Using Serology to Anticipate Measles Post-honeymoon Period Outbreaks

Measles vaccination is a public health 'best buy', with the highest cost of illness averted of any vaccine-preventable disease (Ozawa et al., Bull. WHO 2017;95:629). In recent decades, substantial reductions have been made in the number of measles cases, with an estimated 20 million deaths averted from 2000 to 2017 (Dabbagh et al., MMWR 2018;67:1323). Yet, an important feature of epidemic dynamics is that large outbreaks can occur following years of apparently successful control (Mclean et al., Epidemiol. Infect. 1988;100:419-442). Such 'post-honeymoon period' outbreaks are a result of the nonlinear dynamics of epidemics (Mclean et al., Epidemiol. Infect. 1988;100:419-442). Anticipating post-honeymoon outbreaks could lead to substantial gains in public health, helping to guide the timing, age-range, and location of catch-up vaccination campaigns (Grais et al., J. Roy. Soc. Interface 2008003B6:67-74). Theoretical conditions for such outbreaks are well understood for measles, yet the information required to make these calculations policy-relevant is largely lacking. We propose that a major extension of serological studies to directly characterize measles susceptibility is a high priority.

External Defibrillator Damage Associated With Attempted Synchronized Dual-Dose Cardioversion

The simultaneous use of 2 external defibrillators to administer either dual or sequential cardioversion or defibrillation for refractory cardiac arrhythmias is increasing in both the out-of-hospital and inhospital settings. Using 2 defibrillators to administer higher energy levels than can be achieved with a single defibrillator is considered off-label and is currently not part of published advanced cardiac life support guidelines. We report the first case in which the use of dual-dose cardioversion was associated with external defibrillator damage. Because defibrillator damage, especially if undetected, jeopardizes patient safety and off-label medical product use may void the manufacturer's warranty, this case should urge users to proceed with caution when contemplating this technique.

Positive selection and compensatory adaptation interact to stabilize non-transmissible plasmids

Plasmids are important drivers of bacterial evolution, but it is challenging to understand how plasmids persist over the long term because plasmid carriage is costly. Classical models predict that horizontal transfer is necessary for plasmid persistence, but recent work shows that almost half of plasmids are non-transmissible. Here we use a combination of mathematical modelling and experimental evolution to investigate how a costly, non-transmissible plasmid, pNUK73, can be maintained in populations of Pseudomonas aeruginosa. Compensatory adaptation increases plasmid stability by eliminating the cost of plasmid carriage. However, positive selection for plasmid-encoded antibiotic resistance is required to maintain the plasmid by offsetting reductions in plasmid frequency due to segregational loss. Crucially, we show that compensatory adaptation and positive selection reinforce each other’s effects. Our study provides a new understanding of how plasmids persist in bacterial populations, and it helps to explain why resistance can be maintained after antibiotic use is stopped.

Plasmids are important for bacterial evolution but the evolutionary mechanisms behind their maintenance are unclear. Here the authors show that the interplay between compensatory adaptation and positive selection for plasmid-encoded antibiotic resistance determines plasmid persistence in P. aeruginosa.

Utility of routine follow-up head CT scanning after mild traumatic brain injury: a systematic review of the literature

OBJECTIVE

To evaluate the efficacy of routine follow-up CT scans of the head after complicated mild traumatic brain injury (TBI).

METHODS

74 English language studies published from 1999 to February 2011 were reviewed. The papers were found by searching the PubMed database using a combination of keywords according to Cochrane guidelines. Excluding studies with missing or inappropriate data, 1630 patients in 19 studies met the inclusion criteria: complicated mild TBI, defined as a GCS score 13-15 with abnormal initial CT findings and the presence of follow-up CT scans. For these studies, the progression and type of intracranial haemorrhage, time from trauma to first scan, time between first and second scans, whether second scans were obtained routinely or for neurological decline and the number of patients who had a neurosurgical intervention were recorded.

RESULTS

Routine follow-up CT scans showed hemorrhagic progression in 324 patients (19.9%). Routine follow-up head CT scans did not predict the need for neurosurgical intervention (p=0.10) but a CT scan of the head performed for decline in status did (p=0.00046). For the 56 patients (3.4%) who declined neurologically, findings on the second CT scan were worse in 38 subjects (67%) and unchanged in the rest. Overall, 39 patients (2.4%) underwent neurosurgical intervention.

CONCLUSION

Routine follow-up CT scans rarely alter treatment for patients with complicated mild TBI. Follow-up CT scans based on neurological decline alter treatment five times more often than routine follow-up CT scans.

Low rate of delayed deterioration requiring surgical treatment in patients transferred to a tertiary care center for mild traumatic brain injury

OBJECT

Patients with mild traumatic brain injury (mTBI) only rarely need neurosurgical intervention; however, there is a subset of patients whose condition will deteriorate. Given the high resource utilization required for interhospital transfer and the relative infrequency of the need for intervention, this study was undertaken to determine how often patients who were transferred required intervention and if there were factors that could predict that need.

METHODS

The authors performed a retrospective review of cases involving patients who were transferred to the University of New Mexico Level 1 trauma center for evaluation of mTBI between January 2005 and December 2009. Information including demographic data, lesion type, need for neurosurgical intervention, and short-term outcome was recorded.

