Predicting the Impact of a Nonsterilizing Vaccine against Human Immunodeficiency Virus

Studies of human immunodeficiency virus (HIV) vaccines in animalmodels suggest that it is difficult to induce complete protectionfrom infection (sterilizing immunity) but that it is possibleto reduce the viral load and to slow or prevent disease progressionfollowing infection. We have developed an age-structured epidemiologicalmodel of the effects of a disease-modifying HIV vaccine thatincorporates the intrahost dynamics of infection, a transmissionrate and host mortality that depend on the viral load, the possibleevolution and transmission of vaccine escape mutant viruses,a finite duration of vaccine protection, and possible changesin sexual behavior. Using this model, we investigated the long-termoutcome of a disease-modifying vaccine and utilized uncertaintyanalysis to quantify the effects of our lack of precise knowledgeof various parameters. Our results suggest that the extent ofviral load reduction in vaccinated infected individuals (comparedto unvaccinated individuals) is the key predictor of vaccineefficacy. Reductions in viral load of about 1 log₁₀ copies ml^–1would be sufficient to significantly reduce HIV-associated mortalityin the first 20 years after the introduction of vaccination.Changes in sexual risk behavior also had a strong impact onthe epidemic outcome. The impact of vaccination is dependenton the population in which it is used, with disease-modifyingvaccines predicted to have the most impact in areas of low prevalenceand rapid epidemic growth. Surprisingly, the extent to whichvaccination alters disease progression, the rate of generationof escape mutants, and the transmission of escape mutants arepredicted to have only a weak impact on the epidemic outcomeover the first 25 years after the introduction of a vaccine.

INTRODUCTION

Top

Introduction

Several different human immunodeficiency virus (HIV) vaccinationstrategies have been proposed. These include therapeutic vaccination(administered to those who are already infected) and prophylacticvaccination (administered prior to infection) that either preventsinfection (sterilizing vaccination) or ameliorates disease (disease-modifyingvaccination). Thus far, both therapeutic and sterilizing vaccinationstrategies for HIV have proved elusive (35). However, recentstudies in primates suggest that it is possible to produce disease-modifyingvaccines that significantly reduce viral loads and AIDS mortality(1, 11, 22, 51). These vaccines appear to work primarily byinducing cytotoxic T lymphocyte (CTL) immunity. If these resultscan be reproduced in human infections, it seems likely thatin the short to medium term a human vaccine for HIV may emergethat significantly increases the survival time of infected individuals.Although such disease-modifying vaccines would clearly benefitinfected individuals by delaying disease, their long-term impacton the epidemic as a whole is less clear. In particular, immunologicalescape and subsequent disease progression have been seen inseveral vaccination studies (9, 10). If a vaccine reduces viralloads, then patients may experience a longer latent period ofinfection but still ultimately progress through the same advancedstages of disease seen in a "natural" infection. Thus, overalltransmission may be increased by the addition of this extraasymptomatic period of transmission on top of the normal transmissionperiod (4). In addition, there is concern that optimism overthe effects of vaccination may lead to an increase in high-risksexual behavior and an increase in HIV transmission (18), ashas been observed following antiretroviral therapy (25; T. Kellogg,W. McFarland, and M. Katz, Letter, AIDS 13:2303-2304, 1999).

The aims of any vaccination campaign utilizing a disease-modifyingvaccine should be to maximize the survival time of each infectedindividual and to minimize the number of new infections. Understandinghow disease-modifying vaccines will affect the spread of HIVrequires the incorporation of both intrahost effects (such ashow viral loads and mortality change with time) and populationeffects (such as how vaccination affects the sexual transmissionof HIV and how sexual activity changes with age). Importantquestions to be addressed regarding the potential use of disease-modifyingvaccines are as follows: (i) what will be the likely impactof these vaccines on the epidemic as a whole, (ii) what vaccineeffects are most important in determining this outcome, and(iii) in what settings will the vaccine be most effective?

Mathematical modeling allows a theoretical analysis of suchquestions based on our understanding of the intrahost and interhostdynamics of HIV. Previous models have provided insights intothe effects of antiretroviral therapy, as well as partiallyeffective vaccines (which induce sterilizing immunity in onlya proportion of vaccinated individuals), live attenuated vaccines,and therapeutic vaccines or immunotherapies administered toinfected individuals (3, 5, 15, 16, 18, 19, 45). The CTL-inducingvaccines currently being tested in monkeys appear unable toprevent infection, but instead appear able to modify the subsequentcourse of disease. Thus, although they are only partially effectivein one sense, they differ substantially from previously studiedpartially effective vaccines, which blocked infection in onlya fraction of vaccinees. For this reason, we prefer to referto these new candidate HIV vaccines as disease-modifying vaccines.We have developed a model that allows us to investigate thelikely outcomes of a disease-modifying vaccination strategyas well as to identify the factors that are most important toits success. The model incorporates uncertainty in the rateand duration of vaccination, the effects of vaccination on reducingviral loads and disease progression, the rate of emergence andtransmission of escape mutants, and the extent to which vaccinationmay increase the rate of high-risk sexual activity (Table 1).We used this model to predict the outcome of disease-modifyingvaccination for HIV type 1 (HIV-1) and the impact of factorssuch as the extent to which vaccination reduces the viral loador the disease progression rate of infected individuals, theduration of protection from vaccination, and the emergence ofviral escape mutants.

View this table:
[in this window]
[in a new window]
TABLE 1. Parameter values^a

A structured model of HIV infection, transmission, and vaccination. (i) Disease-modifying vaccines.

