Biomedical subjects

D Greenhalgh

Publications and source records attributed to D Greenhalgh.

At least 19 recordsLinked to original sources

PubMed2001

Three stage AIDS incubation period: a worst case scenario using addict-needle interaction assumptions.

In this paper we develop and analyse a model for the spread of HIV/AIDS amongst a population of injecting drug users. We start off with a brief literature survey and review; this is followed by the derivation of a model which allows addicts to progress through three distinct stages of variable infectivity prior to the onset of full blown AIDS and where the class of infectious needles is split into three according to the different levels of infectivity in addicts. Given the structure of this model we are required to make assumptions regarding the interaction of addicts and needles of different infectivity levels. We deliberately choose these assumptions so that our model serves as an upper bound for the prevalence of HIV under the assumption of a three stage AIDS incubation period. We then perform an equilibrium and stability analysis on this model. We find that there is a critical threshold parameter R(0) which determines the behaviour of the model. If R(0)< or =1, then irrespective of the initial conditions of the system HIV will die out in all addicts and all needles. If R(0)>1, then there is a unique endemic equilibrium which is locally stable if, as is realistic, the time scale on which addicts inject is much shorter than that of the other epidemiological and demographic processes. Simulations indicate that if R(0)>1, then provided that disease is initially present in at least one addict or needle it will tend to the endemic equilibrium. In addition we derive conditions which guarantee this. We also find that under calibration the long term prevalence of disease in our variable infectivity model is always greater than in an equivalent constant infectivity model. These results are confirmed and explored further by simulation. We conclude with a short discussion.

Acquired Immunodeficiency Syndrome↗

PubMed2001

A mathematical treatment of AIDS and condom use.

In this paper we examine the impact of condom use on the sexual transmission of human immunodeficiency virus (HIV) and acquired immune deficiency syndrome (AIDS) amongst a homogeneously mixing male homosexual population. We first derive a multi-group SIR-type model of HIV/AIDS transmission where the homosexual population is split into subgroups according to frequency of condom use. Both susceptible and infected individuals can transfer between the different groups. We then discuss in detail an important special case of this model which includes two risk groups and perform an equilibrium and stability analysis for this special case. Our analysis shows that this model can exhibit unusual behaviour. As normal, if the basic reproduction number, R0, is greater than unity then there is a unique disease-free equilibrium which is locally unstable and a unique endemic equilibrium. However, when R0 is less than unity two endemic equilibrium solutions can also co-exist simultaneously with the disease-free solution which is locally stable. Numerical simulations using realistic parameter values confirm this and we find that in certain circumstances the disease-free solution and one of the endemic solutions are both locally asymptotically stable, while the other endemic solution is unstable. This unusual behaviour has important implications for control of the disease as reducing R0 to less than unity no longer guarantees eradication of the disease. For a restricted special case of this two-group model we show that there is only the disease-free equilibrium for R0 < or = 1 which is globally stable. For R0 > 1 the disease-free equilibrium is unstable and there is a unique endemic equilibrium which is locally stable. We then attempt to fit the model to HIV and AIDS incidence data from San Francisco, USA. The paper concludes with a brief discussion.

Acquired Immunodeficiency Syndrome↗

PubMed2000

Subcritical endemic steady states in mathematical models for animal infections with incomplete immunity.

Many classical mathematical models for animal infections assume that all infected animals transmit the infection at the same rate, all are equally susceptible, and the course of the infection is the same in all animals. However for some infections there is evidence that seropositives may still transmit the infection, albeit at a lower rate. Animals can also experience more than one episode of the infection although those who have already experienced it have a partial immune resistance. Animals who experience a second or subsequent period of infection may not necessarily exhibit clinical symptoms. The main example discussed is bovine respiratory syncytial virus (BRSV) amongst cattle. We consider simple models with vaccination and homogeneous and proportional mixing between seropositives and seronegatives. We derive an expression for the basic reproduction number, R(o), and perform an equilibrium and stability analysis. We find that it may be possible for there to be two endemic equilibria (one stable and one unstable) for R(o)<1 and in this case at R(o)=1 there is a backwards bifurcation of an unstable endemic equilibrium from the infection-free equilibrium. Then the implications for control strategies are considered. Finally applications to Aujesky's disease (pseudorabies virus) in pigs are discussed.