RESULTS

During the 4-year study period, 292 patients (age range newborn to 92 years) were transferred for evaluation of mTBI. Of these 292 patients, 182 (62.3%) had an acute traumatic finding of some kind; 110 (60.4%) of these had a follow-up CT to evaluate progression, whereas 60 (33.0%) did not require a follow-up CT. In 15 cases (5.1% overall), the patients were taken immediately to the operating room (either before or after the first CT). Only 4 patients (1.5% overall) had either clinical or radiographic deterioration requiring delayed surgical intervention after the second CT scan. Epidural hematoma (EDH) and subdural hematoma (SDH) were both found to be significantly associated with the need for surgery (OR 29.5 for EDH, 95% CI 6.6-131.8; OR 9.7 for SDH, 95% CI 2.4-39.1). There were no in-hospital deaths in the series, and 97% of patients were discharged with a Glasgow Coma Scale score of 15.

CONCLUSIONS

Most patients who are transferred with mTBI who need neurosurgical intervention have a surgical lesion initially. Only a very small percentage will have a delayed deterioration requiring surgery, with EDH and SDH being more concerning lesions. In most cases of mTBI, triage can be performed by a neurosurgeon and the patient can be observed without interhospital transfer.

Evolution and emergence of novel human infections

Some zoonotic pathogens cause sporadic infection in humans but rarely propagate further, while others have succeeded in overcoming the species barrier and becoming established in the human population. Adaptation, driven by selection pressure in human hosts, can play a significant role in allowing pathogens to cross this species barrier. Here we use a simple mathematical model to study potential epidemiological markers of adaptation. We ask: under what circumstances could ongoing adaptation be signalled by large clusters of human infection? If a pathogen has caused hundreds of cases but with little transmission, does this indicate that the species barrier cannot be crossed? Finally, how can case reports be monitored to detect an imminent emergence event? We distinguish evolutionary scenarios under which adaptation is likely to be signalled by large clusters of infection and under which emergence is likely to occur without any prior warning. Moreover, we show that a lack of transmission never rules out adaptability, regardless of how many zoonoses have occurred. Indeed, after the first 100 zoonotic cases, continuing sporadic zoonotic infections without onward, human-to-human transmission offer little extra information on pathogen adaptability. Finally, we present a simple method for monitoring outbreaks for signs of emergence and discuss public health implications.

HLA-associated clinical progression correlates with epitope reversion rates in early human immunodeficiency virus infection

Human immunodeficiency virus type 1 (HIV-1) can evade immunity shortly after transmission to a new host but the clinical significance of this early viral adaptation in HIV infection is not clear. We present an analysis of sequence variation from a longitudinal cohort study of HIV adaptation in 189 acute seroconverters followed for up to 3 years. We measured the rates of variation within well-defined epitopes to determine associations with the HLA-linked hazard of disease progression. We found early reversion across both the gag and pol genes, with a 10-fold faster rate of escape in gag (2.2 versus 0.27 forward mutations/1,000 amino acid sites). For most epitopes (23/34), variation in the HLA-matched and HLA-unmatched controls was similar. For a minority of epitopes (8/34, and generally associated with HLA class I alleles that confer clinical benefit), new variants appeared early and consistently over the first 3 years of infection. Reversion occurred early at a rate which was HLA-dependent and correlated with the HLA class 1-associated relative hazard of disease progression and death (P = 0.0008), reinforcing the association between strong cytotoxic T-lymphocyte responses, viral fitness, and disease status. These data provide a comprehensive overview of viral adaptation in the first 3 years of infection. Our findings of HLA-dependent reversion suggest that costs are borne by some escape variants which may benefit the host, a finding contrary to a simple immune evasion paradigm. These epitopes, which are both strongly and frequently recognized, and for which escape involves a high cost to the virus, have the potential to optimize vaccine design.

Antiviral treatment for the control of pandemic influenza: some logistical constraints

Disease control programmes for an influenza pandemic will rely initially on the deployment of antiviral drugs such as Tamiflu, until a vaccine becomes available. However, such control programmes may be severely hampered by logistical constraints such as a finite stockpile of drugs and a limit on the distribution rate. We study the effects of such constraints using a compartmental modelling approach. We find that the most aggressive possible antiviral programme minimizes the final epidemic size, even if this should lead to premature stockpile run-out. Moreover, if the basic reproductive number R(0) is not too high, such a policy can avoid run-out altogether. However, where run-out would occur, such benefits must be weighed against the possibility of a higher epidemic peak than if a more conservative policy were followed. Where there is a maximum number of treatment courses that can be dispensed per day, reflecting a manpower limit on antiviral distribution, our results suggest that such a constraint is unlikely to have a significant impact (i.e. increasing the final epidemic size by more than 10%), as long as drug courses sufficient to treat at least 6% of the population can be dispensed per day.

