Biomedical subjects

C A Gilligan

Publications and source records attributed to C A Gilligan.

At least 19 recordsLinked to original sources

PubMed2007

Disease control and its selection for damaging plant virus strains in vegetatively propagated staple food crops; a theoretical assessment.

Viral diseases are a key constraint in the production of staple food crops in lesser developed countries. New and improved disease control methods are developed and implemented without consideration of the selective pressure they impose on the virus. In this paper, we analyse the evolution of within-plant virus titre as a response to the implementation of a range of disease control methods. We show that the development of new and improved disease control methods for viral diseases of vegetatively propagated staple food crops ought to take the evolutionary responses of the virus into consideration. Not doing so leads to a risk of failure, which can result in considerable economic losses and increased poverty. Specifically in vitro propagation, diagnostics and breeding methods carry a risk of failure due to the selection for virus strains that build up a high within-plant virus titre. For vegetatively propagated crops, sanitation by roguing has a low risk of failure owing to its combination of selecting for low virus titre strains as well as increasing healthy crop density.

Animals↗

PubMed2006

The role of initial inoculum on epidemic dynamics.

Transient dynamics are important in many epidemics in agricultural and ecological systems that are prone to regular disturbance, cyclical and random perturbations. Here, using a simple host-pathogen model for a sessile host and a pathogen that can move by diffusion and advection, we use a range of mathematical techniques to examine the effect of initial spatial distribution of inoculum of the pathogen on the transient dynamics of the epidemic. We consider an isolated patch and a group of patches with different boundary conditions. We first determine bounds on the host population for the full model, then non-dimensionalizing the model allows us to obtain approximate solutions for the system. We identify two biologically intuitive groups of parameters to analyse transient behaviour using perturbation techniques. The first parameter group is a measure of the relative strength of initial primary to secondary infection. The second group is derived from the ratio of host removal rate (via infection) to pathogen removal rate (by decay and natural mortality) and measures the infectivity of initial inoculum on the system. By restricting the model to mimic primary infection only (in which all infections arise from initial inoculum), we obtain exact solutions and demonstrate how these depend on initial conditions, boundary conditions and model parameters. Finally, we suggest that the analyses on the balance of primary and secondary infection provide the epidemiologist with some simple rules to predict the transient behaviours.

Animals↗

PubMed2005

Extinction of epidemics in lattice models with quenched disorder.

The extinction of the contact process for epidemics in lattice models with quenched disorder is analyzed in the limit of small density of infected sites. It is shown that the problem in such a regime can be mapped to the quantum-mechanical one characterized by the Anderson Hamiltonian for an electron in a random lattice. It is demonstrated both analytically (self-consistent mean field) and numerically (by direct diagonalization of the Hamiltonian and by means of cellular automata simulations) that disorder enhances the contact process, given the mean values of random parameters are not influenced by disorder.

Journal Article↗

PubMed2004

Controlling disease spread on networks with incomplete knowledge.

Models for control of highly infectious diseases on local, small-world, and scale-free networks are considered, with only partial information accessible about the status of individuals and their connections. We consider a case when individuals can be infectious before showing symptoms and thus before detection. For small to moderately severe incidence of infection with a small number of nonlocal links, it is possible to control disease spread by using purely local methods applied in a neighborhood centered around a detected infectious individual. There exists an optimal radius for such a control neighborhood leading to the lowest severity of the epidemic in terms of economic costs associated with disease and treatment. The efficiency of a local control strategy is very sensitive to the choice of the radius. Below the optimal radius, the local strategy is unsuccessful; the disease spreads throughout the system, necessitating treatment of the whole population. At the other extreme, a strategy involving a neighborhood that is too large controls the disease but is wasteful of resources. It is not possible to stop an epidemic on scale-free networks by preventive actions, unless a large proportion of the population is treated.

Journal Article↗

PubMed2004

Transmission rates and adaptive evolution of pathogens in sympatric heterogeneous plant populations.

Diversification in agricultural cropping patterns is widely practised to delay the build-up of virulent races that can overcome host resistance in pathogen populations. This can lead to balanced polymorphism, but the long-term consequences of this strategy for the evolution of crop pathogen populations are still unclear. The widespread occurrence of sibling species and reproductively isolated sub-species among fungal and oomycete plant pathogens suggests that evolutionary divergence is common. This paper develops a mathematical model of host-pathogen interactions using a simple framework of two hosts to analyse the influences of sympatric host heterogeneity on the long-term evolutionary behaviour of plant pathogens. Using adaptive dynamics, which assumes that sequential mutations induce small changes in pathogen fitness, we show that evolutionary outcomes strongly depend on the shape of the trade-off curve between pathogen transmission on sympatric hosts. In particular, we determine the conditions under which the evolutionary branching of a monomorphic into a dimorphic population occurs, as well as the conditions that lead to the evolution of specialist (single host range) or generalist (multiple host range) pathogen populations.