Top

A structured model of...

In order to analyze the effects of a disease-modifying vaccine,one needs to consider how the vaccine may alter the viral loadand mortality of an infected individual over the total durationof infection. In addition, because the duration of infectionis long compared to the life span of an individual, one alsoneeds to consider how aging may affect transmission of the virus.A vaccine that reduces disease progression, for example, willlead to disease occurring at an older age. The rate of sexualpartner change (13, 34), the frequency of intercourse, and therisk of transmission decrease with age (48). Importantly, olderindividuals are not only less likely to transmit the virus,but they are more likely to have partnerships with other olderpeople (8, 23), who are themselves less likely to transmit thevirus. Our model, which is age structured, incorporates allof these effects and allows us to calculate the rate of HIVtransmission and mortality in a population (24). We utilizedepidemiological data on the changes in viral load (36, 43) andmortality (7, 50) with the duration of infection as well associal survey data on age-related partner change rates (13,34), age-related risks of transmission (48), and sexual mixingbetween age groups (8, 23) to set parameter ranges in the model.

We use the term "behavioral infectiousness" to describe thechanges in transmission that are dependent on the sexual behaviorof different age groups, and we differentiate those changesfrom changes in transmission due to the disease stage, whichwe term "virological infectiousness." The virological infectiousnessat different times after infection is correlated with the viralload. Our model incorporates the observed epidemiological relationshipthat the probability of transmission increases 2.45-fold forevery log₁₀ increase in the viral load (48). We also assumedthat the rates of male-to-female and female-to-male transmissionare equal, as reported for a study in Rakai, Uganda (29, 48).The risk of transmission from an infected individual in ourmodel is therefore a function of both his or her behavioralinfectiousness and virological infectiousness (see reference24 and Appendix).

Even though we utilized experimental and social survey dataon both virological and behavioral infectiousness, both sourcesof data have their limitations. Sexual survey data, in particular,are notoriously unreliable, with male estimates of the numberof sexual partners outnumbering those of females up to threefold(41). For our study, we utilized the female estimates and balancedthe sexual mixing matrix to compute transmission probabilities(17). Moreover, some authors suggest that sexual behavior maybe quite consistent between regions as diverse as the UnitedStates and Africa (56), while other data suggest that behaviorsmay be quite different across cultures and also over time (26,32, 42). To avoid any dependence of our results on particularpopulation variables, we considered the effects of vaccinationin many different populations (with different epidemiologicand social parameters) that were randomly generated from ourbaseline population, which is based on the described empiricaldata (see Materials and Methods).

(ii) Intrahost dynamics.

Top

(ii) Intrahost dynamics.

In animal models of HIV infection, prior vaccination is ableto reduce viral loads by $~$ 1 log₁₀ copies ml^–1 for acuteinfections and up to $~$ 3 log₁₀ copies ml^–1 for chronic infections(compared to unvaccinated control animals). This protectionappears to be dependent largely on CTL-derived immunity, andmost infectious challenges are performed within weeks or monthsof vaccination (1, 11, 20-22, 38, 51). Studies of highly exposedbut uninfected individuals suggest that immunity may be relativelyshort-lived and that regular boosting with an antigen may beneeded to maintain protection (31). Consistent with this observation,CTL numbers appear to decline rapidly after the treatment ofHIV infections (44). However, more recent data suggest thatthe half-life of the CTL response to vaccination may be on theorder of a decade (30). Therefore, it is likely that vaccine-elicitedimmunity may progressively be lost and that only recently vaccinatedindividuals would be expected to receive the full benefit ofvaccination. The level of protection (measured by the reductionin viral load following infection compared to the viral loadof an unvaccinated individual) will decline with time sincethe last vaccination until all immunity is lost. We have adoptedthe assumption that the total duration of vaccine protectionwill be between 5 and 10 years (Table 1). With such a durationof protection, a short average time between vaccinations (5to 10 years) (Table 1) is required for widespread coverage.Note that if the duration of vaccine protection were significantlyshorter (1 to 5 years), a higher frequency of revaccination(every 1 to 5 years) would be required.

Immune responses select for viral escape mutants, which areviruses that have mutated the regions of protein targeted bythe host so that they are no longer recognized by T cells orantibodies (9, 10, 40, 46). Studies of natural infections suggestthat strong CTL responses may be maintained for years withoutinducing escape mutations, although under other circumstancesescape may occur rapidly (28, 47). The rate of viral escapefrom CTL immune responses is uncertain and probably varies withthe strength of immune pressure, structural constraints of theviral protein, and the viral load. Based on experimental evidence,we adopted a rate for the evolution of escape mutant virusesof 0.2 to 2 year^–1 (equivalent to an average time to evolutionof an escape mutant of 6 months to 5 years; Table 1) (9, 10).Current evidence suggests that after mutants escape from vaccine-inducedimmune responses, disease progression is similar to that ofa natural infection (9, 10). Thus, we assumed that once a vaccineescape mutant develops, any disease-modifying effects of thevaccine are lost and vaccinated individuals progress at thesame rate as unvaccinated individuals with an equivalent viralload. In addition, the population transmission of vaccine escapemutants was taken into account (see Materials and Methods).

