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Biomedical subjects

M G Roberts

Publications and source records attributed to M G Roberts.

At least 37 records · Page 2Linked to original sources
PubMed1996

An SEI model with density-dependent demographics and epidemiology.

Two compartmental models for the dynamics of an infectious disease in a wild-animal population are analysed. The models feature density-dependent birth, death, and contact rates, and pseudovertical disease transmission. For the SI model it is shown that up to four steady states may exist, depending on the parameter values, and that one of these states is globally stable. For the SEI model four equivalent steady states exist, but periodic solutions are now possible for some parameter values.

Animals↗
PubMed1995

Threshold quantities for helminth infections.

For parasites with a clearly defined life-cycle we give threshold quantities that determine the stability of the parasite-free steady state for autonomous and periodic deterministic systems formulated in terms of mean parasite burdens. We discuss the biological interpretations of the quantities, how to deal with heterogeneity in both parasite and host populations, how to incorporate the effects of periodic discontinuities, and the relation of the threshold quantities to the basic reproduction ratio Ro. Examples from the literature are given. The analysis of the periodic case extends easily to 'micro-parasitic' systems.

Animals↗
PubMed1995

The population dynamics of communities of parasitic helminths.

This paper considers the dynamics of a host (animal) species that would grow exponentially in the absence of parasitism, and a community of parasite species that may regulate this growth. The model consists of a single differential equation for the host and one for each of the parasite species. This level of simplicity is achieved by assuming that each parasite species has a negative binomial distribution within the host population, with either zero covariance between the species (exploitation competition), or a specified covariance structure (interference competition). Conditions on the model parameters that determine the abundance of the different species are formulated, as are conditions that determine when a parasite species can invade a community and when a species is likely to be squeezed out. The results show that highly aggregated parasite species are more likely to coexist, but are less able to regulate their host population. A negative correlation between the distributions of the parasite species enhances both their ability to coexist and their ability to regulate the host population. The results of this analysis apply more generally to other systems where communities of exploiter species coexist on discretely distributed hosts, for example, insects on plants.

Animals↗
PubMed1995

A pocket guide to host-parasite models.

Mathematical models have been used to describe the population dynamics of a wide range of host-parasite interactions. Mick Roberts here discusses mathematical models for the dynamics of helminth endoparasites of non-human mammalian hosts, paying particular attention to the density-dependent factors that regulate the parasite populations, and the interaction between parasite and wild or feral animal host populations.

Journal Article↗
PubMed1995

A model for the control of Echinococcus multilocularis in France.

In some areas of France the prevalence of Echinococcus multilocularis in foxes is as high as 50%, whereas less than one in a thousand voles (principally Microtus arvalis) are infected. In these regions the control of rabies in foxes is achieved by using helicopters to spread bait containing oral vaccine in capsules. A mathematical model has been constructed in an attempt to determine if the addition of praziquantel to bait would be effective in eradicating E. multilocularis, or at least achieve a useful measure of control. It has been shown that the qualitative population dynamics of E. multilocularis are not affected by the detail of its epidemiology in the intermediate host population. The model is, however, sensitive to assumptions about the distribution and longevity of the adult worm in the definitive host. Given these assumptions, a method is provided that determines the feasibility of eradication conditional on the pre-control prevalence in foxes, or predicts the post-control prevalence if eradication is not feasible. If experiments could be designed to provide better information about the biological factors that determine the epidemiology of this parasite in the definitive host, a more reliable assessment of the feasibility of control would be achieved.

Animals↗
PubMed1995

The dynamics of nematode infections of farmed ruminants.

In this paper the dynamics and control of nematode parasites of farmed ruminants are discussed via a qualitative analysis of a differential equation model. To achieve this a quantity, 'the basic reproduction quotient' (Q0), whose definition coincides with previous definitions of R0 for macroparasites, but extends to models with periodic time-varying transition rates between parasite stages or management interventions, is introduced. This quantity has the usual threshold property: if Q0 is less than one the parasite population cannot maintain itself in the host population, and in the long term becomes extinct; but if Q0 is greater than one the parasite can invade the host population. An alternative quantity, R(E), that is often easier to calculate is also introduced, and shown to have the same threshold property. The use of these two quantities in analysing models for the dynamics of nematodes in complex situations is then demonstrated, with reference to the dynamics of mixed parasite species in one host; the effects of breeding host animals for resistance to parasitism; and the development of parasite strains that are resistant to chemotherapy. Five examples are discussed using parameters for the dynamics of nematode infections in sheep, and some statements on control policies are derived.

