arXiv subjects

Tom Britton

Publications and source records attributed to Tom Britton.

58 records · Page 4Linked to original sources

arXiv2009

The time to extinction for an SIS-household-epidemic model

We analyse a stochastic SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e., have no more infectives in the population. We study the effects of population size and within household transmission upon the time to extinction. This is done through two approximations. The first approximation is suitable for all levels of within household transmission and is based upon an Ornstein-Uhlenbeck process approximation for the diseases fluctuations about an endemic level relying on a large population. The second approximation is suitable for high levels of within household transmission and approximates the number of infectious households by a simple homogeneously mixing SIS model with the households replaced by individuals. The analysis, supported by a simulation study, shows that the mean time to extinction is minimized by moderate levels of within household transmission.

q-bio.PE↗

arXiv2008

Epidemic modelling: aspects where stochasticity matters

Epidemic models are always simplifications of real world epidemics. Which real world features to include, and which simplifications to make, depend both on the disease of interest and on the purpose of the modelling. In the present paper we discuss some such purposes for which a \emph{stochastic} model is preferable to a \emph{deterministic} counterpart. The two main examples illustrate the importance of allowing the infectious and latent periods to be random when focus lies on the \emph{probability} of a large epidemic outbreak and/or on the initial \emph{speed}, or growth rate, of the epidemic. A consequence of the latter is that estimation of the basic reproduction number $R_0$ is sensitive to assumptions about the distributions of the infectious and latent periods when using the data from the early stages of an outbreak, which we illustrate with data from the SARS outbreak. Some further examples are also discussed as are some practical consequences related to these stochastic aspects.

math.PR↗

arXiv2007

Epidemics on random graphs with tunable clustering

In this paper, a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large outbreak in the epidemic. It is investigated how these quantities varies with the clustering in the graph and it turns out for instance that, as the clustering increases, the epidemic threshold decreases. The network is modelled by a random intersection graph, in which individuals are independently members of a number of groups and two individuals are linked to each other if and only if they share at least one group.

math.PR↗

arXiv2007

Graphs with specified degree distributions, simple epidemics and local vaccination strategies

Consider a random graph, having a pre-specified degree distribution F but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose one individual in the community is externally infected by an infectious disease and that the disease has its course by assuming that infected individuals infect their not yet infected friends independently with probability p. For this situation the paper determines R_0 and tau_0, the basic reproduction number and the asymptotic final size in case of a major outbreak. Further, the paper looks at some different local vaccination strategies where individuals are chosen randomly and vaccinated, or friends of the selected individuals are vaccinated, prior to the introduction of the disease. For the studied vaccination strategies the paper determines R_v: the reproduction number, and tau_v: the asymptotic final proportion infected in case of a major outbreak, after vaccinating a fraction v.

math.PR↗