MATERIALS AND METHODS

Top

Materials and Methods

The model of HIV infection, transmission, and vaccination wasstructured by sex, age, infection status, vaccination status,and duration of infection (Fig. 1; also see Appendix). The uninfected(susceptible) population (S) was structured according to sexand age (Fig. 1, vertical boxes). New susceptible individualsenter the youngest age group in the population (at the rate ${pi}$ for each sex). Uninfected individuals may become vaccinated(at the rate V) and enter the population, S_V, of susceptiblevaccinated individuals or may become infected with a wild-typeor vaccine escape mutant virus (at rates ${lambda}$ _WT and ${lambda}$ _E, respectively)and enter the population I or I_E, respectively, or may die attheir demographically determined sex- and age-specific mortalityrates (µ_s,a) (Berkeley Mortality Database [http://demog.berkeley.edu/wilmoth/mortality]).Individuals infected with wild-type virus (I) were structuredaccording to sex, age, and time since they were infected (inyearly increments) (Fig. 1), and they progress through 1-yearcategories of duration of infection (at rate p), with empiricallyderived increases in viral loads and rates of HIV-associated(D_s,a,d [7]) and natural (µ_s,a [Berkeley Mortality Database])mortality (24). Vaccinated susceptible individuals (S_V) werestructured according to sex, age (Fig. 1, vertical axis), andlevel of protection from vaccination (Fig. 1, horizontal axis).The level of protection in the vaccinated population was definedby the reduction in viral load (compared to unvaccinated individuals)that these individuals would experience after infection. Sinceit is assumed that vaccine-induced protection wanes with time(at the rate ${omega}$ ), individuals pass through progressively lowerlevels of protection until all protection is lost and they returnto the unvaccinated population (S). Vaccinated individuals maybecome infected at a higher rate than unvaccinated individualsdue to the potential effects of vaccination on increasing high-risksexual activity (R). Vaccinated individuals who become infectedmove into different stages of the vaccinated infected population(I_V) at the disease progression rate p_V. The vaccinated infectedpopulation is divided into those with low viral loads and mortalityrates (2, 39) due to vaccination (I_V1) (Fig. 1, light gray boxes)and those who have progressed to have viral loads and mortalityrates equivalent to those seen for natural infections (I_V2)(Fig. 1, dark gray boxes). Only those who were recently vaccinatedat the time of infection will attain the maximum protectionfrom vaccination (and enter the lowest category of I_V1). Thosewith waning vaccine-derived immunity will experience lower levelsof protection with time.

View larger version (26K):
[in this window]
[in a new window]
FIG. 1. Outline of the model. The schematic illustration of the model indicates the different compartments, movement between compartments, and the dynamics of aging and disease progression within compartments (see Appendix). As indicated on the right, squares indicate age classes. (See Materials and Methods for detailed description.)

The transmission of CTL escape mutant viruses has recently beendocumented (27). This has important implications for the long-termefficacy of a vaccine. If the transmission of viral escape mutantsto another vaccinated individual occurs, then the vaccine-inducedimmune response may be unable to recognize the mutant virus,blunting the effect of the vaccine. However, the viral epitopesthat are recognized by CTLs vary between individuals (largelyon the basis of HLA restriction [40]). Infection of an HLA-mismatched(recipient) partner with an escape mutant restricted to an irrelevant(donor) HLA allele will often not affect CTL recognition ofthe virus. Thus, since most sexual partners will not share HLAalleles (and therefore CTL epitopes), only a fraction of transmissions(H_E = 5 to 50%) from individuals infected with escape mutantswill result in transmission of the escape mutant and evasionof the vaccine-induced immune response. The remainder of caseswill result in the transmission of a virus that is mutated atan irrelevant CTL epitope and is therefore effectively a wild-typevirus that can be controlled by the vaccine-induced immune responseof the recipient.

Some vaccinated infected individuals (I_V) may become "superinfected"with an escape mutant virus (at the rate R ${lambda}$ _E) or develop an escapemutant virus through mutation (at the rate ${varepsilon}$ ) and therefore movefrom their current category (I_V1 or I_V2) into an equivalentcategory of infection with an escape mutant virus (I_E1 or I_E2).Individuals who are newly infected with an escape mutant virus(I_E) are assumed to have similar mortality rates and diseaseprogression to individuals infected with wild-type virus, anddisease is assumed to progress at a normal rate. Individualsinfected with an escape mutant virus can thus transmit eitherthe mutant virus (with the probability H_E) or wild-type virus(at the rate H_WT [1 – H_E]) (27).

Using this age and time-since-infection structured model basedon population data, we were able to capture the effects of reducingthe viral load and/or disease progression rate on mortalityand transmission. We were also able to take into account factorssuch as the duration of vaccine-mediated immunity and the rateof viral escape. A vaccine that slows disease progression, forexample, leads to advanced disease and high viral loads beingdelayed until an older age, that is, the high virological infectiousnessexperienced in late disease is delayed until the patient isolder and has low behavioral infectiousness. On the other hand,viral-load-reducing vaccines lead to lower virological transmissionearly after infection (Fig. 2).