Animals↗
PubMed1994

Modelling of parasitic populations: cestodes.

The philosophy of mathematical modelling as it applies to the epidemiology of cestode populations is reviewed. A model provides, via the "threshold theorem", a criterion for deciding in advance if a control programme can succeed in eradicating the parasite. In order to use this criterion it is necessary to have an estimate of the basic reproduction ratio, R0, which can only be obtained if reliable epidemiological data are available before the control programme is started. A model has been used to describe the population dynamics of Echinococcus granulosus, Taenia hydatigena and Taenia ovis in sheep and dogs in New Zealand. For these parasites, data from a 40-year longitudinal study, as well as short-term field and laboratory studies, were available. A model has also been used to evaluate a proposed control programme directed against Echinococcus multilocularis in foxes and voles in France. Here the type and extent of control intervention is predetermined by the existing rabies control programme. These two examples, which demonstrate the different techniques required to model cestodes in domestic and wild-animal populations, are reviewed, and the use of a model as the basis for a benefit/cost analysis of control options is discussed. These techniques could, in principal, be used to design control programmes for Taenia saginata or Taenia solium in humans.

Animals↗
PubMed1994

The regulation of an age-structured population by a fatal disease.

A model describing the effect of a fatal disease on an age-structured population which would otherwise grow is presented and analysed. If the disease is capable of regulating host numbers, there is an endemic steady age distribution (SAD), for which an analytic expression is obtained under some simplifying assumptions. The ability of the disease to regulate the population depends on a parameter R(alpha), which is defined in terms of the given age-dependent birth and death rates, and where alpha is the age-dependent disease-induced death rate. If R(alpha) < 1 the endemic SAD is attained, while R(alpha) > 1 means the disease cannot control the population's size. The number R(0) is the expected number of offspring produced by each individual in the absence of the disease; for a growing population we require R(0) > 1. A stability analysis is also performed and it is conjectured that the endemic SAD is locally asymptotically stable whenever it is attained. This is demonstrated explicitly for a very simple example where all rates are taken as constant.

Age Factors↗
PubMed1993

Thresholds and stability analysis of models for the spatial spread of a fatal disease.

A simple two-class (susceptibles and infectives) model describing the dynamics of a fatal disease in a variable-size population is presented and analysed. Spatial dependence is introduced into the model by considering two different mechanisms for the geographic spread of the disease: nonlocal interaction between susceptibles and infectives, and migratory spread of the animals. The steady states and their stability for these spatially dependent models are deduced; no spatially heterogeneous steady states were possible. For nonlocal interaction, there were two spatially uniform steady states: the trivial state (no infectives or susceptibles), which was unstable, and the endemic state (constant proportion of the population infected), which was locally asymptotically stable. With migratory spread, the number of spatially uniform steady states was dependent on the boundary conditions imposed. With hostile (Dirichlet) boundary conditions, only the trivial steady state was possible and its local stability found to depend on the rate of diffusion of the total population. With no-flux (Neumann) boundary conditions, the steady states are the trivial and endemic states; these were unstable and locally asymptotically stable, respectively.

Animals↗
PubMed1992

The dynamics and control of bovine tuberculosis in possums.

A model for the dynamics of an infectious disease in a wild animal population is analysed. The model incorporates susceptible, infected but not infectious, and infectious classes, with no recovery from disease, density-dependent regulation of host birth and death rates, and pseudo-vertical transmission. The existence and local stability of equilibrium levels are determined. Expressions for the intensity of three alternative control measures - the culling, sterilization, and vaccination of host animals - required to eradicate the disease are obtained. Finally, the model is applied to possible control measures against bovine tuberculosis infection in possums in New Zealand.

Animals↗
PubMed1992

The population dynamics of nematode infections of ruminants: the effect of seasonality in the free-living stages.

A previously published differential equation model for the dynamics of nematode infections of ruminants is modified to allow for time-dependent development and loss rates in the free-living stages. This converts the nonlinear autonomous system to one with periodic coefficients. Fourier transform methods are used to analyse the response of the modified system to these forced oscillations. For biologically reasonable parameter values, the annual pattern of parasitism is determined for the nonautonomous system, and compared with that for the autonomous system with periodic perturbations, and a system incorporating both effects. It is found that, whereas periodic perturbations due to management intervention determine the qualitative annual patterns of larval abundance and host infection, the seasonal dynamics of the larval stages change the magnitude of the adult worm burden.

Animals↗
PubMed1991

The population dynamics of nematode infections of ruminants: periodic perturbations as a model for management.

