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DPW and SMB designed the study, analyzed the data, and contributed to writing the paper.

SMB is a member of the editorial board of

The authors have declared that no competing interests exist.

Recently, a global commitment has been made to expand access to antiretrovirals (ARVs) in the developing world. However, in many resource-constrained countries the number of individuals infected with HIV in need of treatment will far exceed the supply of ARVs, and only a limited number of health-care facilities (HCFs) will be available for ARV distribution. Deciding how to allocate the limited supply of ARVs among HCFs will be extremely difficult. Resource allocation decisions can be made on the basis of many epidemiological, ethical, or preferential treatment priority criteria.

Here we use operations research techniques, and we show how to determine the optimal strategy for allocating ARVs among HCFs in order to satisfy the equitable criterion that each individual infected with HIV has an equal chance of receiving ARVs. We present a novel spatial mathematical model that includes heterogeneity in treatment accessibility. We show how to use our theoretical framework, in conjunction with an equity objective function, to determine an optimal equitable allocation strategy (OEAS) for ARVs in resource-constrained regions. Our equity objective function enables us to apply the egalitarian principle of equity with respect to access to health care. We use data from the detailed ARV rollout plan designed by the government of South Africa to determine an OEAS for the province of KwaZulu–Natal. We determine the OEAS for KwaZulu–Natal, and we then compare this OEAS with two other ARV allocation strategies: (i) allocating ARVs only to Durban (the largest urban city in KwaZulu–Natal province) and (ii) allocating ARVs equally to all available HCFs. In addition, we compare the OEAS to the current allocation plan of the South African government (which is based upon allocating ARVs to 17 HCFs). We show that our OEAS significantly improves equity in treatment accessibility in comparison with these three ARV allocation strategies. We also quantify how the size of the catchment region surrounding each HCF, and the number of HCFs utilized for ARV distribution, alters the OEAS and the probability of achieving equity in treatment accessibility. We calculate that in order to achieve the greatest degree of treatment equity for individuals with HIV in KwaZulu–Natal, the ARVs should be allocated to 54 HCFs and each HCF should serve a catchment region of 40 to 60 km.

Our OEAS would substantially improve equality in treatment accessibility in comparison with other allocation strategies. Furthermore, our OEAS is extremely different from the currently planned strategy. We suggest that our novel methodology be used to design optimal ARV allocation strategies for resource-constrained countries.

A mathematical model that allows to determine a strategy for distribution of limited medical resources (in this case antiretrovirals) such that each individual in need will have an equal chance of receiving treatment.

Antiretroviral drugs can change the lives of patients with HIV/AIDS. Their high price, however, means that many poor countries do not have enough of these drugs to treat all the people who need them. The decision of who will get treatment is very difficult, and different ways to come up with ethical solutions to the problem have been proposed.

One of the approaches is to try to make sure that every infected person has the same chance to get antiretroviral drugs. David Wilson and Sally Blower, the authors of this study, wanted to find a scientific strategy to achieve this goal of equal access.

They used mathematical models to calculate how to distribute available drugs among hospitals and doctor's offices so that each patient in a particular area had an equal chance to get treated.

When they used their approach on a real example, the South African province of KwaZulu–Natal, they found that making some changes to the current plans for drug distribution would lead to more equal access among all of the individuals with HIV in the province. Instead of only 17 out of the 54 health care facilities in KwaZulu–Natal distributing the drugs (which is the current plan of the South African government), Wilson and Blower calculate that it would be fairer if all 54 facilities distributed the medicines.

Mathematical models like the one used here are always based on assumptions and simplifications. As a consequence, they are never perfect matches for a real-life situation, but they can help to guide complicated decisions. This article suggests that the approach Wilson and Blower developed could help to determine strategies for equitable allocation of limited HIV treatment resources.

The authors hope that the tools they developed will be used by policy makers in resource-poor countries to guide their strategies. They are keen to work with these policy makers to adapt and optimize the method to local settings and priorities.