View larger version (22K):
[in this window]
[in a new window]
FIG. 2. Effects of disease-modifying vaccine. After infection in an unvaccinated individual, both the viral load and mortality rise with time (solid line). Disease-modifying vaccines may act primarily by reducing the viral load after infection (dashed line) or by reducing disease progression (dashed-dotted line). A lower viral load in vaccinated individuals compared to unvaccinated individuals leads to reduced transmission (since transmission is dependent on the viral load) (top) and reduced mortality (bottom). If disease progresses at a normal rate, then viral loads and mortality rise at the same rate as in unvaccinated individuals, but starting at a lower baseline level (dashed line). Therefore, viral loads and mortality in a vaccinated individual will eventually rise to be equivalent to those seen in early natural infections, after a delay approximately equal to the reduction in viral load divided by the annual increase in viral load (0.09 log₁₀ copies ml^–1 year^–1). If vaccination slows disease progression, then the viral load and mortality may be stable or rise slowly (dashed-dotted line). The reduction in viral load induced by vaccination will reduce the virological infectiousness of infected individuals, whereas a delay in the rise in viral load will reduce behavioral infectiousness since people do not achieve high viral loads until they are older and less sexually active.

Previous modeling has suggested that increased sexual risk behavioras a result of optimism over the effectiveness of vaccination(18) or antiretroviral therapy (14, 15) may increase the transmissionof HIV. Factors such as increased sexual risk behavior as aresult of vaccination can be incorporated into the model byincreasing the rate of partner change among vaccinated individuals(18, 37). The extent to which optimism over vaccination mayincrease risky behavior is unknown. However, sexual behaviorin the general population has changed relatively little as aresult of HIV. Therefore, in accordance with published studies,we considered that the increase in risky behavior would varybetween 0 and 30% (52, 55) (corresponding in the model to a0 to 30% increase in the effective average partner change rate[Table 1]).

The model was used to investigate the effects of two differentpossible vaccines, one that predominantly reduced viral loadand another that predominantly slowed disease progression. Theseanalyses were initially performed on a baseline population,defined using parameters obtained from the literature (Tables2 and 3). The initial prevalence of infection was approximately0.5% of sexually active individuals, consistent with the currentprevalence in most regions of the world outside sub-SaharanAfrica (53). We performed 1,000 simulations of the effect ofvaccination, using different vaccine parameters (Table 1), andthen performed a risk analysis and sensitivity analysis (thetechnique is described in detail in reference 12) of these results.

View this table:
[in this window]
[in a new window]
TABLE 2. Parameters governing changes in female sexual behavior with age used in the baseline model^a

View this table:
[in this window]
[in a new window]
TABLE 3. Parameters governing changes in mortality and transmission with duration of infection used in the baseline model^a

To avoid any dependence of the results on particular populationvariables, we also performed a further analysis to investigatethe effects of vaccination in different populations. To do so,we created 100 new "populations" by randomly varying the parametersused. The parameters for each new population were obtained bymultiplying each baseline parameter value (i.e., each of thevalues in Table 2 and 3, independently) by a normally distributedrandom number with a mean of 1 and a variance of 0.2. Becausethe growth rate of the epidemic in the baseline population wasrelatively slow, with a doubling time of approximately 5 years,we also multiplied the transmission rate parameter (ß)by a random number between 0.5 and 2, reflecting the possibilitythat transmission may be higher or lower in different populations.The effects of vaccination in different populations were thentested by simulating 100 vaccination scenarios for each of the100 new populations. As a further control for our results, sincethe baseline population was in a relatively low-prevalence setting(0.5%), we also analyzed the impact of initiating vaccinationat different stages of the epidemic (i.e., at a prevalence of0.5, 1, 2, 4, 8, or 16%) in the different populations (100 populationsx 100 vaccination scenarios x 6 prevalence rates = 60,000 simulations).

RESULTS

Top

Results

Reducing viral load. The baseline population model was used to analyze a scenarioin which vaccination resulted in a reduction in viral load of0.5 to 1.5 log₁₀ copies ml^–1 after infection comparedto unvaccinated controls. In order to test the effects of viralload reduction alone, we adopted the assumption that vaccinationwould have only minor effects on the normal rate of diseaseprogression (80 to 120% of the normal rate) associated witha given viral load (39). This is referred to as a viral-load-reducingvaccine. Thus, a vaccinated individual who becomes infectedwill have a lower initial viral load than an unvaccinated individual,but their viral loads will increase from this level at approximatelythe same rate (0.09 log₁₀ copies ml^–1 year^–1) (36,43) (Fig. 2). This imposes a delay (approximately equal to theviral load reduction/0.09 years) until the viral load in thevaccinated individual reaches the level initially observed inthe unvaccinated individual and thus increases survival by thesame amount (Fig. 2). Because of the uncertainty in these andother effects of the vaccine, a simulation approach was usedin which the value of each of the vaccination parameters wasrandomly assigned at the start of a simulation from within arange estimated from the literature (12) (Table 1). Withoutvaccination, the outcome of the model was exponential growthof the HIV incidence and mortality over the 25 years of thesimulations (data not shown). By performing a large number ofsimulations, we obtained both a probability distribution ofoutcomes and an assessment of how sensitive the outcome is tochanges in individual parameters. One thousand simulations withvaccination were performed, and the results were compared withthose for no vaccination (Fig. 3) to quantify how many deathsor infections were averted by vaccination.

View larger version (32K):
[in this window]
[in a new window]
FIG. 3. Predicting the effects of disease-modifying vaccination. (A) One thousand simulations were performed for each of two cases: (i) a population given a viral-load-reducing vaccine that reduced the viral load between 0.5 and 1.5 log₁₀ copies ml^–1 while the progression rate varied between 80 and 120% of normal (left) and (ii) a population given a progression-slowing vaccine that reduced the viral load between 0.1 and 0.5 log₁₀ copies ml^–1 and the disease progression rate from 0 to 80% of normal (right). The means ( ${blacklozenge}$ ), medians (solid bars), 25th and 75th percentiles (open bars), and outliers (lines) of the proportions of deaths averted (top) and infections averted (bottom) compared to the unvaccinated control are shown. Shaded areas indicate those simulations where more deaths and infections occurred with vaccination than without. Thus, the number of simulations in the shaded areas divided by the total number of simulations gives the fraction of simulations with worse outcome with vaccination; these numbers are quoted in the text. (B) The proportion of vaccinated individuals (top) and proportion of infections involving a vaccine escape mutant virus (bottom) at different times after the commencement of vaccination with the viral-load-reducing vaccine used for panel A.

