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A deterministic SAIR model with vaccination and treatment: dynamical behaviors and control strategies

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Abstract

In order to provide valuable information for the timely design and determination of public health measures during epidemic outbreaks, a deterministic SAIR model with vaccination programs and saturated treatment is established in this paper, as they have been demonstrated to be effective ways to change the evolution and prevent the spread of infectious diseases. The dynamical behaviors of the proposed model is analyzed theoretically and numerically. It is found that multiple endemic equilibria occur under certain conditions, suggesting that decreasing the basic reproduction number \(\mathcal {R}_0\) is insufficient for disease eradication and improving the efficiency of vaccination and treatment can have a significant impact on disease progression. Furthermore, sensitivity analysis is conducted to quantify how changes in concerned parameters impact \(\mathcal {R}_0\), and the proposed model is applied to the pandemic wave of COVID-19. Finally, optimal control problem with time-varying vaccination and treatment is studied and cost-effectiveness analysis is examined under different scenarios.

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Data Availability

All the data used to support the findings of this study are included in our manuscript and can be accessed freely from the references.

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Acknowledgements

This research was supported by National Natural Science Foundation of China (#62376212) and Scientific Research Program Project of Education Department of Shaanxi Province, China (#23JP114).

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  1. School of Sciences, Xi’an University of Technology, Jinhua South Road No. 5, Xi’an, 710048, Shaanxi, China

    Yun Ouyang, Suxia Zhang & Jinhu Xu

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  1. Yun Ouyang
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  2. Suxia Zhang
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  3. Jinhu Xu
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Correspondence to Suxia Zhang.

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Ouyang, Y., Zhang, S. & Xu, J. A deterministic SAIR model with vaccination and treatment: dynamical behaviors and control strategies. J. Appl. Math. Comput. 71, 573–604 (2025). https://doi.org/10.1007/s12190-024-02238-6

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