Report by the World Health Organization and the Joint United Nations Programme on HIV/AIDS on ethics and equitable access to HIV/AIDS treatment:

Ruth Macklin's report on ethics and equity in access to HIV treatment:

The Pro-Poor Health Policy Team's report on priority in HIV/AIDS treatment:

News article from the World Health Organization Bulletin on the South African HIV/AIDS treatment program:

The HIV/AIDS epidemic is having a devastating impact in sub-Saharan Africa and other resource-constrained regions. Recently, the World Health Organization and other organizations have committed to expand access to antiretrovirals (ARVs) in the developing world, the United States government has pledged to provide $15 billion for AIDS in Africa and the Carribean, and drug prices have fallen [

Here, we use operations research to address this important resource allocation problem and to design ARV allocation strategies that are rational and equitable. The allocation decisions that we make here are based on ethical criteria, and not on epidemiological or preferential treatment priority criteria. Specifically, we determine the optimal allocation strategy that would ensure that each individual with HIV has an equal chance of receiving ARVs. We present a novel spatial mathematical model of treatment accessibility that we use in conjunction with an equity objective function to determine an optimal equitable allocation strategy (OEAS) for ARVs in a resource-constrained region. We quantify how changing the size of the catchment region surrounding each HCF, and the number of HCFs utilized for ARV distribution, alters the OEAS. Specifically, we use data from the detailed ARV rollout plan designed by the government of South Africa to determine an OEAS (based upon a variety of assumptions) for the province of KwaZulu–Natal. We also discuss how our proposed ARV allocation strategy differs from the currently proposed plan.

Our current analysis is applied to the South African province of KwaZulu–Natal, although our methodology could be applied to any resource-constrained setting. KwaZulu–Natal is the largest province in South Africa with a population of approximately 9.4 million and has more people infected with HIV than any other province (approximately 21% of all cases in South Africa [

Black crosses indicate the location of the 17 HCFs that have been designated for ARV rollout by the South African government, and the spatial distribution of communities distinguished by the number of individuals infected with HIV (by both size and color). Durban (represented by the large red diamond) is the capital city of the province and has more individuals with HIV than any other community. Pietermaritzburg and Newcastle (represented by orange diamonds) have the next greatest numbers of individuals with HIV.

(A) A histogram indicating heterogeneity in the distance from communities in KwaZulu–Natal to the closest HCF. The treatment accessibility function used in our model is a Gaussian distribution, exp(−^{2}), indicating that accessibility is strongly related to distance

(B) The catchment region is shown with an effective radius of 20 km for coverage from each HCF (

(C) The catchment region is shown with an effective radius of 40 km for coverage from each HCF (

(D) The catchment region is shown with an effective radius of 60 km for coverage from each HCF (

In each case, the red dots indicate the location of the HCF, the green circles represent the locations where treatment accessibility has been reduced to 50% relative to someone located at the HCF, and the blue circles represent the locations where treatment accessibility has been reduced to 1% relative to someone located at the HCF. The locations of communities are presented as black diamonds. The large black diamonds denote large communities (with population greater than 10,000 people), and the small black diamonds denote small communities (with population less than 10,000 people). Substantially more area of the province is covered if HCFs have catchment regions of 60-km radius, relative to catchment regions of 40-km radius, and substantially less area of the province is covered if HCFs have a catchment region of only 20-km radius. However, the proportion of people with access does not differ greatly between the different catchment sizes because of the great spatial heterogeneity in the prevalence of people with HIV.

The location and population of each community (city, town, or village) is indicated. Sources: [

Source: KwaZulu–Natal Department of Health (

We have developed a novel spatial mathematical model of treatment accessibility that we use to determine an OEAS for ARVs in a resource-constrained region. To the best of our knowledge, this is the first analysis to address how to deal with the extremely difficult problem of allocating a scarce supply of ARVs in order to design a rational and equitable allocation strategy. We model the “spatial diffusion of treatment” to the locations of disease, rather than modeling the “spatial diffusion of disease,” which is the conventional approach [

We developed an equity objective function to assess how the limited supply of ARVs should be allocated to each HCF to ensure that an equal proportion of infected people in each community receive treatment. To apply our theoretical framework to KwaZulu–Natal we model the specific location of the 17 HCFs and the 51 communities of 500 or more individuals (see

