Introduction

AIDS is officially diagnosed by the presence of one or more defining conditions. In order to monitor the progress of HIV within the body a marker path is used to describe the incubation period, where markers are a consequence of disease. One of the most commonly used markers for this purpose is CD4 cell count. In general, the lower the CD4 cell count, the worse the condition of the immune system and hence the severity of the illness. Markers have proved to be of great importance in monitoring the effect of therapy; in particular, measurements of CD4 can give an indication as to whether HIV has become resistant to the current treatments available. The year 1987 saw the development of a premier anti-HIV drug, zidovudine (AZT). Treating an individual with just one such antiretroviral drug is known as mono-therapy and can result in significantly greater CD4 cell recovery compared with no therapy. The suggestion that continuous triple or quadruple therapy in acute HIV infection would give an even higher probability of short- to medium-term viral suppression (Smith et al, 2004) and the fact that HIV can become resistant to any one drug, has meant that, in 1995, a combination (cocktail) of potent and highly active antiretroviral drugs (HAART), which the patient is required to take on a regular basis and indefinitely, was introduced. Treatment regimens now involve a combination of two or three different drugs, with an increasing number of individuals receiving quadruple therapy (Beck et al, 1999). Prior to the introduction of these new combination therapies, nearly 50% of young men who became infected with HIV died within 12 years of initial infection (NIH, 2002). Following the introduction of these advanced treatments, there has been a well-documented reduction in mortality and risk of AIDS-defining illnesses (Van Sighem et al, 2003), including a reduction in the hazard ratio for death which fell from an already reduced value of 0.47 in 1997 to 0.16 in 2001 (CASCADE Collaboration, 2003). In fact, progression to an AIDS-defining illness, in those who can tolerate treatment and do not develop drug resistance, has been effectively stopped as long as HIV is diagnosed, and treated properly, early enough in the course of clinical progression (McHenry et al, 2002). Part of the decline in AIDS cases and deaths from AIDS might also be attributed to changes in the infected and treated population during the years 1996–2000, and not just the initial impact of cocktail therapies, as the population shifted towards one in a less advanced stage of HIV-1 infection at the start of HAART with a growing fraction of therapy-naïve patients (Van Sighem et al, 2003). This argument helps justify the extended transition time of changing parameter values, to allow for a treatment effect, as indicated later in this article.

The aim of this paper is to model the effect that treatments and therapies have had on the HIV/AIDS epidemic, particularly since 1995 when combination antiretroviral drugs were first established. Once a good-fitting, realistic, model is founded, it is implemented to predict short-term estimates of the HIV/AIDS epidemic, assuming there are no immediate changes in the parameter values, extrapolating up until the year 2008. Also, this paper looks at possible future scenarios when parameters are subject to modification, for instance, a change in behaviour due to public awareness or government-sponsored campaigns.

Mathematical model

Generally, infectious disease is modelled using SIR, or SIS, models. These involve dividing the population into sub-populations, those who are: susceptible; infected and recovered (or susceptible again). For HIV/AIDS, since individuals do not recover from the disease, an extension of a SI model is used, with an AIDS stage and a Death from AIDS stage included. These four sub-populations can then be split further to create various other sub-populations, as seen in publications by Hethcote and Van Ark (1980), Griffiths et al (1990), Hethcote et al (1991), Bailey (1993, 1994a, 1994b, 1997), Griffiths and Williams (1994), Pasqualucci et al (1998) and Rossi and Schinaia (1998). For the model implemented here, the sub-populations are split into those individuals who indulge in high-risk activities and those who adopt low-risk behaviour. Roberts and Dangerfield (1990b) divide the subpopulations even further than this, into three risk behaviour groups: high, moderate and low. Also, the infected sub-population can be sub-divided into a number of smaller sections in order to demonstrate the various stages of disease progression that an individual may pass through before being diagnosed with AIDS. The model used in this paper is illustrated in Figure 1; an individual in a particular state will occupy that state for a period of time, and movements between compartments are governed by transfer rates. The sub-populations are denoted by

X(t)

the number of Susceptibles at time t,

Y(t)

the number of High Risk Infectives at time t,

V(t)

the number of Low Risk Infectives at time t,

A(t)

the number of High Risk AIDS cases at time t,

Z(t)

the number of Low Risk AIDS cases at time t

Figure 1.