Animals↗

PubMed2000

Three-stage AIDS incubation period: a best case scenario using addict-needle interaction assumptions.

In this paper we extend the 'needles that kill' model discussed in Kaplan & O'Keefe (1993) to allow addicts to progress through three-stages of variable infectivity prior to the onset of full-blown AIDS, and where the class of infectious needles is split into three according to the different levels of infectivity in addicts. Given the structure of this model we are required to make assumptions regarding the interaction of addicts and needles of different infectivity levels. We deliberately choose these assumptions so that our model serves as a lower bound for the prevalence of HIV under the assumption of a three-stage AIDS incubation period. We find that there is a critical threshold parameter R0 which determines the behaviour of the model. If R0 > 1 then there is a unique endemic equilibrium which is locally stable if, as is realistic, the timescale on which addicts inject is much shorter than that of the other epidemiological and demographic processes. Simulations indicate that if R0 > 1, then provided that disease is initially present in at least one addict or needle then it will tend to the endemic equilibrium. In addition, we derive conditions which guarantee this. We also find that under calibration the long-term prevalence of disease in the 'needles that kill' model is the same as in our three-stage model.

Behavior, Addictive↗

PubMed1999

A test to detect replication in HIV serological data labelled by birth date based on the number of matching pairs in a sample.

Diagnoses of HIV infection are reported to the Public Health Laboratory Service (PHLS) by microbiologists through a voluntary confidential surveillance scheme. Names are not recorded on the database but the date of birth of the individual concerned is usually available. This paper discusses a statistical method to detect repeated counting of individuals in these and similar data based on the number of matching pairs in the sample. The test is based on the theoretical result that the null hypothesis of all birth dates equally likely and all individuals distinct minimizes the expected number of matching pairs in the sample. Five of the 16 birth years in the sample taken in 1991 show evidence of more replication than would be expected by chance using a 5 per cent level test. When the test is repeated taking into account a small but statistically significant seasonal variation in the birth rate, the results are very similar.

Adult↗

PubMed1999

A partial ranking method for identifying repeated inclusion of individuals in anonymized HIV infection reports.

Diagnoses of HIV infection are reported to the Public Health Laboratory Service (PHLS) AIDS Centre under a voluntary surveillance scheme. Names are not held in the data set, but the date of birth of the individual concerned is usually available. This paper describes a statistical method for identifying whether there are likely to be individuals repeatedly represented in the resulting data set, which is considered by birth year. A partial ordering method is used that is especially useful for years where the number of birth years in the sample is too small for chi2 tests to be used. At the 5% level, one of the five birth years tested in the data supplied to us by the PHLS shows evidence of more replication than would be expected from independent random sampling from the population. The results are compared with an alternative maximum-likelihood-based test that reaches the same conclusions. Maximum likelihood methods are further used to estimate the percentage of overcounting of individuals in the sample at 2.7%.

AIDS Serodiagnosis↗

PubMed1999

Hopf bifurcation in epidemic models with a time delay in vaccination.

Two SIR models for the spread of infectious diseases which were originally suggested by Greenhalgh & Das (1995, Theor. Popul. Biol. 47, 129-179; 1995, Mathematical Population Dynamics: Analysis of Heterogeneity, pp. 79-101, Winnipeg: Wuerz Publishing) are considered but with a time delay in the vaccination term. This reflects the fact that real vaccines do not immediately confer permanent immunity. The population is divided into susceptible, infectious, and immune classes. The contact rate is constant in model I but it depends on the population size in model II. The death rate depends on the population size in both models. There is an additional mortality due to the disease, and susceptibles are vaccinated and may become permanently immune after a lapse of some time. Using the time delay as a bifurcation parameter, necessary and sufficient conditions for Hopf bifurcation to occur are derived. Numerical results indicate that that for diseases in human populations Hopf bifurcation is unlikely to occur at realistic parameter values if the death rate is a concave function of the population size.

