The impact of ambient air pollution on an influenza model with partial immunity and vaccination

Xiaomeng Wang; Xue Wang; Xinzhu Guan; Yun Xu; Kangwei Xu; Qiang Gao; Rong Cai; Yongli Cai; Xiaomeng Wang; Xue Wang; Xinzhu Guan; Yun Xu; Kangwei Xu; Qiang Gao; Rong Cai; Yongli Cai

doi:10.3934/mbe.2023451

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 10284-10303. doi: 10.3934/mbe.2023451

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Research article

The impact of ambient air pollution on an influenza model with partial immunity and vaccination

1.
School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, China
2.
Department of Acute Infectious Disease Control and Prevention, Huaian Center for Disease Control and Prevention, Huaian 223003, China
3.
Department of Disinfection and Vector Borne Disease Control, Huaian Center for Disease Control and Prevention, Huaian 223003, China

Academic Editor: Jia Li

Received: 26 January 2023 Revised: 28 February 2023 Accepted: 08 March 2023 Published: 31 March 2023

In this paper, we investigate the effects of ambient air pollution (AAP) on the spread of influenza in an AAP-dependent dynamic influenza model. The value of this study lies in two aspects. Mathematically, we establish the threshold dynamics in the term of the basic reproduction number $ \mathcal{R}_0 $: If $ \mathcal{R}_0 < 1 $, the disease will go to extinction, while if $ \mathcal{R}_0 > 1 $, the disease will persist. Epidemiologically, based on the statistical data in Huaian, China, we find that, in order to control the prevalence of influenza, we must increase the vaccination rate, the recovery rate and the depletion rate, and decrease the rate of the vaccine wearing off, the uptake coefficient, the effect coefficient of AAP on transmission rate and the baseline rate. To put it simply, we must change our traveling plan and stay at home to reduce the contact rate or increase the close-contact distance and wear protective masks to reduce the influence of the AAP on the influenza transmission.
- ambient air pollution,
- influenza model,
- partial Immunity,
- vaccination,
- basic reproduction number,
- control
Citation: Xiaomeng Wang, Xue Wang, Xinzhu Guan, Yun Xu, Kangwei Xu, Qiang Gao, Rong Cai, Yongli Cai. The impact of ambient air pollution on an influenza model with partial immunity and vaccination[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 10284-10303. doi: 10.3934/mbe.2023451

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Abstract

In this paper, we investigate the effects of ambient air pollution (AAP) on the spread of influenza in an AAP-dependent dynamic influenza model. The value of this study lies in two aspects. Mathematically, we establish the threshold dynamics in the term of the basic reproduction number $ \mathcal{R}_0 $: If $ \mathcal{R}_0 < 1 $, the disease will go to extinction, while if $ \mathcal{R}_0 > 1 $, the disease will persist. Epidemiologically, based on the statistical data in Huaian, China, we find that, in order to control the prevalence of influenza, we must increase the vaccination rate, the recovery rate and the depletion rate, and decrease the rate of the vaccine wearing off, the uptake coefficient, the effect coefficient of AAP on transmission rate and the baseline rate. To put it simply, we must change our traveling plan and stay at home to reduce the contact rate or increase the close-contact distance and wear protective masks to reduce the influence of the AAP on the influenza transmission.

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