We propose and analyse a model for the dynamics of directly transmitted nematode infections of ruminants which allows for the long-term effects of the annual removal of hosts. The model is a simple continuous-time formulation which captures the principal features of parasite transmission and the acquisition of immunity to infection by the host. Analysis of the simplest version of the model, which assumes a constant host population through time, indicates that its equilibrium is locally stable for feasible biological parameters. The regular removal of hosts involved in most management strategies is modelled in terms of periodic perturbations. The analysis indicates that the periodic removal of parasitized hosts corresponds effectively to a reduction in the basic reproductive rate of infection. We also demonstrate that the system exhibits a dramatic peak in parasite numbers during each grazing season at its dynamic equilibrium. This phenomenon (which is characteristically observed in real systems) is discussed in terms of the balance between acquired immunity and periodic perturbations of the parasite population.

Animals↗
PubMed1990

Ultrasound effects on miniature end plate potential discharge frequency are contingent upon acoustic environment.

The effects of low level ultrasonic stimulation (250 mW cm-2; 1.5 MHz; continuous wave) on the frequency of miniature end-plate potential (MEPP) production, at the frog neuromuscular junction, have been examined in two situations. In a simple exposure environment, where the muscle was immersed in Ringer solution and stretched over a polyurethane resin base at room temperature, the ultrasound stimulus produced a marked increase in the MEPP discharge rate, with only a small concomitant rise (1.0-1.6 degrees C) in local temperature. Control temperature increases of a similar magnitude produced only small changes in the rate of MEPP production. The experiment was repeated in an environment with better defined field conditions. The muscle was suspended in a chamber sealed at the base with an acoustically transparent polycarbonate material, 0.05 mm thick, and contained in a thermostatically controlled bath lined with an acoustically absorbent material. In this situation, no increase in MEPP frequency was observed in response to ultrasonication, although the local measured temperature increase was similar in both magnitude and time course. It is suggested that these results may depend upon differences between standing wave conditions and free field progression of the beam through the sample.

Acetylcholine↗
PubMed1990

Population dynamics in echinococcosis and cysticercosis: regulation of Taenia hydatigena and T. ovis in lambs through passively transferred immunity.

A comparison has been made of the interactions between passively transferred and actively acquired immunity in regulating populations of Taenia hydatigena and T. ovis. When ewes were grazed prior to parturition under a high infection pressure, immunity was transferred to their offspring for up to 8 weeks. A qualitative difference between the species was the destruction of larval T. ovis prior to their establishment ('pre-encystment immunity') and that of T. hydatigena after they had become established ('post-encystment immunity') in the challenged lambs. The major difference in terms of population regulation between the two parasites was that infection occurred with T. hydatigena but not with T. ovis in those lambs reared from birth for 16 weeks under high infection pressure. Passive, like active immunity, is a density-dependent constraint. It plays an important role in the population regulation of T. ovis, but not of T. hydatigena. This is discussed in terms of transmission in the natural environment, an hypothesis on humoral protection and the need to elucidate pathways of protection when immunization schedules are being evaluated for controlling the taeniid zoonoses.

Animals↗
PubMed1988

Population dynamics in echinococcosis and cysticercosis: economic assessment of control strategies for Echinococcus granulosus, Taenia ovis and T. hydatigena.

An official control programme against Echinococcus granulosus and Taenia hydatigena has been in operation in New Zealand for more than 28 years and against Taenia ovis for more than 18 years. This unique effort to control three metazoan parasites at the same time has led to a change from endemic to extinction status for E. granulosus but only a change from hyperendemic to endemic status for T. hydatigena and T. ovis. This has presented problems in determining the most cost-effective future control strategies. To facilitate this, a benefit/cost analysis of 20 options for the combined control of E. granulosus, T. hydatigena and T. ovis in New Zealand was undertaken. This showed that for E. granulosus a future change from the current non-targeted to a targeted approach is strongly indicated. For T. ovis 6 options were cost-effective using a discount rate of 10%. These were (1) a targeted control package using a vaccine in the non-targeted attack phase; (2) a targeted control package using a larvicide in the attack phase; (3) the transfer of all losses due to and responsibility for the control of T. ovis to the producer who administers a larvicide to sheep to be killed for dog food; (4) the transfer of all losses due to and responsibility for the control of T. ovis to the producer who administers praziquantel every 6 weeks to dogs; (5) and (6) two options involving the discontinuation of control. Control of T. hydatigena was assumed to be an incidental outcome of the policies for the other two parasites.

Animals↗