A multi-season epidemic model with random genetic drift and transmissibility
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916754830131200 |
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| author | Britton, Tom Pugliese, Andrea |
| author_facet | Britton, Tom Pugliese, Andrea |
| contents | We consider a model for an influenza-like disease, in which, between seasons, the virus makes a random genetic drift $δ$, (reducing immunity by the factor $δ$) and obtains a new random transmissibility $τ$ (closely related to $R_0$). Given the immunity status at the start of season $k$: $\textbf{p}^{(k)}$, describing community distribution of years since last infection, and their associated immunity levels $\boldsymbolι^{(k)}$, the outcome of the epidemic season $k$, characterized by the effective reproduction number $R_e^{(k)}$ and the fractions infected in the different immunity groups $\textbf{z}^{(k)}$, is determined by the random pair $(δ_k, τ_k)$. It is shown that the immunity status $(\textbf{p}^{(k)}, \boldsymbolι^{(k)})$, is an ergodic Markov chain, which converges to a stationary distribution $\bar π(\cdot) $. More analytical progress is made for the case where immunity only lasts for one season. We then characterize the stationary distribution of $p_1^{(k)}$, being identical to $z^{(k-1)}$. Further, we also characterize the stationary distribution of $(R_e^{(k)}, z^{(k)})$, and the conditional distribution of $z^{(k)}$ given $R_e^{(k)}$. The effective reproduction number $R_e^{(k)}$ is closely related to the initial exponential growth rate $ρ^{(k)}$ of the outbreak, a quantity which can be estimated early in the epidemic season. As a consequence, this conditional distribution may be used for predicting the final size of the epidemic based on its initial growth and immunity status. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A multi-season epidemic model with random genetic drift and transmissibility Britton, Tom Pugliese, Andrea Probability Populations and Evolution We consider a model for an influenza-like disease, in which, between seasons, the virus makes a random genetic drift $δ$, (reducing immunity by the factor $δ$) and obtains a new random transmissibility $τ$ (closely related to $R_0$). Given the immunity status at the start of season $k$: $\textbf{p}^{(k)}$, describing community distribution of years since last infection, and their associated immunity levels $\boldsymbolι^{(k)}$, the outcome of the epidemic season $k$, characterized by the effective reproduction number $R_e^{(k)}$ and the fractions infected in the different immunity groups $\textbf{z}^{(k)}$, is determined by the random pair $(δ_k, τ_k)$. It is shown that the immunity status $(\textbf{p}^{(k)}, \boldsymbolι^{(k)})$, is an ergodic Markov chain, which converges to a stationary distribution $\bar π(\cdot) $. More analytical progress is made for the case where immunity only lasts for one season. We then characterize the stationary distribution of $p_1^{(k)}$, being identical to $z^{(k-1)}$. Further, we also characterize the stationary distribution of $(R_e^{(k)}, z^{(k)})$, and the conditional distribution of $z^{(k)}$ given $R_e^{(k)}$. The effective reproduction number $R_e^{(k)}$ is closely related to the initial exponential growth rate $ρ^{(k)}$ of the outbreak, a quantity which can be estimated early in the epidemic season. As a consequence, this conditional distribution may be used for predicting the final size of the epidemic based on its initial growth and immunity status. |
| title | A multi-season epidemic model with random genetic drift and transmissibility |
| topic | Probability Populations and Evolution |
| url | https://arxiv.org/abs/2505.17933 |