For the baseline population, the mean number of deaths avertedby vaccination reached 10.7% by 10 years and 35.2% by 25 years(Fig. 3). The number of deaths did not increase in any of thevaccination scenarios. Vaccination also averted a mean of 8.4%of new infections by 10 years and 26.7% of new infections by25 years. However, HIV incidence rose in the first few yearscompared to simulations without vaccination (by 1% at 2 years,which is equivalent to –1% of the incidence averted) (Fig.3) before commencing a decline in most scenarios. The fractionof simulations in which the cumulative HIV incidence increasedcompared to simulations with no vaccine dropped from 11.2% at10 years to 3.5% by 25 years (Fig. 3, shaded areas). Thus, aviral-load-reducing vaccine has the potential to reduce HIVdeaths, but it has a small risk of a long-term increase in HIVincidence.

The rise in new infections in the first few years after theintroduction of vaccination, even in simulations that laterled to a large decrease in HIV incidence, provides an interestingparadox. Why would an otherwise successful vaccine increaseinfection in the short term? The answer clearly lies in theincrease in risky sexual behavior accompanying vaccination.The vaccine neither prevents infection nor affects individualswho are already infected. Therefore, those who were infectedbefore vaccination was introduced are just as infectious, butvaccinated individuals become more susceptible if they increasetheir sexual risk behavior. Because early after the introductionof the vaccine in simulations, the majority of infected individualswere infected prior to vaccination, this leads to an overallincrease in transmission. At later time points, however, manyof the infected individuals were vaccinated prior to infectionand thus had low viral loads and a lower rate of transmission.Provided that the reduction in viral load is at least 1.0 log₁₀copies ml^–1, the reduced transmission due to vaccinationwould be sufficient to counterbalance a rise in risk behaviorof up to 30% (Fig. 4).

View larger version (38K):
[in this window]
[in a new window]
FIG. 4. Sensitivity analysis. The relationships between the viral load reductions (left), increases in sexually risky behavior (center), and proportions of individuals vaccinated at 10 years (right) and HIV mortality and incidence at 25 years for the viral-load-reducing (A) and progression-slowing (B) vaccines are shown. Each dot represents the outcome of one simulation with parameters chosen at random from the range given in Table 1. The results for 1,000 simulations of each scenario are shown. Cumulative incidence and mortality data are expressed as percentages of the unvaccinated control values (therefore, values of >100% indicate an increase in cumulative HIV incidence as a result of vaccination). The proportion of individuals vaccinated varied with the vaccination rate and the rate of loss of vaccine protection.

We investigated the sensitivity of the outcome to differentparameter assumptions in the model. The results of this sensitivityanalysis on HIV mortality and incidence at 25 years are summarizedin Fig. 4 and Table 4. The proportion of individuals with vaccineprotection, which is largely a function of the rate of vaccinationand the duration of vaccine-induced immunity, varied from approximately38 to 79% (Fig. 3B). Because vaccination reduced viral loadsand thus the mortality rate, the proportion of the populationwith vaccine protection strongly influenced the mortality ratein the entire population (Fig. 4). Thus, both the vaccinationrate and the rate of loss of vaccine protection were key factorsin predicting the outcome. The level of viral load reductionand the increase in high-risk sexual behavior also had a stronginfluence on the outcome. Unexpectedly, neither the rate ofviral escape nor the rate of transmission of escape variantswas a key factor in determining incidence or mortality in theviral-load-reducing scenario. In addition, the rate of diseaseprogression also appeared to have little effect on either incidenceor mortality (Table 4).

View this table:
[in this window]
[in a new window]
TABLE 4. Correlation between HIV incidence and mortality and model parameters^a

Slowing disease progression. The results presented above predict the effects of a vaccinethat reduces viral loads by 0.5 to 1.5 log₁₀ copies ml^–1,without a significant change in the disease progression rate.We then asked whether a vaccine that reduces the viral loadby <0.5 log₁₀ copies ml^–1 could reduce HIV incidenceand mortality if it were accompanied by a significant reductionin disease progression. This question is interesting becauseit is currently unclear whether the reduced viral load seenwhen vaccinated monkeys are infected is stable or increasesslowly (1, 11, 22, 51). The model was thus used to considerthe effects of a progression-slowing vaccine that had a minimaleffect on viral load (reducing viral loads by only 0.1 to 0.5log₁₀ copies ml^–1) but a significant effect on reducingthe disease progression rate (p_V is 0 to 80% of the normal rate).Thus, the viral load and mortality rate for vaccinated infectedindividuals would increase more slowly than those for unvaccinatedindividuals (or not at all, in the case of p_V = 0).