Communicable Disease Control↗

PubMed1998

Human keratin-1.bcl-2 transgenic mice aberrantly express keratin 6, exhibit reduced sensitivity to keratinocyte cell death induction, and are susceptible to skin tumor formation.

Nonmelanoma skin cancers (NMSC) are among the most common malignancies in the world. Typically, these neoplasms grow slowly and are comparatively indolent in their clinical behavior. The most frequent molecular alterations implicated in the pathogenesis of these neoplasms involve genes known to be regulators of cell death including p53, Ha-ras and bcl-2. In order to evaluate the significance cell death deregulation during skin carcinogenesis, we generated a transgenic mouse model (HK1.bcl-2) using the human keratin 1 promoter to target the expression of a human bcl-2 minigene to the epidermis. Transgenic HK1.bcl-2 protein was expressed at high levels specifically in the epidermis extending from the stratum basale through the stratum granulosum. The epidermis of HK1.bcl-2 mice exhibited multifocal hyperplasia without associated hyperkeratosis and aberrant expression of keratin 6. The rate of proliferation was similar in HK1.bcl-2 and control epidermis although suprabasal BrdUrd incorporating cells were present only in HK1.bcl-2 skin. Keratinocytes from the HK1.bcl-2 mice were significantly more resistant to cell death induction by U.V.-B, DMBA, and TPA, compared to control keratinocytes. Furthermore, papillomas developed at a significantly greater frequency and shorter latency in the HK1.bcl-2 mice compared to control littermates following initiation with DMBA and promotion with TPA. Together these results support a role for bcl-2 in the pathogenesis of NMSC.

9,10-Dimethyl-1,2-benzanthracene↗

PubMed1997

Mathematical modelling of the spread of HIV/AIDS amongst injecting drug users.

In this paper we develop and analyse a model for the spread of HIV/AIDS amongst a population of injecting drug users. Our work is based on a model originally due to Kaplan (1989, Rev. Inf. Diseases 11, 289-98). We start off with a brief literature survey and review; this is followed up by a detailed description of Kaplan's model. We then outline a more realistic extension of Kaplan's model. Then we perform an equilibrium and stability analysis on this model. We find that there is a critical threshold parameter Rzero which determines the behaviour of the model. If Rzero < or = 1 there is a unique disease-free equilibrium, and if Rzero < 1 the disease dies out. If Rzero > 1 this disease-free equilibrium is unstable, and in addition there is a unique endemic equilibrium which is locally stable. If a certain condition is satisfied (and for Kaplan's model this condition is always satisfied), additional complete global-stability results are shown. These results are confirmed and explored further by simulation.

Acquired Immunodeficiency Syndrome↗

PubMed1996

Effects of heterogeneity on the spread of HIV/AIDS among intravenous drug users in shooting galleries.

In this article we study the effects of heterogeneity on the spread of HIV and AIDS among a population of injecting drug users. We allow for variability in the rate at which addicts visit shooting galleries, their choice of shooting gallery, and whether or not they clean their needles before use. If the sizes of the different groups of drug users remain constant then there is a key parameter R0, which determines the behavior of the epidemic. If R0 is less than or equal to one then the disease will die out, whereas if R0 exceeds one then the fractions of infected individuals and the fractions of infected needles tend to their unique equilibrium values. These are global results. If we allow for recruitment of new susceptible drug users and deaths from AIDS in the population then the unique endemic equilibrium may become unstable and limit cycles can arise by Hopf bifurcation.

Acquired Immunodeficiency Syndrome↗

PubMed1995

Modelling epidemics with variable contact rates.

