periodic solution was globally asymptotically stable, while if $ \mathcal{R}_0 $ was greater than the unity, then the disease persisted. We validated the theoretical findings using several numerical examples.
- Zika virus behavior,
- seasonality,
- global stability,
- uniform persistence
Citation: Miled El Hajji, Mohammed Faraj S. Aloufi, Mohammed H. Alharbi. Influence of seasonality on Zika virus transmission[J]. AIMS Mathematics, 2024, 9(7): 19361-19384. doi: 10.3934/math.2024943

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Abstract

In order to study the impact of seasonality on Zika virus dynamics, we analyzed a non-autonomous mathematical model for the Zika virus (ZIKV) transmission where we considered time-dependent parameters. We proved that the system admitted a unique bounded positive solution and a global attractor set. The basic reproduction number, $ \mathcal{R}_0 $, was defined using the next generation matrix method for the case of fixed environment and as the spectral radius of a linear integral operator for the case of seasonal environment. We proved that if $ \mathcal{R}_0 $ was smaller than the unity, then a disease-free periodic solution was globally asymptotically stable, while if $ \mathcal{R}_0 $ was greater than the unity, then the disease persisted. We validated the theoretical findings using several numerical examples.

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