The mean number of deaths averted by the introduction of a progression-slowingvaccine increased from 6.4% at 10 years to 12.4% at 25 years.However, the number of deaths actually increased in 10.7% ofthe simulations at 25 years, suggesting an important risk ofa rise in HIV-associated deaths as a result of vaccination (Fig.3). Vaccination resulted in an increase in HIV incidence earlyafter the introduction of vaccination, with a rise in incidenceof 0.6% at 10 years. However, by year 25, vaccination reducedthe mean incidence 3% compared to simulations with no vaccination.Thus, despite decreasing HIV-associated mortality in the shortterm, a progression-slowing vaccine has a high risk of increasingthe number of infected individuals.

A sensitivity analysis suggested that the disease progressionrate again had relatively little effect on either mortalityor incidence at 25 years (Fig. 4; Table 4). The level of reductionin viral load and the increase in risky sexual behavior wereagain the key factors in determining HIV-associated mortality.However, the proportion of the population that was protectedhad a variable influence on the number of new infections thatwere prevented. In scenarios in which there were large increasesin risky behavior associated with vaccination and in which vaccinationonly mildly reduced transmission, the higher the proportionof the population vaccinated, the higher the average rate ofrisky behavior and the higher the rate of transmission. Therefore,if increased risky sexual behavior after vaccination leads toan increase in HIV incidence, simply increasing the vaccinationrate will not correct this and will instead lead to an increasein incidence. Thus, unless risky behavior can be controlled,there is a high risk that although vaccination may increasethe survival of vaccinated individuals, it may lead to a long-termincrease in HIV incidence and mortality.

Impact of vaccine in different populations. In order to test the robustness of the conclusions presentedabove and to test whether these effects are likely to be seenacross different populations, we randomly varied the baselinepopulation parameters (as described in Materials and Methods)in order to generate 100 new populations. (Eleven of the populationswere excluded from the analysis because the epidemics failedto reach a prevalence of 0.5% within 50 years of simulation.)We then simulated 100 viral-load-reducing vaccination scenarios(varying the vaccination parameters as in the simulations above)for each of these populations and assessed the impact of vaccinationon HIV incidence and mortality at 25 years.

Figure 5 shows the mean proportions of deaths and infectionsaverted at 10 (A) and 25 years (B) after the introduction ofvaccination in different populations. The proportion of deathsaverted and the proportion of infections averted were stronglydependent on the growth rate of the epidemic. A larger impactof a vaccine on a faster growing epidemic is to be expected.Since epidemic growth is nonlinear, any vaccine effects on theepidemic growth rate will have a larger impact on the overallnumber of deaths and new infections when the growth rate itselfis high. The more slowly growing the epidemic, the longer ittakes for the vaccine to affect the outcome. Thus, if we measureoutcome at a fixed time (e.g., 10 years), the vaccine will havehad less of an effect on a slowly growing epidemic than on arapidly growing one. However, in extremely rapidly growing epidemics(doubling times of <2 to 3 years), the early benefits ofvaccination in reducing HIV incidence (seen at 10 years) arereduced by 25 years. This occurs because although vaccinationdelays the peak of the epidemic, in very rapidly growing epidemicsthe peak in the vaccinated population will still occur within25 years. The observed effects of vaccination in preventingnew infections will not be as large as those seen in populationsin which vaccination delays the peak of the epidemic beyond25 years. Thus, the impact of vaccination is dependent on thetimescale of our observation: although vaccination may slowthe epidemic, it may not necessarily reduce the final size ofit substantially (54).

View larger version (22K):
[in this window]
[in a new window]
FIG. 5. Effects of vaccination on different populations. One hundred new populations were created by randomly varying the baseline population parameters, and the effects of vaccination were assessed by simulating 100 vaccination scenarios in each new population introduced at a 0.5% prevalence (as described in Materials and Methods). The average percentages of deaths (top) and infections (bottom) averted due to vaccination after 10 years (A) and 25 years (B) were plotted against the doubling times of the epidemics immediately prior to the introduction of vaccination. Each point represents the results for a different population. To investigate the effects of initial HIV prevalence, we studied vaccination introduced at an initial HIV prevalence of 0.5, 1, 2, 4, 8, or 16% (colored as indicated) (C). The average proportions of deaths (top) and infections (bottom) averted for each population at each initial HIV prevalence were plotted against the doubling time of the epidemic immediately prior to the introduction of vaccination.

Next, we studied the effect of different epidemic dynamics andthe epidemic stage on the benefits of vaccination. For eachof the 100 populations, we let the epidemic develop withoutvaccination until the infection prevalence reached 1, 2, 4,8, or 16%. For each population, the time to reach these ratesof prevalence was different because the epidemics had differentgrowth rates (Fig. 5C). We thus could analyze the impact ofvaccination on epidemics characterized by different prevalenceand growth rates. At any given growth rate, the lower the initialprevalence, the larger the impact of a vaccine in terms of infectionsand deaths averted (that is, early intervention is advantageous).On the other hand, if epidemics with the same initial prevalencegrow at different rates, there will be an epidemic with a specificgrowth rate for which the impact of the vaccine is maximal.For example, at an initial prevalence of 0.5%, the maximum proportionof infections averted occurs with a doubling time of about 3to 4 years. In contrast, at an initial prevalence of 16%, themaximum proportion of infections averted is seen with doublingtimes of more than $~$ 7 years.

The mean number of deaths averted by vaccination at 25 yearswas more than $~$ 10% for all populations, regardless of the growthrate or initial prevalence of infection. However, an increasednumber of deaths was seen in a small number of vaccination scenarios,indicating a risk of increased HIV infection with vaccinationin some epidemics. If we restricted the analysis to vaccinationscenarios in which the drop in viral load after vaccinationwas at least 1 log₁₀ copies ml^–1, then there was a reductionin deaths in all of the populations and under all of the vaccinationconditions considered. Thus, provided a vaccine can reduce theviral load of vaccinated infected individuals by at least 1log compared with that of unvaccinated individuals, we believethere is an extremely low risk that it could increase HIV-associatedmortality within the first 25 years.