Understanding the impact of Hib conjugate vaccine on transmission, immunity and disease in the United Kingdom

A rise in invasive Haemophilus influenzae type b (Hib) infections occurred 8 years after vaccine introduction in the United Kingdom. Aspects of Hib vaccine delivery unique to the United Kingdom have been implicated. The authors developed a fully age-structured deterministic susceptible-infected-resistant-susceptible mathematical model, expressed as a set of partial differential equations, to better understand the causes of declining vaccine effectiveness. We also investigated the consequences of the vaccine's impact on reducing Hib transmission for maintenance of immunity. Our findings emphasized the importance of maintaining high post-immunization antibody titres among age groups at greatest risk of invasive infections. In keeping with UK population-based estimates, low direct efficacy of immunological memory against disease was found, cautioning against over-reliance on evidence of priming alone as a correlate of population protection. The contribution of herd immunity to disease control was reinforced. Possible intervention strategies will be explored in subsequent work.

A scrapie epidemic in Cyprus

Scrapie is endemic in the sheep flocks of many countries, but good epidemiological information on this disease is scarce. Data on the initial stages of an epidemic are even more rare. We describe the ongoing epidemic of scrapie in Cyprus that has been tracked since it began in the mid-1980s. The early stages of the spread of scrapie from farm to farm, between 1985 and 2000, is analysed with a simple mathematical model. The flock-to-flock basic reproductive number (R0) for the spread of scrapie was estimated at between 1.4 and 1.8. The impact of interventions on the control of the epidemic are discussed from an epidemiological and economic point of view. Early identification of scrapie cases on farms can have a large impact on the number of farms affected. The long period before detection of disease in a flock means that policies based on whole-flock slaughter can be inefficient in preventing spread. Under a range of scenarios, a concentration of resources on early detection and quarantine may be more effective in terms of both the costs and control of the epidemic.

Introduction. Emerging infections: what have we learnt from SARS?

In the summer of 2003, as the first global severe acute respiratory syndrome (SARS) epidemic stuttered to a close, The Royal Society set about organizing a meeting that would take stock of the year's events and ask ‘what can we learn from SARS about emerging infections in general?’ Emerging infections are more than just a current biological fashion. The bitter ongoing experience of AIDS and the looming threat of an influenza pandemic teach us that the control of infectious disease is a problem we have not yet solved. It is a problem that needs to be addressed by a broad community. Scientists, policy makers and health care workers all need to be prepared, but prepared to do what? The purpose of the meeting was to use SARS as an example to enumerate the generic issues that must be considered when planning for the control of emerging infections.

Epidemiological implications of the susceptibility to BSE of putatively resistant sheep

The experimental infection of sheep with bovine spongiform encephalopathy (BSE) by the oral route and the likelihood that sheep were fed BSE-infected meat and bone meal has led to extensive speculation as to whether or not sheep are naturally infected with BSE. In response, the UK government has initiated the National Scrapie Plan (NSP), an ambitious £120 million per year project to create a BSE- and scrapie-resistant national sheep flock, by selectively breeding for a genotype of sheep believed to be resistant to both diseases. This genotype has recently been shown to be susceptible to BSE by intracerebral (i.c.) inoculation. Should these sheep be sufficiently susceptible to BSE via natural transmission, the NSP might fail. Here we estimate the susceptibility of this genotype to horizontal (sheep-to-sheep) transmission of BSE by comparison with more extensive oral and i.c. exposure data for other sheep genotypes. We show that a previous estimate of the risk of BSE transmission to sheep via the feedborne route remains robust. However, using a mathematical model for the within-flock transmission of BSE, we show that, while the best estimate indicates that the NSP should be successful, current data cannot exclude the failure of the NSP.

Scrapie epidemic in a fully PrP-genotyped sheep flock

In scrapie-affected sheep flocks, host PrP genotype plays a vital role in determining which sheep will succumb to scrapie and the incubation period. Consequently, within-flock scrapie dynamics is best understood within the context of the genotype profile of the flock. Here we describe a 17 month epidemic of scrapie in a commercially farmed flock of 230 genotyped Texel sheep. At the start of the study, 70% of the sheep were of three genotypes only: ARR/ARQ, ARH/ARQ and ARQ/ARQ. Only 15% of sheep encoded the disease-associated VRQ allele and only a single sheep (0.4%) was of the most susceptible VRQ/VRQ genotype. For susceptible genotypes there was a marked deficit (P<0.025) of older animals (> or =3 years), implying that some cases of scrapie had occurred previously. In the ensuing 17 months, 18 sheep of known genotype were confirmed positive for the disease: seven VRQ/ARQ, six VRQ/ARH, two VRQ/ARR, three ARQ/ARQ. Median ages at death were 2.7, 2.8, 4.2 and 3.8 years respectively. Mortality rates were 55, 86, 13 and 3% respectively. Survival analysis revealed a highly significant effect of genotype on survivorship, but no difference between VRQ/ARQ and VRQ/ARH, or between VRQ/ARR and ARQ/ARQ. There was no difference in the survivorship of middle- and older-age cohorts of susceptible sheep. Scrapie risk group (as defined by PrP genotype) was not associated with submission as a scrapie suspect but later found to be negative, or with dying of unknown causes on the farm.

