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Biomedical subjects

R M May

Publications and source records attributed to R M May.

At least 19 recordsLinked to original sources
PubMed1992

Coexistence and competition in HIV infections.

In this paper we extend our explanation of a model for the dynamics of the interaction between HIV and the cells of the immune system (Nowak et al., 1990). We show that the Simpson index of viral diversity is a Lyapunov function for a simplified version of this model. We also present a more general mathematical characterization of the nature of the diversity threshold exhibited by the model, including for the first time heterogeneity in parameters like virus replication rate, cytopathicity and antigenicity. The more general diversity threshold condition includes the different contributions of strains with higher replication rates and cytopathicities or strains that are only weakly recognized by the immune system. This leads to some new insights and a more detailed understanding of why the viral diversity falls once the diversity threshold is exceeded.

HIV↗
PubMed1992

Age-dependent choice of sexual partners and the transmission dynamics of HIV in Sub-Saharan Africa.

A mathematical model of the transmission of HIV-1 within heterosexual populations in Sub-Saharan Africa is described and its properties analysed. The model incorporates epidemiological and demographic processes and extends previous work in this area via the inclusion of age and sex dependency in rates of sexual partner change, and sexual partner choice dependent on age. Parameter assignments are made on the basis of current data on the transmission dynamics of HIV-1 and the demography of human populations in Africa. Both age-dependent rates of sexual activity and the sexual contact of males with females younger than themselves act to enhance the predicted demographic impact. With realistic parameter values, the model suggests AIDS is able to reverse the sign of population growth rates from positive to negative values over a timescale of a few decades. The sensitivity of this prediction is examined in relation to changes in the pattern of sexual contact between different age classes of females and males, different patterns of change in the age-dependent rate of sexual partner change, different assumptions concerning the doubling time of the epidemic in its early stages, and the relative efficiencies of viral transmission between men and women, and vice versa. The impact AIDS is predicted to have on the number of young and elderly persons as a fraction of the number of productive adults (the dependancy ratio) is examined under various assumptions concerning the weighting to be applied to mirror the burden imposed by the care of those with AIDS. The paper includes an assessment of the influence of the timing of changes in sexual behaviour, or the promotion of the use of condoms, on the predicted course of the epidemic. The paper concludes with a discussion of data needs and the model refinements required to more accurately mirror current understanding of the epidemiology of HIV-1.

Acquired Immunodeficiency Syndrome↗
PubMed1992

The influence of concurrent partnerships on the dynamics of HIV/AIDS.

Most models of the spread of HIV/AIDS assume that the probability of transmission from an infected individual to a susceptible partner has some constant value per sexual act, compounding independently randomly (so that ten acts with one person chosen from a particular group has, on average, the same risk as one act with each of ten different people from that group). Guided by available data, other models treat the transmission process as being some characteristic (but highly variable) value per partnership, independent of the number of acts. This latter approach does not allow for the possible effects of concurrent partnerships, and therefore does not take account of the possibility that an initially uninfected partner of a given susceptible individual may become infected over the duration of their partnership. We present a new model, based on transmission per partnership, that takes account of partnership duration. If the number of overlapping partnerships is high enough (so that R0 greater than 1 among "standing crops" of partners), any initial infection will spread very fast--on the time scale of a few times the latent interval (a few months)--among existing networks of partners. After this initial "fast phase," the subsequent epidemic proceeds more slowly along conventional lines as new partnerships are formed. These properties of the model are illustrated numerically and by analytic studies (using singular perturbation theory). The possibility of such "two time-scale" phenomena could have implications for data analysis based on statistical back-projection.

Acquired Immunodeficiency Syndrome↗
PubMed1991

Antigenic diversity thresholds and the development of AIDS.

Longitudinal studies of patients infected with HIV-1 reveal a long and variable incubation period between infection and the development of AIDS. Data from a small number of infected patients show temporal changes in the number of genetically distinct strains of the virus throughout the incubation period, with a slow but steady rise in diversity during the progression to disease. A mathematical model of the dynamic interaction between viral diversity and the human immune system suggests the existence of an antigen diversity threshold, below which the immune system is able to regulate viral population growth but above which the virus population induces the collapse of the CD4+ lymphocyte population. The model suggests that antigenic diversity is the cause, not a consequence, of immunodeficiency disease. The model is compared with available data, and is used to assess how the timing of the application of chemotherapy or immunotherapy influences the rate of progress to disease.

Acquired Immunodeficiency Syndrome↗
PubMed1991

The spread of HIV-1 in Africa: sexual contact patterns and the predicted demographic impact of AIDS.