Cardiff HIV/AIDS epidemic model.

Full figure and legend (74K)

Following an individual through the Cardiff model, that individual can stay within the sub-population they are in, transfer to another sub-population with an adjoining arrow, exit the model from causes other than AIDS (eg dying from causes other than AIDS at any stage in the model as well as, if not infected by the virus, exiting the model by no longer participating in high-risk behaviour or homosexual sexual activities), or exit the model due to AIDS, that is, death from AIDS. It is beneficial to maintain as simple a model as possible; the inclusion of too many unimportant parameters will result in greater ambiguity because of the increased levels of estimation involved. This work, like that of Dangerfield and Roberts (1989, 1994, 1996), and Roberts and Dangerfield (1990a), uses a compartmental model to emulate the transmission of HIV in the male homosexual community. There are a number of basic assumptions implied in the creation of the Cardiff Model, including the assumption that an individual can only enter the model, and a susceptible can only become infected, if participating in high-risk activities. Also, an individual can move from high-risk to low-risk within the infective sub-populations, the change in behaviour potentially resulting from the impact of educational programmes, enhanced awareness and counselling; however, it is not expected that an individual will return to their prior high-risk behaviour at any point, although it is relatively easy to add this reverse movement to the model. Another simplification imposed is the exclusion of the low-risk susceptible sub-population. This ensures that the model is in its most basic form without affecting expected numbers of AIDS/HIV incidence, prevalence or deaths produced by the model. There is a parameter related to each possible movement through the Cardiff model. These parameters are shown in Figure 1 and are defined as follows:

the arrival rate into the high-risk susceptible category,

₁

the rate that susceptibles exit the model from causes other than AIDS,

₂

the rate that infectives exit the model from causes other than AIDS,

₂

the rate that high-risk infectives transfer to the low-risk category,

₃

the rate that high-risk AIDS cases transfer to the low-risk category,

b

proportion of high-risk infectives who, on diagnosis with AIDS, continue their high-risk behaviour,

g

proportion of low-risk infectives who, on diagnosis with AIDS, change their behaviour to high-risk,

c(Y(t)+A(t))/(X(t)+Y(t)+A(t))=the rate at which homosexual men become infected, where c is the infectivity rate, and (Y(t)+A(t))/(X(t)+Y(t)+A(t)) represents the proportion of high-risk HIV-infected individuals at time t,

_i

the transition rate from stage i of HIV infection to stage i+1, i=1, ..., m,

the death rate from AIDS.

From Figure 1, we may set up the following equations:

The model incorporates m stages within the infective categories, in accordance with the natural history of HIV infection (Longini et al, 1996). We denote the transition rate per unit time from stage i to stage i+1 by _i, where i=1, ..., m and stage m+1 relates to the full-blown AIDS condition. This notation is applied due to the assumption that there are only '1-step' forward movements between stages. Y_i(t) and V_i(t) (i=1, ..., m) denote the number of HIV infectives at time t in stage i of the high-risk and low risk sub-categories, respectively. We may use equations (1a), (1b), (1c), (1d) and (1e) to estimate such quantities as HIV incidence, HIV prevalence, AIDS incidence and AIDS prevalence as functions of time. If we take t=1/52 (years), then HIV incidence for that year is given by , where X(i) (i=1, 2, ..., 52) denotes the number of high-risk susceptibles present in week i. Similarly, AIDS incidence is given by

where Y_m(i) and V_m(i) denote the total number of high-risk and low-risk infectives present in the last stage of HIV infection, respectively, in week i. The term prevalence refers to the number of HIV (and AIDS) cases alive at any given time t. Thus, HIV prevalence is defined as Y(t)+V(t)+A(t)+Z(t), whereas AIDS prevalence, alone, is defined as A(t)+Z(t).

One of the many benefits of having individual equations, belonging to each subcategory of the HIV infective populations, is that by solving Equations (1b), (1c), (1d) and (1e), the HIV prevalence for each stage of HIV progression can be obtained. Sabin et al (1994) state that knowledge of the numbers within each stage of HIV infection can be valuable in areas such as health care planning; information on how many HIV infectives are there in the later stages of HIV disease will provide good estimates for future AIDS incidence which can then be used in budgeting for potential health care and treatment costs.