The potential size and duration of an epidemic of bovine spongiform encephalopathy in British sheep

Because there is a theoretical possibility that the British national sheep flock is infected with bovine spongiform encephalopathy (BSE), we examined the extent of a putative epidemic. An age cohort analysis based on numbers of infected cattle, dose responses of cattle and sheep to BSE, levels of exposure to infected feed, and number of BSE-susceptible sheep in the United Kingdom showed that at the putative epidemic peak in 1990, the number of cases of BSE-infected sheep would have ranged from fewer than 10 to about 1500. The model predicts that fewer than 20 clinical cases of BSE in sheep would be expected in 2001 if maternal transmission occurred at a rate of 10%. Although there are large uncertainties in the parameter estimates, all indications are that current prevalence is low; however, a simple model of flock-to-flock BSE transmission shows that horizontal transmission, if it has occurred, could eventually cause a large epidemic.

Modelling the national scrapie eradication programme in the UK

In accordance with a policy to eliminate all transmissible spongiform encephalopathies from the food chain, a national untargeted ram breeding programme to eliminate scrapie in the UK is in the final stages of planning. Here we formulate a model of flock-to-flock scrapie transmission, in order to consider the effect of a targeted breeding programme which is in the early stages of consideration. We estimate the size of the susceptible flock population, and discuss implications for potential control programmes. Targeting all rams and ewes in highly susceptible flocks rather than rams in all flocks will eradicate scrapie more quickly, and so is likely to be beneficial as long as suitable penalties or incentives are available to facilitate their identification. A more restricted programme aimed only at highly affected flocks would be much easier to implement and crucially will eradicate scrapie just as quickly. This will leave behind a residue population of susceptible sheep, which could then be gradually removed by a more general breeding programme.

Infectious disease dynamics: What characterizes a successful invader?

Against the background of human immunodeficiency virus (HIV) and acquired immune deficiency syndrome (AIDS) and other potentially emerging (or re-emerging) infectious diseases, this review will focus on the properties which enable an infectious agent to establish and maintain itself within a specified host population. We shall emphasize that for a pathogen to cross a species barrier is one thing, but for it successfully to maintain itself in the new population is must have a 'basic reproductive number', R(0), which satisfies R(0) > 1. We shall further discuss how behavioural factors interweave with the basic biology of the production of transmission stages by the pathogen, all subject to possible secular changes, to determine the magnitude of R(0). Although primarily focusing on HIV and AIDS, we shall review wider aspects of these questions.

The flock-to-flock force of infection for scrapie in Britain

A postal survey of British sheep farmers provided information on the proportion of farms that experienced their first case of scrapie in each year between 1962 and 1998. We found no evidence of a large increase in the proportion of scrapie-affected farms prior to, during or following the epidemic of BSE in British cattle. After correcting for between-farm heterogeneity in the probability of acquiring scrapie, we estimated the yearly between-flock force of infection since 1962. The current force of infection is estimated at approximately 0.0045 per farm per year and combined with a simple model of scrapie spread provides an estimate of the average duration of a scrapie outbreak on an individual farm. Considering all farms, the average outbreak lasts for five years, but if only those farms that have cases in animals born on the farm are considered, it lasts 15 years. We use these parameter estimates to compare the proportion of farms with scrapie in time periods of different lengths. In the survey, 2.7% of farms had a case in 1998. The 5.3% of farms reporting having a case between 1993 and 1997 is consistent with the hypothesis that the scrapie force of infection remained constant over this period.

The signature of scrapie: differences in the PrP genotype profile of scrapie-affected and scrapie-free UK sheep flocks

The amino-acid sequence of the PrP protein plays an important role in determining whether sheep are susceptible to scrapie. Although the genetics of scrapie susceptibility are now well understood, there have been few studies of the PrP gene at the population level, especially in commercially farmed sheep. Here we describe the PrP genetic profiles of the breeding stock of four UK sheep flocks, comprising nearly 650 animals in total. Two flocks had been scrapie affected for about eight years and two were scrapie free. Scrapie-resistant PrP genotypes predominated in all flocks but highly susceptible genotypes were present in each case. The distribution of PrP genotypes was similar in the scrapie-affected and scrapie-free flocks. The former, however, showed a slight but significant skew towards more susceptible genotypes despite their previous losses of susceptible sheep. Surprisingly, this skew was apparent in younger, but not older, sheep. We suggest that these patterns may occur if sheep flocks destined to become scrapie affected are predisposed by a genetic profile skewed towards susceptibility. The age structure of the scrapie-affected flocks suggests that the number of losses attributable directly or indirectly to scrapie considerably exceeds that recognized by the farmers, and also that significant losses may occur even in sheep of a moderately susceptible genotype. Similar patterns were not detected in the scrapie-free flocks, indicating that these losses are associated with scrapie infection as well as genotype.

