Biomedical subjects

Roger G Bowers

Publications and source records attributed to Roger G Bowers.

11 recordsLinked to original sources

PubMed2006

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. The model is compared with stochastic simulations of epidemics on contact networks. The network framework is applied to the investigation of the epidemiological dynamics of between-herd transmission of Salmonella spp. The main results help to explain differences in observed epidemiological patterns and to identify possible causes for different strains of Salmonella developing so much variation in their infection dynamics in UK dairy herds. Numerical results show that shorter infectious period, more persistent immune response and more rapid removal of faeces result in a lower prevalence of infection and a greater tendency for (damped) oscillation. A possible control strategy is consequently suggested. Furthermore, the effect of network structure on long-term dynamics is examined.

Animals↗

PubMed2006

Pair-level approximations to the spatio-temporal dynamics of epidemics on asymmetric contact networks.

The process of infection during an epidemic can be envisaged as being transmitted via a network of routes represented by a contact network. Most differential equation models of epidemics are mean-field models. These contain none of the underlying spatial structure of the contact network. By extending the mean-field models to pair-level, some of the spatial structure can be contained in the model. Some networks of transmission such as river or transportation networks are clearly asymmetric, whereas others such as airborne infection can be regarded as symmetric. Pair-level models have been developed to describe symmetric contact networks. Here we report on work to develop a pair-level model that is also applicable to asymmetric contact networks. The procedure for closing the model at the level of pairs is discussed in detail. The model is compared against stochastic simulations of epidemics on asymmetric contact networks and against the predictions of the symmetric model on the same networks.

Communicable Diseases↗

PubMed2006

A semi-stochastic model of the transmission of Escherichia coli O157 in a typical UK dairy herd: dynamics, sensitivity analysis and intervention/prevention strategies.

When modelling the transmission of infection within small populations, it is necessary to consider the possibility of stochastic fade-out of infection. We present a semi-stochastic model for the transmission of a microparasite, in this case Escherichia coli O157, within a multigroup system, namely a typical UK dairy herd. The model includes birth, death, maturation, the dry/lactating cycle and various types of transmission (i.e. direct, pseudovertical (representing direct faecal-oral transmission between dam and calf within the first 48 h) and indirect (via free-living infectious units in the environment)). We present the results of our simulation study alongside data from empirical studies and also compare simulation results with those for the corresponding deterministic model. We then examine the effects of reducing shedding in the food-producing groups on outbreak size and prevalence of infection. A sensitivity analysis of herd prevalence reveals that, for both the deterministic and the semi-stochastic model, the prevalence within the herd is most sensitive to two parameters relating to the weaned group. This supports our previously reported conclusions for the deterministic model, which were based on an analysis of the next-generation matrix. The sensitivity analysis also indicates that herd prevalence is greatly affected by two other parameters relating to the lactating group. We conclude by discussing the possible efficacy of suggested intervention strategies.

Animals↗

PubMed2005

Adaptive dynamics of Lotka-Volterra systems with trade-offs: the role of interspecific parameter dependence in branching.

We determine the adaptive dynamics of a general Lotka-Volterra system containing an intraspecific parameter dependency--in the form of an explicit functional trade-off between evolving parameters--and interspecific parameter dependencies--arising from modelling species interactions. We develop expressions for the fitness of a mutant strategy in a multi-species resident environment, the position of the singular strategy in such systems and the non-mixed second-order partial derivatives of the mutant fitness. These expressions can be used to determine the evolutionary behaviour of the system. The type of behaviour expected depends on the curvature of the trade-off function and can be interpreted in a biologically intuitive manner using the rate of acceleration/deceleration of the costs implicit in the trade-off function. We show that for evolutionary branching to occur we require that one (or both) of the traded-off parameters includes an interspecific parameter dependency and that the trade-off function has weakly accelerating costs. This could have important implications for understanding the type of mechanisms that cause speciation. The general theory is motivated by using adaptive dynamics to examine evolution in a predator-prey system. The applicability of the general theory as a tool for examining specific systems is highlighted by calculating the evolutionary behaviour in a three species (prey-predator-predator) system.

Algorithms↗

PubMed2004

The geometric theory of adaptive evolution: trade-off and invasion plots.

The purpose of this paper is to take an entirely geometrical path to determine the evolutionary properties of ecological systems subject to trade-offs. In particular we classify evolutionary singularities in a geometrical fashion. To achieve this, we study trade-off and invasion plots (TIPs) which show graphically the outcome of evolution from the relationship between three curves. The first invasion boundary (curve) has one strain as resident and the other strain as putative invader and the second has the roles of the strains reversed. The parameter values for one strain are used as the origin with those of the second strain varying. The third curve represents the trade-off. All three curves pass through the origin or tip of the TIP. We show that at this point the invasion boundaries are tangential. At a singular TIP, in which the origin is an evolutionary singularity, the invasion boundaries and trade-off curve are all tangential. The curvature of the trade-off curve determines the region in which it enters the singular TIP. Each of these regions has particular evolutionary properties (EUS, CS, SPR and MI). Thus we determine by direct geometric argument conditions for each of these properties in terms of the relative curvatures of the trade-off curve and invasion boundaries. We show that these conditions are equivalent to the standard partial derivative conditions of adaptive dynamics. The significance of our results is that we can determine whether the singular strategy is an attractor, branching point, repellor, etc. simply by observing in which region the trade-off curve enters the singular TIP. In particular we find that, if and only if the TIP has a region of mutual invadability, is it possible for the singular strategy to be a branching point. We illustrate the theory with an example and point the way forward.

