Damian Clancy

Mathematical models of Neospora caninum infection in dairy cattle: transmission and options for control.

The transmission and control of Neospora caninum infection in dairy cattle was examined using deterministic and stochastic models. Parameter estimates were derived from recent studies conducted in the UK and from the published literature. Three routes of transmission were considered: maternal vertical transmission with a high probability (0.95), horizontal transmission from infected cattle within the herd, and horizontal transmission from an independent external source. Putative infection via pooled colostrum was used as an example of within-herd horizontal transmission, and the recent finding that the dog is a definitive host of N. caninum supported the inclusion of an external independent source of infection. The predicted amount of horizontal transmission required to maintain infection at levels commonly observed in field studies in the UK and elsewhere, was consistent with that observed in studies of post-natal seroconversion (0.85-9.0 per 100 cow-years). A stochastic version of the model was used to simulate the spread of infection in herds of 100 cattle, with a mean infection prevalence similar to that observed in UK studies (around 20%). The distributions of infected and uninfected cattle corresponded closely to Normal distributions, with S.D.s of 6.3 and 7.0, respectively. Control measures were considered by altering birth, death and horizontal transmission parameters. A policy of annual culling of infected cattle very rapidly reduced the prevalence of infection, and was shown to be the most effective method of control in the short term. Not breeding replacements from infected cattle was also effective in the short term, particularly in herds with a higher turnover of cattle. However, the long-term effectiveness of these measures depended on the amount and source of horizontal infection. If the level of within-herd transmission was above a critical threshold, then a combination of reducing within-herd, and blocking external sources of transmission was required to permanently eliminate infection.

The final size and severity of a generalised stochastic multitype epidemic model

We consider a stochastic model for the spread of an epidemic amongst a population split into m groups, in which infectives move among the groups and contact susceptibles at a rate which depends upon the infectives original group, its current group, and the group of the susceptible. The distributions of total size and total area under the trajectory of infectives for such epidemics are analysed. We derive exact results in terms of multivariate Gontcharoff polynomials by treating our model as a multitype collective Reed-Frost process and slightly adapting the results of Picard and Lefevre (1990). We also derive asymptotic results, as each of the group sizes becomes large, by generalising the method of Scalia-Tomba (1985), (1990)

Dose-response relationships for Foot and Mouth disease in cattle and sheep

The relationships between the inhaled dose of foot and mouth disease virus and the outcomes of infection and disease were examined by fitting dose-response models to experimental data. The parameters for both the exponential and beta-poisson models were estimated using maximum likelihood and Bayesian methods. The median probability of infection given a single inhaled TCID50 was estimated to be 0.031 with 95% Bayesian credibility intervals (CI) of 0.018-0.052 for cattle, and 0.045 (CI = 0.024-0.080) for sheep. These estimates were used to construct dose-response curves and uncertainty distributions for use in quantitative risk assessments.

A network model of E. coli O157 transmission within a typical UK dairy herd: the effect of heterogeneity and clustering on the prevalence of infection.

Cattle are considered to be the main reservoir for Vero cytotoxin-producing Escherichia coli (VTEC) O157, a cause of food-poisoning (and even death) in humans. Here, the transmission of E. coli O157 within a typical UK dairy herd is modelled using a semi-stochastic network model. The model incorporates demographic as well as infection processes. Indirect transmission is modelled homogeneously, while direct transmission is modelled via a dynamic contact network. The aim was to investigate the effects of heterogeneity and clustering on the prevalence of infection within the herd and discover whether, particularly in terms of choosing an intervention strategy, it is necessary to include heterogeneity in direct contacts when modelling this sort of system. Results show that heterogeneity in direct contacts can make it more difficult for the pathogen to persist, particularly when the average number of contacts (per animal) in each group is small. They also show that the relationship between clustering and prevalence is not simple. For example, increasing the average number of contacts can increase clustering and prevalence. However, when the average number of contacts in each group is sufficiently high, higher clustering leads to lower prevalence. It would seem that clustering can aid the flow of infection under certain circumstances, but hinder it under others (probably by preventing wider dissemination). Further results show that indirect transmission (as it is modelled here) effectively removes the effect of heterogeneity in direct contacts. In terms of investigating proposed interventions, the results suggest that a network model would only be required if there was evidence to suggest that direct transmission was the major source of infection.

Approximations for the Long-Term Behavior of an Open-Population Epidemic Model

A simple stochastic epidemic model incorporating births into the susceptible class is considered. An approximation is derived for the mean duration of the epidemic. It is proved that the epidemic ultimately dies out with probability 1. The limiting behavior of the epidemic conditional on non-extinction is studied using approximation methods. Two different diffusion approximations are described and compared.