Scrapie infections initiated at varying doses: an analysis of 117 titration experiments

An analysis of 117 titration experiments in the murine scrapie model is presented. The experiments encompass 30 years' work and a wide range of experimental conditions. To check that the experimental designs were reasonably consistent over time, comparisons were made of size, duration, source of inoculum, etc., in each experiment. These comparisons revealed no systematic trends that would render invalid comparisons across experiments. For 114 of the experiments it was possible to calculate the dose at which half of the challenged animals were infected (the ID50). These 114 experiments were then combined on the basis of relative dose (i.e. tenfold dilution relative to the ID50). This created a data set in which over 4000 animals were challenged with doses of scrapie ranging from four orders of magnitude below to five orders of magnitude above the ID50. Analysis of this data reveals that mean incubation periods rise linearly with logarithmic decreases in dose. A one unit increase in relative dose (i.e. a tenfold increase in actual dose) will, on average, decrease the incubation period by 25 days. At ID50 the average incubation period in this data set is 300 days. Within a single dose, in a single experimental model, incubation periods have a distribution close to normal. Variability in incubation period also rises linearly as dose decreases. There is no age or sex effect upon the probability of infection, but female mice have incubation periods that are, on average, nine days shorter than their male counterparts and young mice have incubation periods that are longer by seven days. Although many of these patterns are apparent in the results of single titration curves, they can be more rigorously investigated by considering the outcome for thousands of mice.

Descriptive epidemiology of scrapie in Great Britain: results of a postal survey

In 1998, a questionnaire was sent to 11,554 British sheep farmers to determine how many believed that scrapie cases had occurred in their flock; 61.4 per cent of them responded anonymously. The results indicated that 14.9 per cent of farmers with more than 30 breeding ewes thought that they had ever experienced scrapie in their flock and 2.7 per cent thought that they had had cases in the past 12 months. A comparison of these results with the number of farmers reporting suspect scrapie cases to MAFF, in accordance with the statutory requirement, suggests that only 13 per cent of farmers who suspect that they may have cases of scrapie are currently reporting them. Scrapie occurred in all regions of the country but there was an apparent regional variation. Larger farms and those with purebred sheep appeared to be at greater risk of having cases. Other differences between affected and unaffected farms included lambing practices and sheep purchasing policy. On the majority of farms the first case occurred in a purchased animal. The survey also revealed a need for the provision of further information about scrapie to farmers.

Viral dynamics of acute HIV-1 infection

Viral dynamics were intensively investigated in eight patients with acute HIV infection to define the earliest rates of change in plasma HIV RNA before and after the start of antiretroviral therapy. We report the first estimates of the basic reproductive number (R(0)), the number of cells infected by the progeny of an infected cell during its lifetime when target cells are not depleted. The mean initial viral doubling time was 10 h, and the peak of viremia occurred 21 d after reported HIV exposure. The spontaneous rate of decline (alpha) was highly variable among individuals. The phase 1 viral decay rate (delta(I) = 0.3/day) in subjects initiating potent antiretroviral therapy during acute HIV infection was similar to estimates from treated subjects with chronic HIV infection. The doubling time in two subjects who discontinued antiretroviral therapy was almost five times slower than during acute infection. The mean basic reproductive number (R(0)) of 19.3 during the logarithmic growth phase of primary HIV infection suggested that a vaccine or postexposure prophylaxis of at least 95% efficacy would be needed to extinguish productive viral infection in the absence of drug resistance or viral latency. These measurements provide a basis for comparison of vaccine and other strategies and support the validity of the simian immunodeficiency virus macaque model of acute HIV infection.

In vivo HIV-1 replicative capacity in early and advanced infection

OBJECTIVE

Previous studies on patients treated with potent antiretroviral therapy have shown that viral clearance rates do not tend to change between early and advanced HIV-1 infection. Our objective was to investigate whether the other major aspect of virus dynamics, viral replicative capacity, does change. In vitro work has indicated that the viral replicative, capacity increases but in vivo evidence has been lacking.

METHODS

As an in vivo measure of the viral replicative capacity, we studied the rate of rebound of plasma HIV RNA level during a 1-week therapy interruption in previously untreated patients who had received 2 weeks of antiretroviral therapy.

RESULTS

Such therapy in five previously drug-naive patients with high CD4 lymphocyte counts (mean, 611 x 10(6)/l) and five patients with low counts (mean, 49 x 10(6)/l) led to a mean 2.2 log10 copies/ml decrease in plasma HIV-1 levels (from 5-6 log10 copies/ml) in 2 weeks. This was similar in the two groups. Interruption of therapy for the ensuing week resulted in a stable HIV-1 level for approximately 2 days followed by a rebound towards pretherapy level, which was much more marked in the patients with low CD4 cell counts (estimated mean rise 2.22 log10 versus 1.06 log10 copies/ml; P < 0.02). After restarting therapy, HIV RNA levels returned to pre-interruption levels.

CONCLUSIONS

These findings need confirmation, but the ability of HIV-1 to replicate in vivo appears to increase during HIV-1 infection. This increased replicative capacity, for which there are several potential explanations, may be the cause of gradual CD4 lymphocyte depletion.

Mathematical modelling of effectiveness

The effectiveness of a vaccine can be broadly defined as a practical measure of its costs and benefits when used in a community setting. What then is the relationship between a vaccine's efficacy and its effectiveness? Effectiveness certainly includes efficacy, but also encompasses secondary effects of vaccination, long-term efficacy of a vaccine (beyond that measured in conventional efficacy trials), the impact of vaccinating against one strain upon cross-reacting infections, costs of vaccination programmes and logistic considerations for vaccine delivery. This paper considers some of the biological determinants of effectiveness namely; secondary effects, long-term efficacy and competitive interactions amongst strains. Mathematical models of the transmission dynamics of infection and its disruption by vaccination are used as tools to help unravel some of the complexities that may arise when making interventions in non-linear biological systems.

