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All Outputs (7)

The number of individuals alive in a branching process given only times of deaths (2025)
Journal Article
Ball, F., & Neal, P. (2025). The number of individuals alive in a branching process given only times of deaths. Advances in Applied Probability, 1-36. https://doi.org/10.1017/apr.2024.65

The study of many population growth models is complicated by only partial observation of the underlying stochastic process driving the model. For example, in an epidemic outbreak we might know when individuals show symptoms to a disease and are remov... Read More about The number of individuals alive in a branching process given only times of deaths.

The impact of household structure on disease-induced herd immunity (2023)
Journal Article
Ball, F., Critcher, L., Neal, P., & Sirl, D. (2023). The impact of household structure on disease-induced herd immunity. Journal of Mathematical Biology, 87(6), Article 83. https://doi.org/10.1007/s00285-023-02010-7

The disease-induced herd immunity level hD is the fraction of the population that must be infected by an epidemic to ensure that a new epidemic among the remaining susceptible population is not supercritical. For a homogeneously mixing population hD... Read More about The impact of household structure on disease-induced herd immunity.

Strong convergence of an epidemic model with mixing groups (2023)
Journal Article
Ball, F., & Neal, P. (2024). Strong convergence of an epidemic model with mixing groups. Advances in Applied Probability, 56(2), 430-463. https://doi.org/10.1017/apr.2023.29

We consider an SIR (susceptible → infective → recovered) epidemic in a closed population of size n, in which infection spreads via mixing events, comprising individuals chosen uniformly at random from the population, which occur at the points of a Po... Read More about Strong convergence of an epidemic model with mixing groups.

The size of a Markovian SIR epidemic given only removal data (2023)
Journal Article
Ball, F., & Neal, P. (2023). The size of a Markovian SIR epidemic given only removal data. Advances in Applied Probability, 55(3), 895-926. https://doi.org/10.1017/apr.2022.58

During an epidemic outbreak, typically only partial information about the outbreak is known. A common scenario is that the infection times of individuals are unknown, but individuals, on displaying symptoms, are identified as infectious and removed f... Read More about The size of a Markovian SIR epidemic given only removal data.

An epidemic model with short-lived mixing groups (2022)
Journal Article
Ball, F., & Neal, P. (2022). An epidemic model with short-lived mixing groups. Journal of Mathematical Biology, 85(6-7), Article 63. https://doi.org/10.1007/s00285-022-01822-3

Almost all epidemic models make the assumption that infection is driven by the interaction between pairs of individuals, one of whom is infectious and the other of whom is susceptible. However, in society individuals mix in groups of varying sizes, a... Read More about An epidemic model with short-lived mixing groups.

The asymptotic variance of the giant component of configuration model random graphs (2017)
Journal Article
Ball, F., & Neal, P. (2017). The asymptotic variance of the giant component of configuration model random graphs. Annals of Applied Probability, 27(2), https://doi.org/10.1214/16-AAP1225

For a supercritical configuration model random graph it is well known that, subject to mild conditions, there exists a unique giant component, whose size $R_n$ is $O (n)$, where $n$ is the total number of vertices in the random graph. Moreover, there... Read More about The asymptotic variance of the giant component of configuration model random graphs.