Modelling treatment effects

We now need to estimate the values of the various parameters used in the model. To this end, we use estimation techniques in comparing output values from the model for HIV and AIDS incidence with the observed AIDS and HIV incidence data obtained from the European Non-Aggregate AIDS Data Set, or ENAADS (EuroHIV, 2003). The observed data utilized for this fit has formerly been adjusted for under-reporting and reporting delays. However, data over the most recent years may still be deemed unreliable; hence, our comparison covers the years 1979–2002 only. Using the ENAADS data set as the source of the observed AIDS incidence data, the first reported case of AIDS in the UK was in 1979. Thus, we take this as the first year of the HIV/AIDS epidemic and so 1978 is employed as the base year (ie t=0). Several researchers, including Bailey (1991, 1992) and Griffiths and Williams (1995), have implemented the method of maximum likelihood to estimate parameters within an epidemic model. One limitation of the technique is the assumption that parameters remain static. For many of the parameters within the model this is not the case, predominantly due to the introduction of treatments and media campaigns, public awareness and attitudes affecting behavioural patterns over time (Griffiths and Williams, 1994). One way of overcoming this difficulty is to consider a number of maximum likelihood estimates (MLE's) based upon different time eras that are linked together, thus allowing new values for parameters to be estimated at certain time intervals based on behavioural changes and the introduction of various treatment regimens. The HIV/AIDS epidemic lends itself to three time eras: 1978–1986 (pretreatment); 1987–1994 (early treatment) and 1995–2002 (combination treatment). The Poisson distribution (as implemented by Bailey (1991, 1992) and Griffiths and Williams (1995)) offers itself as a suitable statistical distribution to model the number of new AIDS cases diagnosed over a fixed time interval, and has the probability distribution function (p.d.f) below (Equation (2a)).

where a₁, a₂, ..., a_T are the observed AIDS cases for T successive time periods, and ₁, ₂, ..., _T are the expected AIDS cases for T successive time periods.

Next, the expression for the log likelihood of this Poisson model (Equation (2b)) is maximized, subject to the expected AIDS cases, _i.

The expected AIDS cases, _i, are the terms created by the model itself and from the fact that the model is adjusted in accordance with the n parameters to be estimated, _j, j=1, ..., n, it is such that _i are dependent upon _j. Accordingly, the expression L (Equation (2b)) is differentiated by each of the parameters to be estimated, _j, and the results set to zero to give a set of n simultaneous equations. Thus, and S are created, where is the vector of the n parameters to be estimated and S the vector of the associated partial derivatives.

By letting _j be the initial approximation to the MLE , for large T (ie a large number of successive time periods), is asymptotically unbiased and efficient, that is

Also, by definition, the variance–covariance matrix, V, is equal to the inverse of the information matrix, I, which is identified in the multivariate case as:

Subsequently, the iterative procedure (Equation (2c)), which is commonly known as the method of scoring for parameters, is obtained using theory on approximate solutions of likelihood equations (Kendall and Stuart, 1973). Equation (2c) can then be implemented to calculate the estimates of the parameters _j, j=1, 2, ..., n.

Before production of the computational model can begin, the estimation of the number of HIV positive homosexuals, and AIDS case homosexuals, in each stage, at the end of year 1978, that is Y_i(1978) and A(1978), respectively, needs to be determined. The proportions are as shown in Equation (3), based upon work by Bailey (1991), that is, a geometric distribution based on the initial number of AIDS cases in the base year (1978), where a₁₉₇₈ relates to the number of HIV-positive homosexuals at the end of year 1978 and =c/_i.

Now the model has been created, the initial conditions need to be set. Based upon a combination of work by Snary (2000), Lowrie (2000) and Griffiths et al (2000), or gained directly from population statistics, these are defined to be as follows:

• IP=Length of incubation period in years=11.4 (Snary, 2000),
• N₁₉₇₈=number of high-risk homosexuals in the population at the end of year 1978=X(1978)+Y(1978)+V(1978)=10 000,
• ₁=rate at which homosexuals exit the susceptible category from causes other than AIDS=0.003 (DH1, 2002),
• ₂=rate at which homosexuals exit the high and low-risk infective categories from causes other than AIDS=0.03 (Snary (2000) and Lowrie (2000) to 2.d.p.),
• ₂=rate at which high-risk infectives become low-risk=0.1 (Snary, 2000),
• ₃=rate at which high-risk AIDS cases become low-risk=0.5 (Snary (2000) and Griffiths et al (2000)),
• b=proportion of high-risk infectives who stay high-risk once diagnosed with AIDS=0.5 (Snary, 2000),
• g=proportion of low-risk infectives who become High Risk once diagnosed with AIDS=0.1 (Snary, 2000),
• =death rate=1 (Snary, 2000),
• m=number of stages in HIV infection=6 (Snary, 2000).