Population biology, evolution, and immunology of vaccination and vaccination programs

The purpose of prophylactic vaccination is to reduce morbidity and mortality in a population. Many questions related to the design of vaccines and vaccination programs require a population standpoint for their sharp formulation and laboratory and field studies to understand their immunologic background. Practical suggestions of the workshop included increased studies of age-specific immunity, better immunoepidemiologic surveillance, better design of efficacy studies, and more systematic sampling of parasite strains to study the evolutionary pressure exerted by vaccines. Theoretical immunology has much to contribute. One of the realizations of the workshop was the value of a strong interdisciplinary approach in vaccine development, utilizing relevant contributions from immunology, population biology, mathematical modeling, epidemiology, molecular biology, and virology.

Vaccines and their impact on the control of disease

Disease control exerts evolutionary pressures that can lead to the evolution of resistance. This has been seen in a spectacular fashion in the evolution of resistance to antibiotics, anti-virals and anti-parasitics. Despite intense (and often successful) attempts to control infectious diseases through vaccination, there is still rather little evidence of the emergence of strains of pathogen resistant to vaccines. This chapter asks why this should be so and what are the exceptions indicating that the evolution of vaccine resistance, though currently rare, is a possibility that should be planned for.

Resource competition as a mechanism for B cell homeostasis

Cellular competition for survival signals offers a cogent and appealing mechanism for the maintenance of cellular homeostasis [Raff, M. C. (1992) Nature (London) 356, 397-400]. We present a theoretical and experimental investigation of the role of competition for resources in the regulation of peripheral B cell numbers. We use formal ecological competition theory, mathematical models of interspecific competition, and competitive repopulation experiments to show that B cells must compete to persist in the periphery and that antigen forms a part of the resources over which B cells compete.

AIDS: decline and fall of immune surveillance?

Recent observations cast doubt on the view that cytotoxic T cells play a key role in keeping HIV-1 infection in check, and that it is the decline in this mechanism of immune surveillance that permits progression to AIDS.

Modelling HIV vaccination

Relatively recently, mathematical models have been applied to issues r elated to HIV vaccination. Significant progress has been made towards understanding how rather ineffective vaccines will perform in trials and in the community, but some areas still need research.

Vaccination, evolution and changes in the efficacy of vaccines: a theoretical framework

The evolution of vaccine-resistant strains of infectious agents is potentially a huge problem for their control by immunization. Yet, for many infectious diseases, it has been possible to drive them to the verge of extinction without vaccine escape mutants arising. This paper establishes a theoretical framework within which to ask why this should be so, what properties of vaccines allow this situation and what might happen in situations where vaccine escape mutants do arise.

The intrinsic transmission dynamics of tuberculosis epidemics

In developed countries the major tuberculosis epidemics declined long before the disease became curable in the 1940s. We present a theoretical framework for assessing the intrinsic transmission dynamics of tuberculosis. We demonstrate that it takes one to several hundred years for a tuberculosis epidemic to rise, fall and reach a stable endemic level. Our results suggest that some of the decline of tuberculosis is simply due to the natural behaviour of an epidemic. Although other factors must also have contributed to the decline, these causal factors were constrained to operate within the slow response time dictated by the intrinsic dynamics.

The regulation of malaria parasitaemia: parameter estimates for a population model

Classical studies of non-immune individuals infected with Plasmodium falciparum reveal that the infection may be regulated for long periods at a relatively stable parasite density, despite the enormous growth potential of a parasite that continually replicates within host erythrocytes. This suggests that the parasite population may be controlled by density-dependent mechanisms, and in theory the most obvious of these is competition between parasites for host erythrocytes. Here we evaluate the role of this mechanism in the regulation of parasitaemia, by modelling the basic population interaction between parasites and erythrocytes in a form that allows all the essential parameters to be estimated from clinical data. Our results show that competition cannot account for the total regulation of P. falciparum, but when combined with immune mechanisms it may play a more important role than is generally supposed. Further analysis of the model indicates that in the long term, parasite replication at low parasite densities can contribute significantly to the high degree of anaemia observed in natural infection, a conclusion which is not obvious from simple clinical observation.

Modelling T cell memory

A new mathematical model of T helper-cell activation and proliferation is investigated. The model incorporates recent data and theories about memory T cells. It accounts for the interacting population dynamics of resting, activated and memory T helper cells, interleukin 2 and replicating antigen, and is able to mimic a broad range of available data on T helper-cell proliferation and the effects of interleukin 2. The model is tested against existing in vitro data. It is then used to make novel interpretations of some recent experimental findings and predictions about the outcome of further experiments. Predictions made by the model fall into three groups concerning persistent infections, cell transfer experiments, and the return of memory cells to the resting state. The model predicts the existence of a group of persistent infections which result from slow growing replicating antigens and can be cleared by a boosting dose of antigen. A threshold is derived for the number of cells that must be transferred in order to transfer long-term immune memory from one animal to another. The existence of such a threshold implies that when small numbers of cells are transferred, or the transferred cells are in the resting state, cells alone cannot confer long-term memory on a recipient animal. However, if enough activated cells are transferred, it is possible to transfer long-term immune memory without antigen. The biological significance of a pathway whereby memory cells can lose their phenotypic and functional differences to return to the resting state is studied. A threshold concerning the rate of that return is derived; and it is only if the rate of return is above that threshold is there any impact on the response to a replicating antigen.