DISCUSSION

Top

Discussion

Recent studies of HIV vaccination in monkeys suggest that futureHIV vaccines may be unable to prevent infection but may improvethe subsequent course of disease. We use the term disease modifyingto describe these vaccines and to distinguish them from previousdiscussions of partially effective vaccines. Partially effectivevaccines were assumed to prevent infection, but only in a proportionof vaccinated individuals (6, 19). In contrast, disease-modifyingvaccines do not prevent initial infection but simply alter thesubsequent course of infection. Such disease-modifying vaccineshave not previously been used, and their implications for thespread of an epidemic are unclear. We employed a model of HIVepidemic spread that incorporated both intrahost and populationdynamics to investigate the effects of a disease-modifying vaccinefor HIV. Mathematical modeling involves a necessary simplificationof the complexities of disease transmission. Thus, althoughour model is structured to account for the duration of infectionand age, it does not account for the impact of high-risk groupssuch as intravenous drug users, commercial sex workers, or othercore groups within a population. However, the model aims toguide rational vaccine design and development by addressingwhether a disease-attenuating vaccine has the potential to reducethe burden of disease, what features of the vaccine are mostlikely to affect this, and under what circumstances the vaccinewould be most effective.

The results of an uncertainty and sensitivity analysis suggestthat the reduction in viral load in vaccinated infected individuals(compared to unvaccinated individuals) is the key factor tomeasure in attempting to predict the likely outcome of vaccination.Surprisingly, according to our model the extent to which a vaccineslows disease progression and the rate of immunological escapeof vaccine-induced immune responses have relatively little effecton the long-term outcome. The level of increase in sexuallyrisky behavior as a result of optimism over vaccination alsocorrelated strongly with the epidemic outcome, as has been observedfor antiretroviral therapy (25; Kellogg et al., letter) andpredicted previously in other models (15, 18, 33). It is interestingto speculate that a disease-modifying vaccine, which does notprevent infection, may well induce less optimism and less increasein risky sexual behavior than a vaccine that promises protectionfrom infection.

The baseline scenario is a low-prevalence epidemic (0.5%) thatis growing relatively slowly (doubling time, $~$ 5 years). In orderto investigate whether these results may be applicable to otherpopulations, we also considered the impact of vaccination ondifferent simulated populations, with vaccination being introducedat different stages of the epidemic. These results indicatethat both the growth rate of the epidemic and the stage of theepidemic (in terms of the initial prevalence of infection) caninfluence the impact of vaccination. In general, vaccinationhas more influence on more rapidly growing epidemics and whenit is introduced earlier in the course of the epidemic. However,the impact of vaccination also varies according to the timeframe of analysis, i.e., the number of new infections may increasein the first few years after the introduction of vaccination(Fig. 3). Similarly, in a very fast growing epidemic, the maximalimpact of vaccination may occur at about 10 years, with thesubsequent effects of vaccination declining over time (Fig.5) (45, 54). When considering the impact of a vaccine on differentpopulations, the growth rate of the epidemic, the current prevalenceof HIV, and the timescale over which we wish to assess the resultsare all important factors to consider. Disease-modifying vaccineswould have a maximum effect if they were introduced into relativelyearly-stage epidemics (such as those seen in areas of Asia)but a smaller impact if they were introduced into late-stage,high-prevalence epidemics (such as those seen in areas of sub-SaharanAfrica). However, our results demonstrate that if vaccinationis able to reduce the viral load of vaccinated infected individualsby at least 1 log₁₀ copies ml^–1, then the number of HIV-associateddeaths is predicted to be reduced at 25 years for all of thescenarios considered.

Importantly, the model also suggests that the success of anyhuman vaccine trial should not be judged solely on short-termmeasures of how many infections were prevented in the vaccinatedgroup. Indeed, it is likely that disease-modifying vaccineswill lead to a short term (1 to 5 years) increase in HIV incidenceif they lead to increased high-risk sexual activity. However,this does not preclude long-term benefits. Thus, rather thansimply measuring HIV incidence in vaccinees and controls, vaccinetrials should also aim to closely monitor viral loads of infectedindividuals in order to quantitate any reduction in viral loadin vaccinated individuals. Campaigns promoting safe sex shouldalso be continued to prevent vaccine-related increases in riskysexual behavior. The close monitoring of large numbers of patientsmay be necessary to measure the average reduction in viral loador to detect a slowing of disease progression in vaccinatedindividuals compared to controls. However, it is the reductionin viral load that appears to be the most important featureof a disease-modifying vaccine for predicting its ability tocontrol the spread of HIV. The model suggests that reductionsin viral load of about 1 log₁₀ copies ml^–1 may be sufficientto produce long-term reductions in HIV incidence and mortality.This reduction in viral load is relatively modest compared tothat observed in vaccinated monkeys ( $~$ 3 log₁₀ copies ml^–1)(11, 51).