In this paper we look at models for epidemics where the contact rate is a monotone increasing function of the population density. The background death rate also depends on the population density. We first examine the case of a constant contact rate (motivated by AIDS) and here obtain some global stability results. We consider an SIR model where a typical individual starts off susceptible, at some stage catches the disease and after a short infectious period becomes permanently immune. We also look at the effects of vaccination. First we perform an equilibrium and local stability analysis. Next we reformulate the model in terms of the proportions of individuals susceptible, infected, and immune to obtain some global stability results. We find three possible equilibrium values: one where the population is extinct, one where the disease has died out but the population has not died out, and a unique equilibrium where disease is present. We determine conditions for global stability of these equilibria. For certain parameter values none of these equilibria are locally stable. In this case there is a formal proportional endemic equilibrium with a strictly positive proportion of infected individuals. We expect the population size to die out but the proportions of susceptible, infected, and immune individuals to tend to this endemic proportional equilibrium. We find two critical contact rates which help determine the behaviour of the system. Next we extend some of these results to the case where the contact rate depends on population density. Finally the paper examines these results further using numerical methods.

Acquired Immunodeficiency Syndrome↗

PubMed1994

Some bounds on estimates for reproductive ratios derived from the age-specific force of infection.

In this paper we shall look at estimation of reproductive ratios for common childhood infections such as chickenpox, measles, mumps, and hepatitis A with and without a vaccination program. The paper starts with a survey of previous work in this area. We suppose that we are given data in the form of an age-related serological profile with a given vaccination program. This is used to estimate the reproductive ratio and evaluate vaccination campaigns. The effect of different mixing patterns, such as homogeneous mixing, assortative mixing, proportional mixing, and symmetric mixing are discussed. R phi denotes the reproductive ratio when a steady-state vaccination campaign phi is used. Assortative mixing maximizes the reproductive ratio R phi. A mixing pattern which minimizes R phi and a lower bound for R phi for the important symmetric mixing case are found. The most usual situation is that we are given the age-serological profile with no vaccination so that we have bounds for the basic reproductive ratio R0. These results are illustrated with an application to vaccination against hepatitis A in Bulgaria. Numerical evaluations of the effect of different elimination vaccination strategies are examined.

Adult↗

PubMed1993

Cotransfection of HPV-18 and v-fos DNA induces tumorigenicity of primary human keratinocytes.

Human keratinocytes were cotransfected with the FBJ/R v-fos oncogene and the HPV-18 genome and selected on the basis of their resistance to inducers of terminal differentiation. Unlike keratinocytes immortalized by HPV-18 DNA alone, the HPV-18/v-fos transformants exhibited prominent intracellular vacuolization and formed progressively growing, squamous cell tumors when injected subcutaneously into nude mice. Cytogenetic analysis of two clonally selected transformed cell lines (18/fos clone 1 and 18/fos clone 2) revealed minimal alterations in karyotype, although a consistent rearrangement of chromosome 10, iso(10q), was observed. Further analysis of 18/fos clone 1 confirmed the expression of the fos gene as well as the HPV-18 E7 protein. Alterations in fos gene expression, which appear to be an important facet of epidermal differentiation in vivo, could potentially contribute to the malignant progression of HPV immortalized cells.

Animals↗

PubMed1992

Development of an in vitro model to study carcinogen-induced neoplastic progression of initiated mouse epidermal cells.