Adaptation, Physiological↗

PubMed2004

Bayesian analysis of botanical epidemics using stochastic compartmental models.

A stochastic model for an epidemic, incorporating susceptible, latent, and infectious states, is developed. The model represents primary and secondary infection rates and a time-varying host susceptibility with applications to a wide range of epidemiological systems. A Markov chain Monte Carlo algorithm is presented that allows the model to be fitted to experimental observations within a Bayesian framework. The approach allows the uncertainty in unobserved aspects of the process to be represented in the parameter posterior densities. The methods are applied to experimental observations of damping-off of radish (Raphanus sativus) caused by the fungal pathogen Rhizoctonia solani, in the presence and absence of the antagonistic fungus Trichoderma viride, a biological control agent that has previously been shown to affect the rate of primary infection by using a maximum-likelihood estimate for a simpler model with no allowance for a latent period. Using the Bayesian analysis, we are able to estimate the latent period from population data, even when there is uncertainty in discriminating infectious from latently infected individuals in data collection. We also show that the inference that T. viride can control primary, but not secondary, infection is robust to inclusion of the latent period in the model, although the absolute values of the parameters change. Some refinements and potential difficulties with the Bayesian approach in this context, when prior information on parameters is lacking, are discussed along with broader applications of the methods to a wide range of epidemiological systems.

Algorithms↗

PubMed2004

Inferring the dynamics of a spatial epidemic from time-series data.

Spatial interactions are key determinants in the dynamics of many epidemiological and ecological systems; therefore it is important to use spatio-temporal models to estimate essential parameters. However, spatially-explicit data sets are rarely available; moreover, fitting spatially-explicit models to such data can be technically demanding and computationally intensive. Thus non-spatial models are often used to estimate parameters from temporal data. We introduce a method for fitting models to temporal data in order to estimate parameters which characterise spatial epidemics. The method uses semi-spatial models and pair approximation to take explicit account of spatial clustering of disease without requiring spatial data. The approach is demonstrated for data from experiments with plant populations invaded by a common soilborne fungus, Rhizoctonia solani. Model inferences concerning the number of sources of disease and primary and secondary infections are tested against independent measures from spatio-temporal data. The applicability of the method to a wide range of host-pathogen systems is discussed.

Disease Outbreaks↗

PubMed2004

On 'Analytical models for the patchy spread of plant disease'.

Epidemiologists are interested in using models that incorporate the effects of clustering in the spatial pattern of disease on epidemic dynamics. Bolker (1999, Bull. Math. Biol. 61, 849-874) has developed an approach to study such models based on a moment closure assumption. We show that the assumption works above a threshold initial level of disease that depends on the spatial dispersal of the pathogen. We test an alternative assumption and show that it does not have this limitation. We examine the relation between lattice and continuous-medium implementations of the approach.

Disease Outbreaks↗

PubMed2003

Response of a deterministic epidemiological system to a stochastically varying environment.

Fluctuations in the natural environment introduce variability into the biological systems that exist within them. In this paper, we develop a model for the influence of random fluctuations in the environment on a simple epidemiological system. The model describes the infection of a dynamic host population by an environmentally sensitive pathogen and is based on the infection of sugar beet plants by the endoparasitic slime-mold vector Polymyxa betae. The infection process is switched on only when the temperature is above a critical value. We discuss some of the problems inherent in modeling such a system and analyze the resulting model by using asymptotic techniques to generate closed-form solutions for the mean and variance of the net amount of new inoculum produced within a season. In this way, the variance of temperature profile can be linked with that of the inoculum produced in a season and hence the risk of disease. We also examine the connection between the model developed in this paper and discrete Markov-chain models for weather.

Beta vulgaris↗

PubMed2003

Solution of epidemic models with quenched transients.

We consider a model for single-season disease epidemics, with a delay (latent period) in the onset of infectivity and a decay ("quenching") in host susceptibility described by time-varying rates of primary and secondary infections. The classical susceptible-exposed-infected (SEI) model of epidemiology is a special case with constant rates. The decaying rates force the epidemics to slow down, and eventually stop in a "quenched transient" state that depends on the full history of the epidemic including its initial state. This equilibrium state is neutrally stable (i.e., has zero-value eigenvalues), and cannot be studied using standard equilibrium analysis. We introduce a method that gives an approximate analytical solution for the quenched state. The method uses an interpolation between two exactly solvable limits and applies to the whole, five-dimensional parameter space of the model. Some applications of the solutions for analysis of epidemics are given.

