Human immunodeficiency virus (HIV) infects approximately 0.5% of the world population and is a major cause of morbidity and mortality worldwide. A vaccine for HIV is urgently required, and a variety of vaccine modalities have been tested in animal models of infection. A number of these studies have shown protection in monkey models of infection, although the ability of the vaccine to protect appears to vary with the viral strain and animal model used (8
). The recent failure of a large vaccine study in humans (1
) suggests that further understanding of the basic dynamics of infection and the impact of vaccination are required in order to understand the variable efficacies of vaccination in different infections.
The initial ability of HIV to propagate within the host is determined by the abundance of target cells (e.g., CD4+ T lymphocytes) the virus can infect in order to produce progeny, by the replicative capacity of the virus, and by how cytopathic it is to infected cells. At later stages of the disease, in addition to changes in the target cell availability, there may also be changes in virus-specific properties, such as the ability of the virus to reproduce and the survival of productively infected cells as a result of changes in immune pressure and viral evolution. These parameters may be variable among individuals and within one individual over time and affect the impact of vaccination. In order to compare the efficacies of vaccination strategies, we need a quantitative measure of the factors that influence virus replication.
In this work, we focus on the basic reproductive ratio (R0
) as a measure of vaccine efficacy in the acute phase of infection. In epidemiology, R0
measures the potential for the spread of an epidemic and is defined as the average number of people infected by one infected individual in a susceptible population. If this number is below 1, the disease will not spread in a population. Therefore, the knowledge of R0
allows one to estimate the fraction of a population that needs to be vaccinated in order to eradicate the disease. Analogously, in host-pathogen dynamics, the basic reproductive ratio is defined as the number of infected cells generated by one infected cell during its lifetime at the start of infection, i.e., before any depletion of target cells. In order for the infection to spread within the host, this number has to be larger than 1; otherwise, the infection will be cleared before it has a chance to spread. The basic reproductive ratio will depend on the ability of virus to infect cells (“infectivity”), on the rate of virion production by infected cells, on the lifetime of infected cells, and on the rate at which free virus is cleared. The aim of vaccines is therefore to create virus-specific immunity that changes any of these parameters and thus decreases the basic reproductive ratio of the virus, preferably below 1 (so that infection does not spread beyond the initially infected cells). The importance of R0
in HIV vaccination, in order to assess how much protection a particular vaccine can achieve, has been stressed previously (11
). Specifically, a variety of different animal models have been used to study HIV vaccination. They differ in a number of ways, particularly in the virulence and cell tropism of the virus. Comparison between models may be difficult because of differences in the underlying dynamics of infection. For example, it may be more difficult to prevent CD4+
T-cell depletion in a very virulent animal model than in other infections, because of the higher underlying growth rate. Thus, a vaccine may appear efficacious in one model but ineffective in another, despite the fact that it may have the same impact on viral growth. Measurement of R0
allows comparison of the effectiveness of different vaccines within a given animal model, as well as across different models. It could be a very useful and common standard to compare different vaccination protocols.
The basic reproductive ratio can be determined from the rate of exponential growth of virus in the initial period, during which the target cell levels are almost constant (14
). However, in monkeys infected with the same type of simian immunodeficiency virus (SIV) there is in fact very little variation in the basic reproductive ratio determined from the initial exponential growth between controls and vaccinees, despite the variety of outcomes later in infection. Different factors identified as possible predictors of disease progression (29
), such as the peak viral load, target cell nadir, decay rate of virus following peak viremia, set point viral load, and chronic target cell levels, all correlate poorly or not at all with the differences in the reproductive ratio determined from the primary exponential growth phase (29
). In particular, it is not possible to assess the efficacy of cytotoxic-T-lymphocyte (CTL)-based vaccines on the basis of the basic reproductive ratio, because there is no effect of vaccination on viral growth before approximately 10 days postinfection, which is at the end of the exponential growth period (4
We have recently shown the existence of a strong correlation between the viral load at peak and the target cell depletion in the acute phase (7
). Using this correlation, one can show that vaccination results in the reduction of the peak viral load and of acute CD4+
T-cell depletion, thus improving the chronic-phase prognosis.
The dependence of the nadir in the CD4+
T-cell count on the viral peak can be obtained from the standard model of virus dynamics (7
). Here, we show that this relationship between the viral peak and the number of target cells 1 week after the peak (corresponding approximately to the minimum number of target cells in primary infection) is parameterized by the basic reproductive ratio of the virus. In other words, the decrease in the peak viral load leads to less target cell depletion at nadir, and both are a consequence of a lower basic reproductive ratio. Thus, we can in principle determine the basic reproductive ratio from experimental data on the viral peak and target cell nadir. We show that this relationship is indeed supported by experimental data from CXCR4-tropic simian-human immunodeficiency virus (SHIV) infection (for viral loads and CD4+
T-cell counts in peripheral blood) and for CCR5-tropic SIV infection data (for plasma viral loads and memory CD4+
T-cell depletion in the gut).
We show that the reproductive ratio estimated from the viral peak and the target cell nadir, which we call the “reproductive ratio at the peak,” is significantly lower than the basic reproductive ratio estimated from the exponential growth. In addition, we found that in vaccinated animals the reproductive ratio at the peak is on average twofold lower than in control animals. We attribute this difference to the cellular immune response appearing before the peak viral load, around day 10 of infection, and changing the properties of the virus and infected-cell dynamics (e.g., decreasing the lifetime of infected cells through the cytolytic function of CTLs or changing infectivity or virus production through the release of cytokines). Thus, we propose that the “reproductive ratio at the peak,” a measurement that includes information on both the viral peak and the target cell nadir, can be useful as a standard to compare vaccine protocols.