Prophylactic vaccines, risk behavior change, and the probability of eradicating HIV in San Francisco

Theory is linked with data to assess the probability of eradicating human immunodeficiency virus (HIV) in San Francisco through the use of prophylactic vaccines. The necessary vaccine efficacy levels and population coverage levels for eradication are quantified. The likely impact of risk behavior changes on vaccination campaigns is assessed. The results show it is unlikely that vaccines will be able to eradicate HIV in San Francisco unless they are combined with considerable reductions in risk behaviors. Furthermore, if risk behavior increases as the result of a vaccination campaign, then vaccination could result in a perverse outcome by increasing the severity of the epidemic.

Modelling the impact of mass vaccination against hepatitis B. I. Model formulation and parameter estimation

A new model of the transmission dynamics of hepatitis B virus in countries with high transmission rates is presented. The model is age and sex stratified, and includes details of host demography. Details of hepatitis B natural history, such as the existence of infectious and non-infectious carriers, are included. The biological assumptions of the model are discussed in full and related to the model's equations. Hepatitis B epidemiological data is reviewed with special emphasis on the estimation of model parameter values from field data. A full set of model parameter values are derived. Possible uses of the model in the assessment of strategies of mass vaccination are discussed.

Quasispecies dynamics and the emergence of drug resistance during zidovudine therapy of HIV infection

OBJECTIVE

To investigate the roles of mutation, competition and population dynamics in the emergence of drug resistant mutants during zidovudine therapy.

DESIGN

A mathematical model of the population dynamics of the viral quasispecies during zidovudine therapy was investigated.

METHODS

The model was used to simulate changes in the numbers of uninfected and infected cells and the composition of the viral quasispecies in the years following initiation of therapy. Resulting scenarios in asymptomatic and AIDS patients were compared. The model was also used to investigate the efficacy of a treatment regimen involving alternating zidovudine and dideoxyinosine therapy.

RESULTS

The behaviour of the model can be divided into three stages. Before therapy, mutation maintains a small pool of resistant mutants, outcompeted to very low levels by sensitive strains. When therapy begins there is a dramatic fall in the total viral load and resistant strains suddenly have the competitive advantage. Thus, it is resistant strains that infect the rising number of uninfected CD4+ cells. During this second stage the rapid effects of population dynamics swamp any effects of mutation between strains. When the populations of infected and uninfected cells approach their treatment equilibrium levels, mutation again becomes important in the slow generation of highly resistant strains.

CONCLUSIONS

The short-term reduction in viral replication at the initiation of therapy generates a pool of uninfected cells which cause the eventual increase in viral burden. This increase is associated with (but not caused by) a rise in frequency of resistant strains which are at a competitive advantage in the presence of the drug. When therapy is ceased, reversion of resistance is slow as resistant strains are nearly as fit as sensitive strains in the absence of drug.

Germinal centre destruction as a major pathway of HIV pathogenesis

Human immunodeficiency virus (HIV)-induced destruction of follicular dendritic cells (FDCs), which are important in immunological memory, may be a major pathway of HIV pathogenesis. We use a mathematical model to investigate this hypothesis and conclude that a low level of FDC destruction could ultimately result in loss of control of HIV. Their slow turnover makes them good candidates for the part of the immune system that fails during the long period of HIV infection. As FDC destruction is essentially a misdirected immune response, too much immunotherapy may be detrimental. Our model shows how to estimate this critical level of immunotherapy. We derive an expression for the time taken to the loss of immune control. Transient changes in the viral growth rate before the immune system fails do not affect this time, providing a possible explanation for the results of the Concorde trial. We suggest that inducible B cell function is a good potential marker of disease progression, indicating the functional ability of the FDC network. Finally, we rereview data in the light of the FDC theory, paying particular attention to data on CD4+ numbers and function that are inconsistent with the classical view of HIV pathogenesis.

Imperfect vaccines and herd immunity to HIV

A number of prophylactic vaccines against human immunodeficiency virus (HIV) have passed through phase I clinical trials, and phase II clinical trials are now being planned. These vaccines are not expected to be perfect and might fail in a number of different ways. This paper shows how to equate different aspects of imperfection in a prophylactic vaccine in terms of impact upon levels of herd immunity, and hence upon the vaccine coverage required for eradication. Such comparisons reveal that an otherwise perfect vaccine that gives protection which wanes with a half-life of 10 years is only as good as a vaccine that works in 30% of people giving them complete, lifelong protection. The paper goes on to compare predicted patterns of seroconversion that would be observed in clinical trials and in community-wide vaccination campaigns for vaccines that confer the same levels of herd immunity but are imperfect in different ways.

