Research Repository

See what's under the surface


A stochastic SIR network epidemic model with preventive dropping of edges (2019)
Journal Article
Ball, F., Britton, T., Yin Leung, K., & Sirl, D. (in press). A stochastic SIR network epidemic model with preventive dropping of edges. Journal of Mathematical Biology,

A Markovian SIR (Susceptible – Infectious - Recovered) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours. An ef... Read More

Individual preventive social distancing during an epidemic may have negative population-level outcomes (2018)
Journal Article
Leung, K. Y., Ball, F., Sirl, D., & Britton, T. (2018). Individual preventive social distancing during an epidemic may have negative population-level outcomes. Interface, 15, doi:10.1098/rsif.2018.0296. ISSN 1742-5662

The outbreak of an infectious disease in a human population can lead to individuals responding with preventive measures in an attempt to avoid getting infected. This leads to changes in contact patterns. However, as we show in this paper, rational be... Read More

Susceptibility sets and the final outcome of collective Reed–Frost epidemics (2018)
Journal Article
Ball, F. (2018). Susceptibility sets and the final outcome of collective Reed–Frost epidemics. Methodology and Computing in Applied Probability, doi:10.1007/s11009-018-9631-6. ISSN 1387-5841

This paper is concerned with exact results for the final outcome of stochastic SIR (susceptible → infective → recovered) epidemics among a closed, finite and homogeneously mixing population. The factorial moments of the number of initial susceptibles... Read More

Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure (2017)
Journal Article
Ball, F., & Sirl, D. J. (2018). Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure. Journal of Mathematical Biology, 76(1/2), doi:10.1007/s00285-017-1139-0. ISSN 0303-6812

This paper is concerned with the analysis of vaccination strategies in a stochastic SIR (susceptible → infected → removed) model for the spread of an epidemic amongst a population of individuals with a random network of social contacts that is also p... Read More

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), doi:10.1214/16-AAP1225. ISSN 1050-5164

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

The relationships between message passing, pairwise, Kermack–McKendrick and stochastic SIR epidemic models (2017)
Journal Article
Wilkinson, R. R., Ball, F. G., & Sharkey, K. J. (in press). The relationships between message passing, pairwise, Kermack–McKendrick and stochastic SIR epidemic models. Journal of Mathematical Biology, doi:10.1007/s00285-017-1123-8. ISSN 0303-6812

We consider a very general stochastic model for an SIR epidemic on a network which allows an individual’s infectious period, and the time it takes to contact each of its neighbours after becoming infected, to be correlated. We write down the message... Read More

An epidemic in a dynamic population with importation of infectives (2017)
Journal Article
Ball, F., Britton, T., & Trapman, P. (2017). An epidemic in a dynamic population with importation of infectives. Annals of Applied Probability, 27(1), doi:10.1214/16-AAP1203. ISSN 1050-5164

Consider a large uniformly mixing dynamic population, which has constant birth rate and exponentially distributed lifetimes, with mean population size $n$. A Markovian SIR (susceptible $\to$ infective $\to$ recovered) infectious disease, having impo... Read More

Heterogeneous network epidemics: real-time growth, variance and extinction of infection (2017)
Journal Article
Ball, F., & House, T. (in press). Heterogeneous network epidemics: real-time growth, variance and extinction of infection. Journal of Mathematical Biology, doi:10.1007/s00285-016-1092-3. ISSN 0303-6812

Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular choice in... Read More

The deterministic Kermack-McKendrick model bounds the general stochastic epidemic (2016)
Journal Article
Wilkinson, R. R., Ball, F. G., & Sharkey, K. J. (in press). The deterministic Kermack-McKendrick model bounds the general stochastic epidemic. Journal of Applied Probability, 53(4), doi:10.1017/jpr.2016.62. ISSN 0021-9002

We prove that, for Poisson transmission and recovery processes, the classic Susceptible $\to$ Infected $\to$ Recovered (SIR) epidemic model of Kermack and McKendrick provides, for any given time $t>0$, a strict lower bound on the expected number of s... Read More