The spread of HIV-1 in Africa is examined here in the light of recent information on the main epidemiological and behavioural determinants of transmission. Mathematical models incorporating demographic, epidemiological and behavioural processes are used to assess the potential demographic impact of the disease AIDS. These analyses highlight the significance of patterns of sexual behaviour, and in particular networks of sexual contact, on the predicted spread of infection. Current data reveal substantial variations in the degree of spread between and in countries, but new analyses support earlier predictions that in the worst-afflicted areas AIDS is likely to change population growth rates from positive to negative values in a few decades.

Acquired Immunodeficiency Syndrome↗
PubMed1991

Potential of community-wide chemotherapy or immunotherapy to control the spread of HIV-1.

Whether zidovudine (3'-azido-3'-deoxythymidine, AZT) should be offered to symptomless individuals infected with human immunodeficiency virus type-1 (HIV-1), in the hope of delaying or even preventing progression to AIDS, has been much debated. The discussion has focused on the efficacy of the drug in delaying progression to disease, the severity of its side-effects, and the likelihood of its prolonged and widespread use resulting in zidovudine-resistant strains of the virus. Little attention has been given to the degree to which treatment reduces the infectiousness of symptomless patients, and to the concomitant implications for the overall transmission rate of HIV-1 in the community. Here we use simple mathematical models to show that community treatment with antiviral drugs or immunotherapies that lengthen the incubation period of AIDS without significantly reducing the infectiousness of treated individuals, can increase the rate at which HIV-1 infection spreads (which is fairly obvious) and can even, under certain circumstances, increase the AIDS-related death rate in the community (which is less obvious).

Acquired Immunodeficiency Syndrome↗
PubMed1991

Drugs, sex and HIV: a mathematical model for New York City.

A data-based mathematical model was formulated to assess the epidemiological consequences of heterosexual, intravenous drug use (IVDU) and perinatal transmission in New York City (NYC). The model was analysed to clarify the relationship between heterosexual and IVDU transmission and to provide qualitative and quantitative insights into the HIV epidemic in NYC. The results demonstrated the significance of the dynamic interaction of heterosexual and IVDU transmission. Scenario analysis of the model was used to suggest a new explanation for the stabilization of the seroprevalence level that has been observed in the NYC IVDU community; the proposed explanation does not rely upon any IVDU or sexual behavioural changes. Gender-specific risks of heterosexual transmission in IVDUs were also explored by scenario analysis. The results showed that the effect of the heterosexual transmission risk factor on increasing the risk of HIV infection depends upon the level of IVDU. The model was used to predict future numbers of adult and pediatric AIDS cases; a sensitivity analysis of the model showed that the confidence intervals on these prediction estimates were extremely wide. This prediction variability was due to the uncertainty in estimating the values of the models' thirty variables (twenty biological-behavioural transmission parameters and the initial sizes of ten subgroups). However, the sensitivity analysis revealed that only a few key variables were significant in contributing to the AIDS case prediction variability; partial rank correlation coefficients were calculated and used to identify and to rank the importance of these key variables. The results suggest that long-term precise estimates of the future number of AIDS cases will only be possible once the values of these key variables have been evaluated accurately.

Female↗
PubMed1991

Iron dextran in the treatment of iron-deficiency anaemia of pregnancy. Haematological response and incidence of side-effects.

Sixty pregnant patients with a haemoglobin (Hb) less than 8 g/dl and proven iron-deficiency anaemia were randomly allocated to two treatment groups. Group A received the usual recommended dose of iron dextran (Imferon; Fisons) and group B received two-thirds of the recommended dose. A further 30 patients received oral iron (group C). There was no difference in Hb value between the three groups 4 weeks after treatment or 3 months after delivery. At 6 months after delivery, a higher mean Hb value was found in the patients in group A than those in groups B and C. Significantly higher serum ferritin levels were found in group A and this difference was still present 6 months postnatally. There was no significant difference in the incidence of delayed reactions between the two groups who received iron dextran.

Anemia, Hypochromic↗
PubMed1991

An assessment of the maximum sustainable yield of ivory from African elephant populations.

A general, logistic population model is used to explore the dynamics of harvested elephant populations. The model includes two features peculiar to elephant populations and the harvesting of ivory. First, because of the shape of the growth curve of tusks with age, the conversion factor that relates the number of elephants killed to the ivory yield in weight is not constant, but a function of the population size. Second, tusks from animals that die from natural causes can be retrieved and included in the total yield of ivory. The implications of the relationship between tusk size and age of an animal on the maximum sustainable yield in terms of ivory tonnage and in terms of the number of tusks are explored. The nonequilibrium implications of the tusk growth curve on the population dynamics under different harvesting strategies are also investigated. Results indicate that the maximum sustainable yield is achieved at very low harvest rates with population levels close to the pristine equilibrium. When tusks from animals that die of natural causes are included in the harvest, the maximum yield may, depending on the mortality and recruitment parameters, occur when there is no direct harvest.