Adaptation, Physiological↗

PubMed2004

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. In particular, when the system is perturbed by higher culling or pathogen-induced mortality we incorporate mechanisms to constrain the lactating herd size to remain constant in the absence of pathogen or to lie within a fairly small interval in the presence of pathogen. A combination of numerical and analytical techniques is used to analyse the models. We find that the epidemiologically dominating management group can change from the dry/lactating cycle to the weaned group with increasing culling rate. Pseudovertical transmission is found to have little effect on the invasion criteria, while indirect transmission has significant influence. Pathogen-induced mortality, recovery, immune response and pathogen removal are found to be factors inducing damped oscillations; variation in these factors between Salmonella serotypes may be responsible for some of the observed differences in within herd dynamics. Specifically, higher pathogen-induced mortality, shorter infectious period, more persistent immune response and more rapid removal of faeces result in a lower number of infectives and smaller epidemics but a greater tendency for damped oscillations.

Animals↗

PubMed2004

The evolution of resistance through costly acquired immunity.

We examine the evolutionary dynamics of resistance to parasites through acquired immunity. Resistance can be achieved through the innate mechanisms of avoidance of infection and reduced pathogenicity once infected, through recovery from infection and through remaining immune to infection: acquired immunity. We assume that each of these mechanisms is costly to the host and find that the evolutionary dynamics of innate immunity in hosts that also have acquired immunity are quantitatively the same as in hosts that possess only innate immunity. However, compared with resistance through avoidance or recovery, there is less likely to be polymorphism in the length of acquired immunity within populations. Long-lived organisms that can recover at intermediate rates faced with fast-transmitting pathogens that cause intermediate pathogenicity (mortality of infected individuals) are most likely to evolve long-lived acquired immunity. Our work emphasizes that because whether or not acquired immunity is beneficial depends on the characteristics of the disease, organisms may be selected to only develop acquired immunity to some of the diseases that they encounter.

Biological Evolution↗

PubMed2003

Baseline criteria and the evolution of hosts and parasites: D0, R0 and competition for resources between strains.

Our understanding of the evolution of diseases has been greatly aided by the use of baseline criteria. Here we examine the theoretical and biological relationships of the well known baseline criteria for the evolution of disease (R0) and the recently introduced corresponding criterion for the evolution of resistance in hosts (D0). We show that there is a formal theoretical equivalence between the two criteria and discuss the characteristics of seperability that determine whether the criteria define the course of evolution. These theoretical determinants correspond biologically to whether strains compete for resources or not. We discuss the biological application of the criteria and argue that D0 may be less widely applicable than R0, but does determine the evolution of resistance in populations with fixed carrying capacities.

Animals↗

PubMed2003

A model appropriate to the transmission of a human food-borne pathogen in a multigroup managed herd.

We describe a model of microparasite transmission within a multigroup managed farming system. The model was formulated to represent transmission of Escherichia coli O157 within a typical UK dairy herd and was used to suggest possible on-farm control strategies. The model includes birth, death, maturation, the dry/lactating cycle and various types of transmission (i.e. direct, pseudovertical (representing direct faecal-oral transmission between dam and calf within the first 48 h) and indirect (via free-living infectious units in the environment)). A combination of numerical and analytical techniques was used to analyse the model. We found that pseudovertical transmission and indirect transmission via infectious units in the 'general' environment can lead to more groups being affected, but otherwise have relatively little effect on the invasion criteria. To reduce infection within the herd, we suggest that efforts be directed at reducing the opportunity for group-specific indirect transmission-particularly within the weaned group.

Animals↗

PubMed2003

Modelling pathogen transmission: the interrelationship between local and global approaches.

We describe two spatial (cellular automaton) host-pathogen models with contrasting types of transmission, where the biologically realistic transmission mechanisms are based entirely on 'local' interactions. The two models, fixed contact area (FCA) and fixed contact number (FCN), may be viewed as local 'equivalents' of commonly used global density- (and frequency-) dependent models. Their outputs are compared with each other and with the patterns generated by these global terms. In the FCN model, unoccupied cells are bypassed, but in the FCA model these impede pathogen spread, extending the period of the epidemic and reducing the prevalence of infection when the pathogen persists. Crucially, generalized linear modelling reveals that the global transmission terms betaSI and beta'SI/N are equally good at describing transmission in both the FCA and FCN models when infected individuals are homogeneously distributed and N is approximately constant, as at the quasi-equilibrium. However, when N varies, the global frequency-dependent term beta'SI/N is better than the density-dependent one, betaSI, at describing transmission in both the FCA and FCN models. Our approach may be used more generally to compare different local contact structures and select the most appropriate global transmission term.

Animals↗

PubMed2002

The adaptive dynamics of Lotka-Volterra systems with trade-offs.

We analyse the adaptive dynamics of a generalised type of Lotka-Volterra model subject to an explicit trade-off between two parameters. A simple expression for the fitness of a mutant strategy in an environment determined by the established, resident strategy is obtained leading to general results for the position of the evolutionary singular strategy and the associated second-order partial derivatives of the mutant fitness with respect to the mutant and resident strategies. Combinations of these results can be used to determine the evolutionary behaviour of the system. The theory is motivated by an example of prey evolution in a predator-prey system in which results show that only (non-EUS) evolutionary repellor dynamics, where evolution is directed away from a singular strategy, or dynamics where the singular strategy is an evolutionary attractor, are possible. Moreover, the general theory can be used to show that these results are the only possibility for all Lotka-Volterra systems in which aside from the trade-offs all parameters are independent and in which the interaction terms are of quadratic order or less. The applicability of the theory is highlighted by examining the evolution of an intermediate predator in a tri-trophic model.

Adaptation, Biological↗