Malaria and immunity during pregnancy and postpartum: a tale of two species.

It is well established that pregnant women are at an increased risk of Plasmodium falciparum infection when compared to non-pregnant individuals and limited epidemiological data suggest Plasmodium vivax risk also increases with pregnancy. The risk of P. falciparum declines with successive pregnancies due to the acquisition of immunity to pregnancy-specific P. falciparum variants. However, despite similar declines in P. vivax risk with successive pregnancies, there is a paucity of evidence P. vivax-specific immunity. Cross-species immunity, as well as immunological and physiological changes that occur during pregnancy may influence the susceptibility to both P. vivax and P. falciparum. The period following delivery, the postpartum period, is relatively understudied and available epidemiological data suggests that it may also be a period of increased risk of infection to Plasmodium spp. Here we review the literature and directly compare and contrast the epidemiology, clinical pathogenesis and immunological features of P. vivax and P. falciparum in pregnancy, with a particular focus on studies performed in areas co-endemic for both species. Furthermore, we review the intriguing epidemiology literature of both P. falciparum and P. vivax postpartum and relate observations to the growing literature pertaining to malaria immunology in the postpartum period.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Population dynamics of HIV within an individual after treatment with zidovudine.

A new mechanism is proposed for the apparent breakthrough of HIV that occurs approximately 6 months after the commencement of therapy with zidovudine (AZT). Using a simple mathematical model of the interacting population dynamics of HIV and its major host cell in the circulation (the CD4+ lymphocyte), predicted patterns of HIV plasma viraemia in the weeks following treatment with zidovudine are generated. These are in close agreement with observed patterns despite the fact that the model contains no mechanisms for the development of drug-resistant strains of virus. It is suggested that the patterns of viral abundance observed during the first 6 months after treatment may be the result of non-linearities in the interactions between HIV and CD4+ cells, and that it is only after the first post-treatment burst of viral production that drug resistance plays an important role.

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.

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.

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.

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.

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.