APPENDIX

Top

Appendix

A model of a heterosexual HIV epidemic structured by sex, age,and duration of infection (24) was modified by the incorporationof categories of susceptible vaccinated individuals (S_V), infectedvaccinated individuals (I_V), and individuals infected with escapemutant viruses (I_E). The last two categories were further dividedinto those who are currently benefiting from reduced viral loadsdue to vaccination (I_V1 and I_E1, respectively) and those whosedisease has progressed to a stage at which their viral loadsare equivalent to those seen in natural infections (I_V2 andI_E2) (Fig. 1). The mortality and transmission of these lastgroups were the same as those for an equivalent stage of naturalinfection (note that here we use stage of infection to denotethe time since infection in a corresponding natural infection,not the usual CDC stage classification). The mortality and transmissionfor the categories of infection with reduced viral loads (I_V1and I_E1) were estimated based on their relationship with viralload. That is, transmission was reduced 2.45-fold and mortalitywas reduced 2.22-fold for every log₁₀ reduction in viral load(2, 39, 48).

The model populations that we studied contained $~$ 1 million individualsof each sex, with an age structure that was determined by allowingan influx of new susceptible individuals ( ${pi}$ ) into the youngestage group of 20,000 per year for each sex and by using publishedfigures for natural mortality (Berkeley Mortality Database).The model was run for 200 years to generate a stable age distributionof uninfected individuals and a total population size of $~$ 2 million.The initial proportion of infected individuals was $~$ 0.1% of thesexually active population, and the age distribution was similarto that of the infected population of the United States in theearly 1990s (49). This population was not chosen to simulatethe AIDS epidemic in the United States but rather as a meansto generate a baseline population with a well-defined age structure.The epidemic was allowed to expand, and vaccination was introducedwhen the prevalence reached a specified level (0.5% in the baselineanalysis and 0.5, 1, 2, 4, 8, or 16% in the analysis of differentpopulations).

The model was defined by a system of differential equationsas outlined below (also see reference 24).

(i) For the unvaccinated susceptible population in the youngestage group,

and for older age groups,

That is, new susceptible individuals enter the populationat the youngest age group at the rate ${pi}$ or from the vaccinatedpopulation through the loss of vaccine protection at the rate ${omega}$ . Individuals leave the population by aging ( ${alpha}$ _a, which is zerofor the oldest age group), vaccination (V), natural death (µ_s,a),or infection with a wild-type or escape mutant virus ( ${lambda}$ _WT and ${lambda}$ _E, respectively).

(ii) For the recently vaccinated, uninfected population,

Thereafter, vaccinated individuals progress throughstages of progressively lower levels of vaccine protection (indicatedby the subscript "n") at the rate ${omega}$

untilthey return to the unvaccinated uninfected population.

(iii) For newly infected unvaccinated individuals infected withwild-type virus,

and for the progressionthrough time since infection (indicated by the subscript "d"),

where the disease progression rate p_d is zero forthe most advanced disease stage.

(iv) For newly infected vaccinated individuals,

where R ${lambda}$ _WTs,a is the force of infection for vaccinatedindividuals. Individuals with the protection level n from vaccinationenter the infected vaccinated population at the equivalent leveland then progress through stages of infection at the rate p_V.

Once viral loads rise to values equal to those seen after naturalinfections, individuals enter the category I_V2:

forthe earliest category and thereafter progress through subsequentstages of infection, as follows:

(v)For the vaccinated population infected with escape mutant virusesat early stages of infection (I_E1),

and once viral loads rise to values equal to thoseseen after natural infections (I_E2),

for the first category, and thereafter,

where the subscripts s anda correspond to gender and age, respectively, and n and d correspondto the duration of infection for those with lower than normalviral loads and normal viral loads, respectively.

The parameters are shown in Fig. 1 and explained in the text.The per capita forces of infection of wild-type and escape mutantviruses ( ${lambda}$ _WT and ${lambda}$ _E) were calculated in two steps (24). First,the infectiousness of the population of age a and sex s wascalculated, for both wild-type and escape mutant viruses (L_WTs,aand L_Es,a, respectively), as follows:

where we have taken into consideration the numberof infected individuals in each category and their virologicalinfectiousness (ß), age-specific transmission rate(T) (48), and the probability that an individual infected withan escape mutant virus will transmit either a wild-type virus(H_WT) or a virus that escapes the vaccine-induced immune responsein the recipient (H_E). We then calculated the force of infectionfor a given sex and age group ( ${lambda}$ _WTs,a, ${lambda}$ _Es,a) by using the followingformulas:

wherethe empirical effective average rate of partner change is c(13, 34) and the rate of sexual mixing between age groups isgiven by the variable M_s,a1:(s*,a2), the mixing of people ofage a1 and sex s with people of age a2 and sex s* (8, 23) Thisforce of infection was then multiplied by the increase in high-risksexual activity of vaccinated individuals (R) in the vaccinatedpopulation (see the text).

ACKNOWLEDGMENTS

Portions of this work were done under the auspices of the U.S.Department of Energy and were supported under contract W-7405-ENG-36.We also acknowledge support from the James S. McDonnell Foundation21st Century Research Awards/Studying Complex Systems (M.P.D.)and by NIH grants R01-RR06555 and R37-AI28433 (A.S.P.). R.M.R.was partially funded by a Marie Curie Fellowship of the EuropeanCommunity program "Quality of Life" under contract number QLK2-CT-2002-51691.

We thank Rob de Boer for helpful comments on the manuscript.

FOOTNOTES

* Corresponding author. Mailing address: MS-K710, T-10, Theoretical Biology & Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM 87545. Phone: (505) 667-6829. Fax: (505) 665-3493. E-mail: asp{at}lanl.gov.

REFERENCES

Top