The parameters to be estimated are

• =the entry rate into the model,
• a₁₉₇₈=the number of HIV positive homosexuals at the end of year 1978,
• c=the infectivity parameter,
• r=the proportion the incubation period lengthens due to the effect of treatment.

These parameters have been chosen for estimation due to the difficulty in obtaining reliable values for them from other sources. The entry rate, , can take a number of forms and is often deliberated within models of the HIV/AIDS epidemic; the number of infected individuals at the start of the epidemic, a₁₉₇₈, causes difficulty in estimation as there are no relevant data available; and the infectivity parameter, c, a sociological parameter, is difficult to ascertain by its very nature. Finally, of the parameters chosen for estimation, the parameter r, the proportional increase in the incubation period (IP), is considered. It can be viewed as a measurement of the effect treatment has had on the epidemic, due to its ability to lengthen the time that HIV-positive individuals live with HIV, thus postponing the onset of AIDS and, consequently, death from AIDS. It is included within the model as a product of the IP, where it is fixed at a value of 1 before the introduction of treatments, and allowed to increase to a value greater than 1 when estimated in the MLE process. Figure 2 illustrates the parameters to be estimated and at which point in time this estimation occurs. The first and second columns on the left of Figure 2 depict the three time eras into which the model is split and the years they span over, respectively. The third column lists the two parameters, , a₁₉₇₈, which are estimated at the start of the epidemic, using observed data, for the entire time period. That is, they are static parameters and, once estimated, do not change value. The next column shows the process by which the infectivity parameter is estimated. Two estimates of c are made over the entire time period: the first, c₁, is in relation to the start of the epidemic when people were unaware of the virus and its significance; the second, c₂, relates to a change in behaviour and attitudes witnessed among homo/bisexual men due to a government campaign promoting safe sex in 1985/1986 (Johnson and Gill, 1989; Evans et al, 1993), that is a much reduced infectivity parameter. Of course, the value of this parameter would not change immediately, but would take time to transform from its original value to its new value. Thus, a smoothing technique is introduced into the model such that the change in parameter value, c, is spread over 2 years (104 weeks) as follows: |c₁-c₂|/104. This increment is then subtracted from the original value, c₁, each time period of 1 week (t), until it reaches its new value, c₂. The treatment effect, r, holds three values over the entire time period due to the fact that introduction of treatments changing the face of the epidemic occurs twice; firstly, in 1987 when antiretrovirals were first established, then later in 1995 when combination therapy was introduced. Initially, before the introduction of treatments, r takes the value of 1 so as not to interfere with the previous model, that is, the IP is its original length. The parameter r is then re-evaluated in the second time period as a result of the first set of treatments being introduced. Again, a smoothing technique is applied for this change in value, to cover 2 years, 1987–1988, this time the increment being equal to |r-r₁|/104. For the introduction of cocktail therapies, such as HAART, in 1995, a more complicated transition takes place. The full results of these new and extremely effective treatment regimens have taken longer to occur than the initial impact of new treatments alone might be expected to, due to the changing population of infectives, to one which is more treatment naïve, and the increase in, and application of, experience and knowledge with respect to the use of combination therapies and drug resistance. Thus, for this change in value, from r₁ to r₂, a smoothing time of 6 years has been engaged. This means a smoothing increment of |r₁-r₂|/312 added to r₁ for each time period of 1 week, until it reaches its new value, r₂. Furthermore, previously the assumption was one of a constant staged incubation period, with ₁=₂=...=₆; however, the introduction of new combination treatments has confirmed this notion to be unrealistic as those individuals in the later stages of HIV infection will not have the same reaction to the new therapies as those who are in the earlier stages of HIV infection. Thus, r has been split into two values over the time of transition; r_i relates to those in stages 1–5 of HIV infection while r₆ relates to those in stage 6 of HIV infection. It is then proposed that the improvement in IP that occurs due to the introduction of combination treatments will be delayed by 1 year for those in stage 6, compared to those in stages 1–5. Thus, the smoothing of value r₁ to r₂ occurs between the years 1994 and 1999 for r_i, with the same values being used for r₆, but 1 year later, such that the transition from r₁ to r₂ occurs between 1995 and 2000 for r₆.