Inferring R0 in emerging epidemics: the effect of common population structure is small (2016)
Journal Article
Trapman, P., Ball, F., Dhersin, J., Tran, V. C., Wallinga, J., & Britton, T. (2016). Inferring R0 in emerging epidemics: the effect of common population structure is small. Interface, 13(121), doi:10.1098/rsif.2016.0288. ISSN 1742-5689

When controlling an emerging outbreak of an infectious disease, it is essential to know the key epidemiological parameters, such as the basic reproduction number R0 and the control effort required to prevent a large outbreak. These parameters are est... Read More

On expected durations of birth-death processes with applications to branching processes and SIS epidemics (2016)
Journal Article
Ball, F., Britton, T., & Neal, P. (2016). On expected durations of birth-death processes with applications to branching processes and SIS epidemics. Journal of Applied Probability, 53(1), doi:10.1017/jpr.2015.19. ISSN 0021-9002

We study continuous-time birth–death type processes, where individuals have independent and identically distributed lifetimes, according to a random variable Q, with E[Q] = 1, and where the birth rate if the population is currently in state (has size... Read More

Reproduction numbers for epidemic models with households and other social structures II: comparisons and implications for vaccination (2016)
Journal Article
Ball, F., Pellis, L., & Trapman, P. (2016). Reproduction numbers for epidemic models with households and other social structures II: comparisons and implications for vaccination. Mathematical Biosciences, 274, doi:10.1016/j.mbs.2016.01.006. ISSN 0025-5564

In this paper we consider epidemic models of directly transmissible SIR (susceptible - infective - recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting either of househo... Read More

Estimating the within-household infection rate in emerging SIR epidemics among a community of households (2015)
Journal Article
Ball, F., & Shaw, L. (in press). Estimating the within-household infection rate in emerging SIR epidemics among a community of households. Journal of Mathematical Biology, 71(6), doi:10.1007/s00285-015-0872-5. ISSN 0303-6812

This paper is concerned with estimation of the within household infection rate λL for a susceptible → infective → recovered epidemic among a population of households, from observation of the early, exponentially growing phase of an epidemic. Specific... Read More

Household epidemic models with varying infection response (2010)
Journal Article
Ball, F. G., Britton, T., & Sirl, D. J. (2011). Household epidemic models with varying infection response. Journal of Mathematical Biology, 63(2), 309-337

This paper is concerned with SIR (susceptible--infected--removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different mode... Read More

An SIR epidemic model on a population with random network and household structure and several types of individuals (2010)
Journal Article
Ball, F. G., & Sirl, D. J. An SIR epidemic model on a population with random network and household structure and several types of individuals. Manuscript submitted for publication

We consider a stochastic SIR (susceptible → infective → removed) epidemic model with several types of individuals. Infectious individuals can make infectious contacts on two levels, within their own ‘household’ and with their neighbours in a random g... Read More

Analysis of a stochastic SIR epidemic on a random network incorporating household structure (2010)
Journal Article
Ball, F. G., Sirl, D. J., & Trapman, P. (2010). Analysis of a stochastic SIR epidemic on a random network incorporating household structure. Mathematical Biosciences, 224(2), doi:10.1016/j.mbs.2009.12.003. ISSN 0025-5564

This paper is concerned with a stochastic SIR (susceptible-infective-removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour o... Read More

Threshold behaviour and final outcome of an epidemic on a random network with household structure (2009)
Journal Article
Ball, F. G., Sirl, D. J., & Trapman, P. (2009). Threshold behaviour and final outcome of an epidemic on a random network with household structure. Advances in Applied Probability, 41(3), ISSN 0001-8678

This paper considers a stochastic SIR (susceptible-infective-removed) epidemic model in which individuals may make infectious contacts in two ways, both within 'households' (which for ease of exposition are assumed to have equal size) and along the e... Read More