Initiation and promotion in mouse skin carcinogenesis produce multiple benign tumors, squamous papillomas, but only a few squamous cell carcinomas. The spontaneous conversion from the benign to the malignant phenotype occurs over many months and in stages, but induced malignant conversion can be accomplished more rapidly by exposure of papilloma-bearing mice to mutagens or by transfection of papilloma cell lines with specific oncogenes. The analysis of genetic targets responsible for carcinogen-induced neoplastic progression would be facilitated by the development of in vitro models where the process is rapid, focal, and quantitative. To this end, primary newborn mouse keratinocytes were initiated in vitro by the introduction of the v-rasHa oncogene via a defective retrovirus. Recipient cells produce squamous papillomas and have a high proliferation rate in culture medium with 0.05 mM Ca2+, but fail to grow in medium with 0.5 mM Ca2+ which is permissive for growth of malignant keratinocytes. When v-rasHa-keratinocytes were exposed to mutagens in vitro, proliferative foci emerged after culture in 0.5 mM Ca2+ for 4 weeks. These foci stained intensely red with rhodamine stain, could be easily quantitated, and readily incorporated bromodeoxyuridine. Dose-response studies with several mutagens indicated that the number of foci increased with concentration to the point where excessive cytotoxicity developed. Mutagens varied in potency for producing foci in the following order: cis-diamminedichloroplatinum greater than or equal to benzo(a)pyrene diolexpoxide I greater than N-methyl-N'-nitro-N-nitrosoguanidine greater than or equal to 4-nitroquinoline-N-oxide greater than N-acetoxy-acetyl- aminofluorene. The tumor promoter 12-O-tetradecanoylphorbol-13-acetate was inactive in the assay. A subset of cell lines derived from foci produced malignant tumors in vivo, while others were not tumorigenic. Analysis of DNA from cell lines and tumors revealed that most tumorigenic cell lines maintained the v-rasHa genome, whereas the viral sequences were deleted in nontumorigenic cell lines. Immunohistochemical analysis indicated that proliferative foci and quiescent v-rasHa keratinocytes expressed keratin 8, a marker of v-rasHa expression in cultured keratinocytes. Cells in foci, but not v-rasHa control cells, expressed keratin 13, a marker which is strongly associated with the malignant progression of skin tumors in vivo. This in vitro assay provides a quantitative model to study chemically induced focal neoplastic progression at the cellular level and to identify agents which may be selective for enhancing malignant conversion.

Animals↗

PubMed1992

Vaccination in density-dependent epidemic models.

This paper examines the effect of vaccination for an epidemic model where the death rate depends on the number of individuals in the population. The basic model which is described is based on measles or other childhood diseases in developing countries or viral diseases such as rabies in animal populations. An equilibrium analysis of the model and the local stability of small perturbations about the equilibrium values are discussed. The biological implications of these results are examined and similar results presented for modifications of the basic model.

Animals↗

PubMed1992

Some threshold and stability results for epidemic models with a density-dependent death rate.

Most classical models for infectious diseases assume that the birth and death rates of individuals and the meeting rates between susceptible and infected individuals do not depend on the total number of individuals in the population. While these assumptions are valid in some situations they are less valid in others. For example, for diseases in animal an insects populations competition for scarce resources might well mean that the death rate depends on the number of individuals. The present paper examines two epidemic models where the death rate is density dependent. For each model the possible equilibrium levels of disease incidence are determined and the stability of these equilibrium levels to small perturbations is discussed. The biological interpretation of these results is presented together with the results of some numerical simulations.

Birth Rate↗

PubMed1992

Some results for an SEIR epidemic model with density dependence in the death rate.

This paper deals with an SEIR epidemic model for an infectious disease where the death rate depends on the number of individuals in the population. It is also assumed that there is an additional death rate suffered by infected individuals. It is found that there are three steady-state values: one where the population is extinct, one where the population maintains itself at a constant level and the disease is extinct, and one where there is a unique equilibrium with disease present. An interesting and unusual feature is that it is possible for this third equilibrium to exist and be locally unstable. Numerical work and simulation show that we can have cycles of disease incidence with increasing amplitude, a constant amplitude, and a decreasing amplitude, depending on the parameter values of the model.

Animals↗

PubMed1990

Vaccination campaigns for common childhood diseases.

Mathematical models exist for vaccination programs for common childhood diseases such as measles, chickenpox, polio, rubella, and mumps. In compartmental models, the population is divided into compartments containing susceptible, infected, and immune individuals, and the model also takes account of the age structure in the population. An equilibrium analysis is performed on the resulting partial differential equations to determine the vaccination program that just eliminates the disease. The stability of the resulting equilibrium solutions is also examined. Particular attention is paid to multistage vaccination strategies that vaccinate given proportions of susceptible individuals at various ages. Finally, some numerical results are analyzed to see what these vaccination coverages mean for certain common childhood diseases.

Child↗