Figure 2.

Sequence of parameter estimation.

Full figure and legend (50K)

Finally, certain constraints need to be placed upon the parameters in order to maintain realism within the model. These are shown below as follows:

• , a₁₉₇₈>0, non-negativity,
• c₁, c₂0.5, non-negativity (since both >0 and c>0) plus boundary for realism,
• c₁c₂, where c₁ is the first estimate of c and c₂ is the second,
• 1r₁, r₂5, restricted to only increase the IP due to the introduction of treatments, plus an upper boundary for realism,
• r₂r₁, ensuring that as time progresses the value of r only increases the length of the IP further, due to the introduction of new treatments.

Results

The maximum likelihood estimation (MLE) technique suggests improvements in fit between observed and expected AIDS incidence, subject to the alteration of the parameters being estimated. However, to allow the inclusion of HIV incidence data into the fitting of the model, a measure of the goodness of fit is introduced for both AIDS incidence and HIV incidence. ² values are summed over all time periods to measure the goodness-of-fit for AIDS incidence data (1979–2002) and HIV incidence data (1995–2002). The sum of these two ² values is then minimized subject to changes in the parameters (, a₁₉₇₈, c and r). The parameter values estimated that created the best fits seen in Figures 3 and 4 are as follows:

Figure 3.

Fit between observed and expected AIDS incidence, 1979–2002.

Full figure and legend (49K)

Figure 4.

Fit between observed and expected HIV incidence, 1995–2002.

Full figure and legend (53K)

These parameters result in a total minimized ² value of 177.313. This is made up of a ² value of 32.825 (3 dp), summed over the years 1979–2002, for the fit between observed and expected AIDS incidence and a ² value of 144.488 (3 dp), summed over the years 1995–2002, for the fit between observed and expected HIV incidence. Within the total AIDS incidence fit, separate values for each treatment era can be withdrawn as follows: Pre-treatment era (1979–1986) AIDS ²=9.476 (3 dp); early treatment era (1987–1994) AIDS ²=4.843 and combination treatment era (1995–2002) AIDS ²=18.506. It is noteworthy that due to the inclusion of HIV data into the fitting process, the original possible overall fit for AIDS incidence is compromised somewhat. However, the overall benefits to the model observed when including the HIV data, far outweigh this slight cost in AIDS fit, which is still outstandingly good. As can be seen from the ² values, the majority of the 'bad fit' stems from the HIV incidence data. This is partly because HIV incidence data is only available for the years 1995–2002 from the ENAADS data set (maintaining consistency with the data set from which observed AIDS cases were extracted). Included in Figure 4 is the count of new diagnosed cases of HIV, obtained from the Health Protection Agency (HPA, 2005) and by direct contact with the Communicable Disease Surveillance Centre (CDSC), which dates back to 1985. It is important to realize that new HIV diagnoses and HIV incidence are not equivalent due to the inconsistency of when individuals are diagnosed with HIV compared to the point in time when infection actually occurs. However, numbers of newly diagnosed HIV cases can still be a good approximation to HIV incidence figures; hence comparisons between the expected HIV incidence produced by the model and the observed new diagnosed HIV infections attained from HPA, may be considered useful. Prior to 1985, it is probable that a shape, like that seen in the expected HIV incidence curve depicted in Figure 4, occurs when compared with suggested trends investigated by Snary (2000), Downs and Houweling (1997), Day Report (1996) and De Angelis et al (1998), all of whom, in general, estimate that HIV incidence numbers peak in 1982/1983 at a level of about 3500–4500 new HIV cases per year. Post 1983, owing to a government campaign promoting safe sex in 1985/1986 (Johnson and Gill, 1989; Evans et al, 1993), levels of HIV incidence are estimated to have fallen quite rapidly and, in more recent years, have maintained their reasonably low, and stable, levels of about 1600 new cases of HIV each year.

