The impact of recovery rate heterogeneity in achieving herd immunity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909516038144000 |
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| author | Turinici, Gabriel |
| author_facet | Turinici, Gabriel |
| contents | Herd immunity is a critical concept in epidemiology, describing a threshold at which a sufficient proportion of a population is immune, either through infection or vaccination, thereby preventing sustained transmission of a pathogen. In the classic Susceptible-Infectious-Recovered (SIR) model, which has been widely used to study infectious disease dynamics, the achievement of herd immunity depends on key parameters, including the transmission rate ($β$) and the recovery rate ($γ$), where $γ$ represents the inverse of the mean infectious period. While the transmission rate has received substantial attention, recent studies have underscored the significant role of $γ$ in determining the timing and sustainability of herd immunity. Additionally, it is becoming increasingly evident that assuming $γ$ as a constant parameter might oversimplify the dynamics, as variations in recovery times can reflect diverse biological, social, and healthcare-related factors.
In this paper, we investigate how heterogeneity in the recovery rate affects herd immunity. We show empirically that the mean of the recovery rate is not a reliable metric for determining the achievement of herd immunity. Furthermore, we provide a theoretical result demonstrating that it is instead the mean recovery time, which is the mean of the inverse $1/γ$ of the recovery rate that is critical in deciding whether herd immunity is achievable within the SIR framework. A similar result is proved for the SEIR model. These insights have significant implications for public health interventions and theoretical modeling of epidemic dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_13130 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The impact of recovery rate heterogeneity in achieving herd immunity Turinici, Gabriel Populations and Evolution Dynamical Systems 92D30, 92C60, 92B05, 92D25 G.3; J.3; I.6.3; I.6.4; I.6.8 Herd immunity is a critical concept in epidemiology, describing a threshold at which a sufficient proportion of a population is immune, either through infection or vaccination, thereby preventing sustained transmission of a pathogen. In the classic Susceptible-Infectious-Recovered (SIR) model, which has been widely used to study infectious disease dynamics, the achievement of herd immunity depends on key parameters, including the transmission rate ($β$) and the recovery rate ($γ$), where $γ$ represents the inverse of the mean infectious period. While the transmission rate has received substantial attention, recent studies have underscored the significant role of $γ$ in determining the timing and sustainability of herd immunity. Additionally, it is becoming increasingly evident that assuming $γ$ as a constant parameter might oversimplify the dynamics, as variations in recovery times can reflect diverse biological, social, and healthcare-related factors. In this paper, we investigate how heterogeneity in the recovery rate affects herd immunity. We show empirically that the mean of the recovery rate is not a reliable metric for determining the achievement of herd immunity. Furthermore, we provide a theoretical result demonstrating that it is instead the mean recovery time, which is the mean of the inverse $1/γ$ of the recovery rate that is critical in deciding whether herd immunity is achievable within the SIR framework. A similar result is proved for the SEIR model. These insights have significant implications for public health interventions and theoretical modeling of epidemic dynamics. |
| title | The impact of recovery rate heterogeneity in achieving herd immunity |
| topic | Populations and Evolution Dynamical Systems 92D30, 92C60, 92B05, 92D25 G.3; J.3; I.6.3; I.6.4; I.6.8 |
| url | https://arxiv.org/abs/2411.13130 |