Journal Article↗

PubMed2001

The effect of cultivation on the size, shape, and persistence of disease patches in fields.

Epidemics of soil-borne plant disease are characterized by patchiness because of restricted dispersal of inoculum. The density of inoculum within disease patches depends on a sequence comprising local amplification during the parasitic phase followed by dispersal of inoculum by cultivation during the intercrop period. The mechanisms that control size, shape, and persistence have received very little rigorous attention in epidemiological theory. Here we derive a model for dispersal of inoculum in soil by cultivation that takes account into the discrete stochastic nature of the system in time and space. Two parameters, probability of movement and mean dispersal distance, characterize lateral dispersal of inoculum by cultivation. The dispersal parameters are used in combination with the characteristic area and dimensions of host plants to identify criteria that control the shape and size of disease patches. We derive a critical value for the probability of movement for the formation of cross-shaped patches and show that this is independent of the amount of inoculum. We examine the interaction between local amplification of inoculum by parasitic activity and subsequent dilution by dispersal and identify criteria whereby asymptomatic patches may persist as inoculum falls below a threshold necessary for symptoms to appear in the subsequent crop. The model is motivated by the spread of rhizomania, an economically important soil-borne disease of sugar beet. However, the results have broad applicability to a very wide range of diseases that survive as discrete units of inoculum. The application of the model to patch dynamics of weed seeds and local introductions of genetically modified seeds is also discussed.

Agriculture↗

PubMed2000

Bubonic plague: a metapopulation model of a zoonosis.

Bubonic plague (Yersinia pestis) is generally thought of as a historical disease; however, it is still responsible for around 1000-3000 deaths each year worldwide. This paper expands the analysis of a model for bubonic plague that encompasses the disease dynamics in rat, flea and human populations. Some key variables of the deterministic model, including the force of infection to humans, are shown to be robust to changes in the basic parameters, although variation in the flea searching efficiency, and the movement rates of rats and fleas will be considered throughout the paper. The stochastic behaviour of the corresponding metapopulation model is discussed, with attention focused on the dynamics of rats and the force of infection at the local spatial scale. Short-lived local epidemics in rats govern the invasion of the disease and produce an irregular pattern of human cases similar to those observed. However, the endemic behaviour in a few rat subpopulations allows the disease to persist for many years. This spatial stochastic model is also used to identify the criteria for the spread to human populations in terms of the rat density. Finally, the full stochastic model is reduced to the form of a probabilistic cellular automaton, which allows the analysis of a large number of replicated epidemics in large populations. This simplified model enables us to analyse the spatial properties of rat epidemics and the effects of movement rates, and also to test whether the emergent metapopulation behaviour is a property of the local dynamics rather than the precise details of the model.

Animals↗

PubMed2000

Metapopulation dynamics of bubonic plague.

Bubonic plague is widely regarded as a disease of mainly historical importance; however, with increasing reports of incidence and the discovery of antibiotic-resistant strains of the plague bacterium Yersinia pestis, it is re-emerging as a significant health concerns. Here we bypass the conventional human-disease models, and propose that bubonic plague is driven by the dynamics of the disease in the rat population. Using a stochastic, spatial metapopulation model, we show that bubonic plague can persist in relatively small rodent populations from which occasional human epidemics arise, without the need for external imports. This explains why historically the plague persisted despite long disease-free periods, and how the disease re-occurred in cities with tight quarantine control. In a contemporary setting, we show that human vaccination cannot eradicate the plague, and that culling of rats may prevent or exacerbate human epidemics, depending on the timing of the cull. The existence of plague reservoirs in wild rodent populations has important public-health implications for the transmission to urban rats and the subsequent risk of human outbreaks.

Animals↗

PubMed2000

Quantitative analysis and model simplification of an epidemic model with primary and secondary infection.

Models of particular epidemiological systems can rapidly become complicated by biological detail which can obscure their essential features and behaviour. In general, we wish to retain only those components and processes that contribute to the dynamics of the system. In this paper, we apply asymptotic techniques to an SEI-type model with primary and secondary infection in order to reduce it to a much simpler form. This allows the identification of parameter groupings discriminating between regions of contrasting dynamics and leads to simple approximations for the model's transient behaviour. These can be used to follow the evolution of the developing infection process. The techniques examined in this paper will be applicable to a large number of similar models.