The balance of power between HIV and the immune system

There are several theories of the pathogenesis of HIV that attempt to explain the long and variable delay between infection and disease. Here, each theory is reviewed within the context of a simple mathematical model of the interactions between HIV and the immune system. From this model, a theoretical index of progression has been derived that combines elements from each proposed mechanism.

Models of interactions between HIV and other pathogens

We investigate possible interactions between HIV and other pathogens that would arise if HIV replication were enhanced by the activation of T helper cells specific to other pathogens. Using mathematical models of the population dynamics of T helper cells, HIV and other pathogens we address three facets of the interactions between HIV and other pathogens: enhanced HIV replication due to immune stimulation by other pathogens; modified immune control of other pathogens due to immunosuppression by HIV; and the vicious circle formed by positive feedback between these two effects. The models predict that there is a correlation between higher levels of activated TH cells and disease progression and that there is a threshold number of activated TH cells above which the HIV infected immune system is unable to control pre-established pathogens. This threshold marks the boundary between a suppressed but still functioning immune system and the vicious circle of CD4 cell depletion that marks the final stages of AIDS.

Competition between zidovudine-sensitive and zidovudine-resistant strains of HIV

OBJECTIVE

To investigate competitive interactions between zidovudine-sensitive and resistant strains of HIV within the context of host-parasite population dynamic interactions between CD4+ cells and HIV.

DESIGN

A mathematical model of the population dynamics of CD4+ cells, sensitive HIV and resistant HIV is developed.

METHODS

The model is analysed numerically and analytically and model predictions are compared with previously published data on population dynamics of HIV and CD4+ cells in patients receiving zidovudine. A threshold result describing the critical dose of zidovudine above which resistant HIV will out-compete sensitive HIV is derived, as are expressions describing the critical effective doses for the eradication of sensitive and resistant strains. Numerical simulations of the dynamics of the shift from the pre-treatment, equilibrium to the treatment equilibrium are presented and an analytic expression approximating the time taken until virus growth restarts is derived.

RESULTS

It is shown that competition between strains of virus is the important factor determining which type of virus will eventually start to grow during the course of zidovudine treatment, but host-parasite interactions are the important determinant of when viral resurgence occurs.

CONCLUSIONS

Although resistant strains are observed after prolonged treatment with zidovudine, this model suggests that it is the growing supply of uninfected CD4+ cells which causes the eventual upsurge in viral burden.

Model-based comparisons of measles immunization strategies using high dose Edmonston-Zagreb type vaccines

The World Health Organization has recently made a new recommendation for measles immunization in areas with very high rates of transmission. The new policy will involve a switch to the high potency Edmonston-Zagreb (E-Z) vaccine (a strain with improved efficacy in the presence of maternally-derived, specific antibody), targeting immunization at six-month-old infants. We present a mathematical model of measles transmission that can be used to assess the likely impact of cohort immunization on the incidence of infection using the new strain of vaccine. Data requirements of the model are discussed, with special reference to the critical issue of age-specific vaccine efficacy. Currently available information on seroconversion rates achieved with the new strain are summarized. Results are presented which endorse the new WHO recommendations, predicting considerable benefits, in particular, to those most at risk of measles morbidity and mortality. Furthermore, integration of E-Z with the third diphtheria, pertussis, tetanus (DPT) dose at three-four months should be considered as an alternative option, particularly if combined with some additional coverage at nine months of age.

A mathematical model of vaccination against HIV to prevent the development of AIDS

Vaccination and post-exposure immunization against the human immunodeficiency viruses (HIV-1 and HIV-2) faces the problem of the extensive genetic and antigenic variability of these viruses. This raises the question of what fraction of all possible antigen strains of the virus must be recognized by the immune response to a vaccine to prevent development of acquired immunodeficiency disease (AIDS). The success of a vaccine can depend on the variability of the target epitopes. The different HIV variants must be suppressed faster than new escape mutants can be produced. In this paper the antigenic variation of HIV during an individual infection is described by a stochastic process. The central assumption is that antigenic drift is important for the virus to survive immunological attack and to establish a persistent infection that leads to the development of AIDS after a long incubation period. The mathematical analysis reveals that the fraction of antigenic variants recognized by the immune response, that is induced by a successful immunogen, must exceed 1-1/R, where R is the diversification rate of the virus population. This means that if each HIV strain can produce, on average, five new escape mutants, then more than 80% of the possible variants must be covered by the immunogen. A generic result of the model is that, no matter how immunogenic a vaccine is, it will fail if it does not enhance immune attack against a sufficiently large fraction of strains. Furthermore, it is shown that the timing of the application of post-exposure immunization is important.

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.

Mixing ecology and epidemiology

Mixing matrices can be used to describe subgroup interactions in mathematical models which have heterogeneity in population structure. A discussion is presented of two different approaches to the formulation of such mixing matrices. The relation between the two different methods is discussed, using examples based upon models of the transmission dynamics of HIV. There follows a discussion of the application of the mixing matrix approach to other areas in population biology, and a complementary overview of recent advances in theoretical ecology that may have applications in theoretical epidemiology.