Other results can also be extracted from the model, including the expected number of deaths from AIDS and the prevalence of HIV/AIDS. These can also be compared with observed data counts in order to establish whether the model is fitting the HIV/AIDS epidemic realistically. Figure 5 shows the fit between expected and observed deaths from AIDS. Within the initial conditions of the model, the survival time, 1/, was defined to take a value of 1, based on work by Snary (2000) and Lowrie (2000). This value has not been altered or estimated within the model and, consequently, has kept its value as 1 throughout the fitting process. This may be deemed as unrealistic due to the introduction of treatments in 1987 and 1995, which have been associated with a much reduced death rate. Observed death rates from AIDS can be obtained from the CDSC and, consequently, a new variable value for can be investigated throughout the epidemic using a goodness-of-fit measurement for the observed and expected deaths data and minimizing the total ² subject to changes in the value of the death rate, . This process of minimizing the ² has been performed and the results exemplified in Figure 5. The total ² value for the fit of deaths from AIDS data reduced from 817.106 (when was fixed at a value of 1 over the entire time period, 1979–2002) to nearly a sixth of the amount, 137.872 (3 dp). The improvement in fit was created by initializing at a fixed value of 1 for the pretreatment era (1979–1986), and reducing to a value of 0.6 in the early treatment era (1987–1994). This change in value of is consistent with work produced by Dangerfield et al (2001), who suggest that the mean survival time (where the mean survival time=1/the mean death rate) changes from 0.9 year to 1.8 year as a result of AZT being introduced in 1988. The death rate, within the Cardiff model, then drops even further, to a value of 0.09 in the combination treatment era (1995–2002). As previously, smoothing techniques are employed; for each change in value of , a smoothing period of 2 years was utilized, (ie smoothing periods over the years 1987–1988 for the first change in value and 1996–1997 for the second).

Figure 5.

Comparison between observed and expected deaths from AIDS, 1985–2002.

Full figure and legend (57K)

Figure 6 illustrates the fit for HIV/AIDS prevalence, as produced by the model with variable values of . Data on observed HIV/AIDS prevalence only dates back to 1996, stemming from a variety of sources: The Public Health Laboratory Service (PHLS, 2002) provided diagnosed figures for years 1996–1998 and 2000; CDSC (2000) and the Department of Health (DH, 2000) provided the 1999 prevalence figure; DH (2002) provided amounts for 2001 and 2002. In addition to these diagnosed prevalence figures, it is expected that a number of HIV positive individuals are unaware of their status; for the years 1999–2002, total prevalence estimates can be obtained from DH (2000) and CDSC (2000) for 1999; PHLS (2002) for 2000; and DH (2002) and CDSC (2002) for 2001 and 2002. These total prevalence estimates (diagnosed and undiagnosed), as obtained from the sources listed above for the years 1999–2002, assume the following percentages of homosexuals are unaware of their serostatus: 25, 19, 23 and 24%, respectively. Figure 6 also shows the expected HIV/AIDS prevalence as produced by the model. This is the sum of the numbers in the four sub-populations, Y(t), V(t), A(t) and Z(t) for each year 1996–2002. Comparison between observed and expected prevalence is difficult due to the few observed statistics available and their inconsistency in origin. However, as an example of a possible good fit, the percentage of homo/bisexual men unaware of their infection status has been fixed at a decreasing linear amount each year, starting at 49% unaware in 1996 and reducing to 28% unaware by 2002 (falling by 3.5% each year). The reduction in the proportions of individuals unaware of their serostatus each year can be argued partly due to the improvements in surveillance and testing over time, but also as a result of the introduction of treatments; the fear of testing and diagnosis of HIV may have diminished due to an increase in confidence of the new treatments available. However, a proportion of the population as large as 49% being unaware of their infection is difficult to validate.

Figure 6.

HIV prevalence investigation and comparison, 1996–2002.