Chenopodiaceae↗

PubMed2000

Population dynamics of plant-parasite interactions: thresholds for invasion.

Thresholds are derived for the invasion of plant populations by parasites. The theory is developed for a generic model that takes into account two features characteristic of plant-parasite interactions: a dual source of inoculum (infection from primary or externally introduced inoculum and secondary infection from contact between susceptible and infected host tissue) and a host response to infection load. Each of the threshold criteria is shown to be the sum of the individual components for primary and secondary infection. This indicates that if parasite invasion is not possible through primary or secondary infection alone, when the two modes of transmission are combined, the parasite may be able to invade. The invasion criteria demonstrate that there is a threshold population of susceptible hosts below which the parasite is unable to invade. If there are nonlinearities in the population dynamics (arising through either the transmission process or the host response), there are also threshold densities for the infected hosts and parasite populations below which invasion does not occur. The implications of the results for the control of plant disease are discussed.

Animals↗

PubMed1999

Design of an intravaginal ring for the controlled delivery of 17 beta-estradiol as its 3-acetate ester.

Suitable ester prodrugs of 17beta-estradiol are identified, thus permitting effective sustained and controlled estrogen replacement therapy (ERT) from an elastomeric, silicone intravaginal ring (IVR). IVR devices of reservoir design were prepared by blending silicone elastomer base with n-propylorthosilicate (cross-linker) and 10% w/w of 17beta-estradiol or an ester prodrug, the mix being activated with 0.5% w/w stannous octoate and cured at 80 degrees C for 2 min. A rate-controlling membrane was similarly prepared, without the active agent. IVR devices were of cross-sectional diameter 9 mm, outer diameter 54 mm, with core cross-sectional diameter of 2 mm and core length varied as required. Sink conditions were evident for the 17beta-estradiol esters in 1.0% aqueous benzalkonium chloride solution. The low release rates into 0.9% w/v saline of the lipophilic valerate and benzoate esters were due to their intrinsically low aqueous solubilities. In vivo, these esters failed to raise plasma estradiol above baseline levels in postmenopausal human volunteers, despite good in vitro release characteristics under sink conditions. The best release rates under sink conditions, in combination with substantial aqueous solubilities as indicated by the release rates into saline, were observed for the acetate and propionate esters. A combination of drug release characteristics, short plasma half-life and a toxicologically acceptable hydrolysis product indicated that 17beta-estradiol-3-acetate was the prodrug of choice for IVR delivery of ERT. In vivo, an IVR device releasing 100 microg/day of estradiol as its 3-acetate ester maintained over 84 days a circulating plasma concentration in the region of 300 pmoll(-1), within the clinically desirable range for ERT.

Administration, Intravaginal↗

PubMed1999

Predicting variability in biological control of a plant-pathogen system using stochastic models.

A stochastic model for the dynamics of a plant-pathogen interaction is developed and fitted to observations of the fungal pathogen Rhizoctonia solani (Kühn) in radish (Raphanus sativus L.), in both the presence and absence of the antagonistic fungus Trichoderma viride (Pers ex Gray). The model incorporates parameters for primary and secondary infection mechanisms and for characterizing the time-varying susceptibility of the host population. A parameter likelihood is developed and used to fit the model to data from microcosm experiments. It is shown that the stochastic model accounts well for observed variability both within and between treatments. Moreover, it enables us to describe the time evolution of the probability distribution for the variability among replicate epidemics in terms of the underlying epidemiological parameters for primary and secondary infection and decay in susceptibility. Consideration of profile likelihoods for each parameter provides strong evidence that T. viride mainly affects primary infection. By using the stochastic model to study the dependence of the probability distribution of disease levels on the primary infection rate we are therefore able to predict the effectiveness of a widely used biological control agent.

Models, Biological↗

PubMed1999

Candida albicans hyphal invasion: thigmotropism or chemotropism?

Hyphae of the human pathogenic fungus Candida albicans exhibit thigmotropic behaviour in vitro, in common with phytopathogenic and saprotrophic fungi. An examination of the literature on C. albicans hyphal penetration of epithelial and endothelial membranes does not support the premise that hyphal thigmotropism plays a major role in tissue invasion. Further experimentation is now required to assess thigmotropic behaviour on host membranes and vaginal epithelial cells are suggested as a test model. It is proposed that while thigmotropism may and invasion of tissue invaginations, chemotropism can explain C. albicans hyphal invasion patterns of both endothelium and epithelium.

Candida albicans↗