Africa↗
PubMed1991

Mathematical biology of HIV infections: antigenic variation and diversity threshold.

Infection with the human immunodeficiency virus (HIV) results in severe damage to the immune system and consequent disease (AIDS) after a long and variable incubation period (on average 8-10 years). Why the incubation period should be so long is a puzzle. We outline an explanation based on the dynamics of the interplay between the immune response and antigenic variation in the virus population. The essential idea is that AIDS results when the diversity of antigenic variants of HIV in an infected patient exceeds some threshold, beyond which the immune system can no longer cope. The paper develops a simple mathematical model for this process, based on experimental observations, and explores several ramifications.

Acquired Immunodeficiency Syndrome↗
PubMed1990

Distinguishing error from chaos in ecological time series.

Over the years, there has been much discussion about the relative importance of environmental and biological factors in regulating natural populations. Often it is thought that environmental factors are associated with stochastic fluctuations in population density, and biological ones with deterministic regulation. We revisit these ideas in the light of recent work on chaos and nonlinear systems. We show that completely deterministic regulatory factors can lead to apparently random fluctuations in population density, and we then develop a new method (that can be applied to limited data sets) to make practical distinctions between apparently noisy dynamics produced by low-dimensional chaos and population variation that in fact derives from random (high-dimensional) noise, such as environmental stochasticity or sampling error. To show its practical use, the method is first applied to models where the dynamics are known. We then apply the method to several sets of real data, including newly analysed data on the incidence of measles in the United Kingdom. Here the additional problems of secular trends and spatial effects are explored. In particular, we find that on a city-by-city scale measles exhibits low-dimensional chaos (as has previously been found for measles in New York City), whereas on a larger, country-wide scale the dynamics appear as a noisy two-year cycle. In addition to shedding light on the basic dynamics of some nonlinear biological systems, this work dramatizes how the scale on which data is collected and analysed can affect the conclusions drawn.

Chickenpox↗
PubMed1979

Population biology of infectious diseases: Part II.

In the first part of this two-part article (Nature 280, 361--367), mathematical models of directly transmitted microparasitic infections were developed, taking explicit account of the dynamics of the host population. The discussion is now extended to both microparasites (viruses, bacteria and protozoa) and macroparasites (helminths and arthropods), transmitted either directly or indirectly via one or more intermediate hosts. Consideration is given to the relation between the ecology and evolution of the transmission processes and the overall dynamics, and to the mechanisms that can produce cyclic patterns, or multiple stable states, in the levels of infection in the host population.

Bacterial Infections↗
PubMed1979

Population biology of infectious diseases: Part I.

If the host population is taken to be a dynamic variable (rather than constant, as conventionally assumed), a wider understanding of the population biology of infectious diseases emerges. In this first part of a two-part article, mathematical models are developed, shown to fit data from laboratory experiments, and used to explore the evolutionary relations among transmission parameters. In the second part of the article, to be published in next week's issue, the models are extended to include indirectly transmitted infections, and the general implications for infectious diseases are considered.

Animals↗
PubMed1979

Prevalence of schistosome infections within molluscan populations: observed patterns and theoretical predictions.

The paper draws together a large and scattered body of empirical evidence concerning the prevalence of snail infection with schistosome parasites in field situations, the duration of the latent period of infection in snails (and its dependence on temperature), and the mortality rates of infected and uninfected snails in field and laboratory conditions. A review and synthesis of quantitative data on the population biology of schistosome infections within the molluscan host is attempted and observed patterns of infection are compared with predictions of a schistosomiasis model developed by May (1977) which incorporates differential snail mortality (between infected and uninfected snails) and latent periods of infection. It is suggested that the low levels of prevalence within snail populations in endemic areas of schistosomiasis are closely associated with high rates of infected snail mortality and the duration of the latent period of infection within the mollusc. In certain instances, the expected life-span of an infected snail may be less than the duration of the latent period of infection. Such patterns generate very low levels of parasite prevalence. A new age prevalence model for schistosome infections within snail populations is developed and its predictions compared with observed patterns. The implications of this study of observed and predicted patterns of snail infection within molluscan populations are discussed in relation to the overall transmission dynamics of schistosomiasis.

Animals↗