Bounds on $R_0$ and final epidemic size when the next-generation matrix $M$ is only partially known
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912953758908416 |
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| author | Bizzotto, Andrea Ball, Frank Britton, Tom |
| author_facet | Bizzotto, Andrea Ball, Frank Britton, Tom |
| contents | We study a multitype SIR epidemic model where individuals are categorized into different types, and where infection spread is characterized by a next-generation matrix $M=\{m_{ij}\}$ with community fractions $\{π_j\}$ for the different types of individuals. We analyse two key quantities: the basic reproduction number $R_0$ and the final epidemic outcome of the different types $\{τ_i\}$. We consider the situation where $M$ is only partly known, through the row sums $\{r_i\}$ or the column sums $\{c_j\}$, and treat both a general $M$ and the special but common situation where $M$ is proportional to a contact matrix satisfying detailed balance. For a general $M$, which is partially observed through $\{r_i\}$ or $\{c_j\}$, we obtain sharp upper and lower bounds of $R_0$ and $\{τ_i\}$, but for the case where $M$ satisfies detailed balance the problem is harder: our obtained bounds for $R_0$ are narrower than the general case but still not sharp, and bounds for the final size are only obtained when there are two types of individual. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23885 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bounds on $R_0$ and final epidemic size when the next-generation matrix $M$ is only partially known Bizzotto, Andrea Ball, Frank Britton, Tom Populations and Evolution We study a multitype SIR epidemic model where individuals are categorized into different types, and where infection spread is characterized by a next-generation matrix $M=\{m_{ij}\}$ with community fractions $\{π_j\}$ for the different types of individuals. We analyse two key quantities: the basic reproduction number $R_0$ and the final epidemic outcome of the different types $\{τ_i\}$. We consider the situation where $M$ is only partly known, through the row sums $\{r_i\}$ or the column sums $\{c_j\}$, and treat both a general $M$ and the special but common situation where $M$ is proportional to a contact matrix satisfying detailed balance. For a general $M$, which is partially observed through $\{r_i\}$ or $\{c_j\}$, we obtain sharp upper and lower bounds of $R_0$ and $\{τ_i\}$, but for the case where $M$ satisfies detailed balance the problem is harder: our obtained bounds for $R_0$ are narrower than the general case but still not sharp, and bounds for the final size are only obtained when there are two types of individual. |
| title | Bounds on $R_0$ and final epidemic size when the next-generation matrix $M$ is only partially known |
| topic | Populations and Evolution |
| url | https://arxiv.org/abs/2602.23885 |