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. We evaluate the evidence for alternative stable states in benthic coral-reef dynamics in the Caribbean, Kenya and Great Barrier Reef (GBR), using stochastic semi-parametric models based on large numbers of time series of cover of hard corals, macroalgae and other components. Only the GBR showed a consistent short-term regional decline in coral cover. There was no evidence for regional increases in macroalgae. The equilibrium distributions of our models were close to recently observed distributions, and differed among regions. In all three regions, the equilibrium distributions were unimodal rather than bimodal, and thus did not suggest the existence of alternative stable states on a regional scale, under current conditions.

Bayesian estimation of the basic reproduction number in stochastic epidemic models

In recent years there has been considerable activity in the development and application of Bayesian inferential methods for infectious disease data using stochastic epidemic models. Most of this activity has employed computationally intensive approaches such as Markov chain Monte Carlo methods. In contrast, here we address fundamental questions for Bayesian inference in the setting of the standard SIR (Susceptible-Infective-Removed) epidemic model via simple methods. Our main focus is on the basic reproduction number, a quantity of central importance in mathematical epidemic theory, whose value essentially dictates whether or not a large epidemic outbreak can occur. We specifically consider two SIR models routinely employed in the literature, namely the model with exponentially distributed infectious periods, and the model with fixed length infectious periods. It is assumed that an epidemic outbreak is observed through time. Given complete observation of the epidemic, we derive explicit expressions for the posterior densities of the model parameters and the basic reproduction number. For partial observation of the epidemic, when the entire infection process is unobserved, we derive conservative bounds for quantities such as the mean of the basic reproduction number and the probability that a major epidemic outbreak will occur. If the time at which the epidemic started is observed, then linear programming methods can be used to derive suitable bounds for the mean of the basic reproduction number and similar quantities. Numerical examples are used to illustrate the practical consequences of our findings. In addition, we also examine the implications of commonly-used prior distributions on the basic model parameters as regards inference for the basic reproduction number.

Bayesian methods for estimating pathogen prevalence within groups of animals from faecal-pat sampling

Pathogens such as Escherichia coli O157:H7 and Campylobacter spp. have been implicated in outbreaks of food poisoning in the UK and elsewhere. Domestic animals and wildlife are important reservoirs for both of these agents, and cross-contamination from faeces is believed to be responsible for many human outbreaks. Appropriate parameterisation of quantitative microbial-risk models requires representative data at all levels of the food chain. Our focus in this paper is on the early stages of the food chain-specifically, sampling issues which arise at the farm level. We estimated animal-pathogen prevalence from faecal-pat samples using a Bayesian method which reflected the uncertainties inherent in the animal-level prevalence estimates. (Note that prevalence here refers to the percentage of animals shedding the bacteria of interest). The method offers more flexibility than traditional, classical approaches: it allows the incorporation of prior belief, and permits the computation of a variety of distributional and numerical summaries, analogues of which often are not available through a classical framework. The Bayesian technique is illustrated with a number of examples reflecting the effects of a diversity of assumptions about the underlying processes. The technique appears to be both robust and flexible, and is useful when defecation rates in infected and uninfected groups are unequal, where population size is uncertain, and also where the microbiological-test sensitivity is imperfect. We also investigated the determination of the sample size necessary for determining animal-level prevalence from pat samples to within a pre-specified degree of accuracy.

An explicit optimal isolation policy for a deterministic epidemic model

Optimal policies involving the isolation of infectives are derived for a deterministic epidemic model with non-standard infection rate function. Denoting by y the number of infective individuals and x the number of susceptible individuals in the population, we replace the classical Kermack-McKendrick infection rate function @bxy (for some constant @b) with @bxy/(x+y). This modified model has been studied by various previous authors, but not in the context of control policies. We show that the optimal isolation policy is to intervene with maximal effort when y=

The final outcome of an epidemic model with several different types of infective in a large population

We consider a stochastic model for the spread of an epidemic amongst a closed homogeneously mixing population, in which there are several different types of infective, each newly infected individual choosing its type at random from those available. The model is based on the carrier-borne model of Downton (1968), as extended by Picard and Lefevre (1990). The asymptotic distributions of final size and area under the trajectory of infectives are derived as the initial population becomes large, using arguments based on those of Scalia-Tomba (1985), (1990). We then use our limiting results to compare the asymptotic final size distribution of our model with that of a related multi-group model, in which the type of each infective is assigned deterministically.