Full figure and legend (59K)

Extrapolations and discussion

Now that a good-fitting, realistic, model has been formulated, it can be used to project the short-term future of the HIV/AIDS epidemic, with the assumption that all parameter values and conditions remain constant. Predicting HIV, AIDS and deaths from AIDS up until the year 2008 (with variable), as seen in Figure 7, shows that levels of incidences are maintaining the stability witnessed in the last few years of the modelled epidemic. This means that, assuming no changes, approximately 1680 people will become infected with HIV each year and AIDS incidence and deaths from AIDS will sustain 200 new cases each year from now until the final year extrapolated, 2008. This may initially seem like a positive trend creating a hopeful insight of the epidemic to come. However, when investigated deeper there are further predictions that may cause concern. Figure 8 shows the prevalence of individuals within the sub-populations, X(t), Y(t), V(t), A(t) and Z(t), extrapolated to the year 2008. While the number of individuals susceptible to HIV/AIDS (X(t)) is relatively constant at just under 5000 susceptibles present each year, for the later years of the epidemic, and both high-risk and low-risk AIDS prevalences (A(t) and Z(t), respectively) are maintaining low counts over the years leading up to 2008, the number of people living with HIV is increasing exponentially year on year. Coincident with the introduction of combination therapies in 1995, prevalence, in both high-risk and low-risk HIV infective categories (Y(t) and V(t), respectively), is rising to levels that may be deemed unsustainable in the near future, increasing to amounts never reached before. This is not surprising since treatments such as HAART have reportedly postponed the onset of AIDS, and/or death, to such an extent that it is now believed that virions in the blood can be virtually cleared, given that treatments are initiated early enough with the correct knowledge and expertise applied. Also, as seen in Figure 7, incidence levels are constant, so more and more people are gathering in the infective stage of the epidemic. It can also be noted from Figure 8 that the prevalence of low-risk Infectives actually overtakes that of the high-risk infectives in 2002, due to the constant transition of individuals from high-risk to low-risk behaviour. As a consequence of the greater prevalence numbers of HIV, future estimates of HIV incidence might increase since there are more people living with HIV in the population to infect other people. Furthermore, treatments are improving the health status of people living with HIV and, consequently, individuals may be more sexually active than before, increasing the risks of further transmission of the virus into the susceptible population. These behaviours may result in an increase in HIV incidence in the future, which would then return an even greater rise in HIV prevalence in years to come. Concerns exist as to whether increased levels of HIV prevalence are sustainable in the long term. Many researchers believe that methods of intervention, such as prevention and awareness campaigns, need to be stepped up to meet the levels of success of new treatments in order to ensure the continuation of the beneficial treatment results seen so far. The cost of treatment for each and every individual living with HIV in the UK may become unaffordable if high prevalence levels persist, and consequently, treatment uptake may diminish if prevalence levels continue to rise, resulting in an increase in AIDS incidence and deaths from AIDS to unprecedented levels.

Figure 7.

Extrapolated HIV, AIDS and deaths from AIDS up to 2008.

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Figure 8.

Extrapolated prevalence in sub-populations up to 2008.

Full figure and legend (76K)

Figure 9 illustrates one possible scenario if prevention and awareness campaigns were introduced successfully in the UK in 2005. To model this, the infectivity parameter has been reduced to a value of zero (c=0) from 2007 onwards, with 2 year smoothing from 2005–2006. This equivalently means that no more infections of HIV occur after 2006 due to hypothetical prevention tactics being introduced in 2005, that is, the entire homo/bisexual population in the UK no longer partakes in high-risk activities from 2007 onwards as a result of government awareness campaigns and media publicity targeting HIV/AIDS, commencing in 2005. The extrapolations in Figure 9 for the sub-populations, and the relevant prevalence estimates, are extended to the year 2012 to demonstrate the longer-term effect on the low-risk HIV infectives (V(t)) when introducing effective preventative measures. The high-risk infective sub-population immediately drops as there are no new infectives entering this sub-population from 2007 onwards. At the same time as this movement in Y(t) occurs, the susceptible population, X(t), increases in size rapidly since there is no longer an exit from this sub-population into the infective category. The low-risk Infective category, V(t), takes longer to react since it is not directly linked to the number of new infections. As time progresses, and the number of prevalent high-risk infectives drops, the prevalence of low-risk infectives begins to slowly fall, this is starting to happen by 2012 as can be seen in Figure 9. If extrapolated further, it can be seen that V(t) drops steadily year on year. Thus, according to the extrapolations created by this model, assuming that highly effective prevention methods are enforced in the year 2005 to such an extent that new infections are brought to a standstill, and all other conditions remain the same as for previous years, the HIV/AIDS epidemic can be restrained to controllable and treatable levels within a few years, with the best case scenario being the defeat of the epidemic altogether.

Figure 9.

Extrapolated prevalence in sub-populations, given a change in behaviour, up to 2012.

Full figure and legend (77K)

References

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