Extinction in host-vector infection models and the role of heterogeneity.

For infections that become endemic in a population, the process may appear stable over a long time scale, but stochastic fluctuations can lead to eventual disease extinction. We consider the effects of model parameters and of population heterogeneities upon the expected time to extinction for host-vector disease systems. We find that non-homogeneous host selection by vectors increases persistence times relative to the homogeneous case, and that the effect becomes even more marked when there are strong associations between particular groups of vectors and hosts.

Precise Estimates of Persistence Time for SIS Infections in Heterogeneous Populations.

For a susceptible-infectious-susceptible infection model in a heterogeneous population, we derive simple and precise estimates of mean persistence time, from a quasi-stationary endemic state to extinction of infection. Heterogeneity may be in either individuals' levels of infectiousness or of susceptibility, as well as in individuals' infectious period distributions. Infectious periods are allowed to follow arbitrary non-negative distributions.

Persistence time of SIS infections in heterogeneous populations and networks.

For a susceptible-infectious-susceptible infection model in a heterogeneous population, we present simple formulae giving the leading-order asymptotic (large population) behaviour of the mean persistence time, from an endemic state to extinction of infection. Our model may be interpreted as describing an infection spreading through either (1) a population with heterogeneity in individuals' susceptibility and/or infectiousness; or (2) a heterogeneous directed network. Using our asymptotic formulae, we show that such heterogeneity can only reduce (to leading order) the mean persistence time compared to a corresponding homogeneous population, and that the greater the degree of heterogeneity, the more quickly infection will die out.

Among-site variability in the stochastic dynamics of East African coral reefs.

Coral reefs are dynamic systems whose composition is highly influenced by unpredictable biotic and abiotic factors. Understanding the spatial scale at which long-term predictions of reef composition can be made will be crucial for guiding conservation efforts. Using a 22-year time series of benthic composition data from 20 reefs on the Kenyan and Tanzanian coast, we developed Bayesian vector autoregressive state-space models for reef dynamics, incorporating among-site variability, and quantified their long-term behaviour.

Generality of endemic prevalence formulae.

In simple infection models, the susceptible proportion s(*) in endemic equilibrium is related to the basic reproduction number R0 by s(*)=1/R0. We investigate the extent to which this relationship remains valid under more realistic modelling assumptions. In particular, we relax the biologically implausible assumptions that individuals' lifetimes and infectious periods follow exponential distributions; allow a general recruitment process; allow for multiple stages of infection; and consider extension to a multigroup model in which the groups may represent, for instance, spatial heterogeneity, or the existence of super-spreaders.

Effectiveness of simulated interventions in reducing the estimated prevalence of Salmonella in UK pig herds.

Salmonella spp are a major foodborne zoonotic cause of human illness. Consumption of pork products is believed to be a major source of human salmonellosis and Salmonella control throughout the food-chain is recommended. A number of on-farm interventions have been proposed, and some have been implemented in order to try to achieve Salmonella control.

Semi-stochastic models for Salmonella infection within finishing pig units in the UK.

A multi-group semi-stochastic model is formulated to describe Salmonella dynamics on a pig herd within the UK and assess whether farm structure has any effect on the dynamics. The models include both direct transmission and indirect (via free-living infectious units in the environment and airborne infection). The basic reproduction number R0 is also investigated.

The effect of population heterogeneities upon spread of infection.

It has often been observed that population heterogeneities can lead to outbreaks of infection being less frequent and less severe than homogeneous population models would suggest. We address this issue by comparing a model incorporating various forms of heterogeneity with a homogenised model matched according to the value of the basic reproduction number [Formula: see text]. We mainly focus upon heterogeneity in individuals' infectivity and susceptibility, though with some allowance also for heterogeneous patterns of mixing.

Data-driven models for regional coral-reef dynamics.

Coral reefs have been affected by natural and anthropogenic disturbances. Coral cover has declined on many reefs, and macroalgae have increased on some. The existence of alternative stable states with high or low coral cover has been widely debated, but not clearly established.

The effect of waning immunity on long-term behaviour of stochastic models for the spread of infection.

In stochastic modelling of infectious spread, it is often assumed that infection confers permanent immunity, a susceptible-infective-removed (SIR) model. We show how results concerning long-term (endemic) behaviour may be extended to a susceptible-infective-removed-susceptible (SIRS) model, in which immunity is temporary. Since the full SIRS model with demography is rather intractable, we also consider two simpler models: the susceptible-infective-susceptible (SIS) model with demography, in which there is no immunity; and the SIRS model in a closed population.

Quantifying exposure to vero-cytotoxigenic Escherichia coli O157 in milk sold as pasteurized: a model-based approach.

Milk sold as pasteurized has historically been implicated in the UK and worldwide as a vehicle for outbreaks of food-borne gastrointestinal disease, with a number of causative pathogenic organisms. One such organism is verocytotoxigenic Escherichia coli, or E. coli, O157 (VTEC O157).

Dynamics of infection with multiple transmission mechanisms in unmanaged/managed animal populations.

Deterministic and stochastic models motivated by Salmonella transmission in unmanaged/managed populations are studied. The SIRS models incorporate three routes of transmission (direct, vertical and indirect via free-living infectious units in the environment). With deterministic models we are able to understand the effects of different routes of transmission and other epidemiological factors on infection dynamics.

Optimal intervention for an epidemic model under parameter uncertainty.

We will be concerned with optimal intervention policies for a continuous-time stochastic SIR (susceptible-->infective-->removed) model for the spread of infection through a closed population. In previous work on such optimal policies, it is common to assume that model parameter values are known; in reality, uncertainty over parameter values exists. We shall consider the effect upon the optimal policy of changes in parameter estimates, and of explicitly taking into account parameter uncertainty via a Bayesian decision-theoretic framework.

Pair approximations and the inclusion of indirect transmission: theory and application to between farm transmission of Salmonella.

The spatial-temporal dynamics of farm animal diseases depend both on disease specific processes and the underlying contact network between farms. Indirect transmission via free-living bacteria in the environment is an important transmission route and contributes significantly to the dynamics. The pair-wise model has been developed to include both direct transmission and indirect transmission via free stages.

Understanding the dynamics of Salmonella infections in dairy herds: a modelling approach.

There is evidence of variation in the infection dynamics of different Salmonella serotypes in cattle--ranging from transient epidemics to long term persistence and recurrence. We seek to identify possible causes of these differences. In this study we present mathematical models which describe both managed population dynamics and epidemiology and use these to investigate the effects of demographic and epidemiological factors on epidemic behaviour and threshold for invasion.