We assume that the number of people with HIV who will travel to a specific HCF is directly proportional to the number of individuals with HIV in that particular community, but that the probability of an individual traveling to receive ARVs (i.e., the treatment accessibility) decreases with distance from the HCF. We define _{i,j}_{i,j}_{i,j},_{i}_{ij},

where _{i,j}_{i}^{2}), where

To determine how many ARVs should be allocated to each HCF, we first calculate how a given supply of ARVs will be distributed from each HCF to the surrounding communities in the catchment region. We calculate the “effective demand” on HCF _{j},

which sums the “effective demand” of all communities on HCF

Therefore, the number of people treated in community

where _{j}_{i},

We establish an equity objective function to determine the optimal equitable allocation of ARVs to each HCF so that all individuals with HIV have an equal chance of receiving treatment. To obtain the same fraction of treated individuals in each community, given that there are

Our goal is to minimize _{1}, _{2},…, _{n}), whilst enforcing the following three constraints: (i) ensure that the total number of ARVs available is equal to the sum of the supply allocated to all HCFs,

(ii) ensure that only a positive number of ARVs are allocated to each HCF (_{j}_{i}_{i}, i

The OEAS of ARVs in KwaZulu–Natal that we determined is complex (see

The three strategies considered are as follows: allocation of ARVs according to the results of minimizing our objective function (first row) allocation of ARVs only to one HCF in Durban (second row), allocation of ARVs equally to each of the 17 HCFs (third row). The proportion of ARVs allocated by these strategies to the 17 different HCFs is indicated in (A), (D), and (G), with each HCF represented by a different color. The spatial allocation of ARVs is shown in (B), (E), and (H), respectively. The respective percentage of infected people that are treated throughout the KwaZulu–Natal province is simulated in (C), (F), and (I). Here, the

The catchment region for HCFs is a factor of large uncertainty. We considered three catchment region sizes: radii of 20 km, 40 km, and 60 km. We also simulated two additional cases with increased numbers and locations of HCFs (27 HCFs as suggested in South Africa's official ARV rollout operational plan [

Box plots of the percentage of infected people that obtain treatment per community for the three different sets of HCFs simulated in our analysis for ARV rollout, namely, using the 17 HCFs likely to be used, the 27 HCFs suggested by the South African government as potential implementation points, and all of the 54 hospitals in the KwaZulu–Natal province. These cases are represented for each of the three catchment region sizes we considered (with radii of 20 km, 40 km, or 60 km) and referenced against the ideal fraction treated (dotted blue line) under perfect conditions of egalitarian distribution, given the limited ARV supply. The red crosses indicate the median percentage of people with HIV that obtain treatment per community.

These pie charts show ARV allocation to HCFs according to our model and optimization for the cases of 17 , 27 , and 54. The allocation is shown for each of the catchment region sizes considered: 20-km radius, 40-km radius, and 60-km radius.

We have established an elegant and simple theoretical framework for determining an equitable and rational allocation of ARVs to HCFs in resource-constrained countries. To the best of our knowledge, this is the first analysis to address this very difficult problem. We determined that increasing the size of the catchment region of each HCF can improve access to HCFs considerably for rural populations. We suggest that studies be performed to collect data on the distance that individuals with HIV are willing and able to travel for treatment. This will facilitate discussions of this important issue, which must be considered in the making of policy decisions. A database consisting of such information has been proposed for South Africa [

We calculated the optimal allocation of ARVs to available HCFs so that all infected individuals will have as close as possible to an equal chance of obtaining treatment. We have shown that increasing the number of HCFs involved in ARV distribution can improve equality of access to ARVs substantially. The current plan in KwaZulu–Natal is to use only 17 HCFs. However, our results clearly show that in order to achieve an optimal equitable allocation strategy, all existing infrastructure (i.e., all 54 HCFs) should be used. The strategy that we are advising may be fairly easy to accomplish at the policy level because the health-care infrastructure (specifically these HCFs) already exists, although consideration must be made for issues such as the training and transportation that is necessary, which may be costly. In contrast, increasing the size of catchment regions may be very difficult. Obviously, increasing both the number of HCFs and the size of the catchment region each services would substantially increase equality of access to health care in KwaZulu–Natal.

Future modeling studies could extend our work by not making the simplifying assumption that all patients have similar ease of travel over the same distance and by including weighting functions on distance impedance for different communities (based on the quality of the road infrastructure, for example, and the availability of transportation) (D. P. Wilson, J. O. Kahn, S. M. Blower, unpublished data). Here, we have shown how to calculate optimal ARV allocation strategies based upon the principle of equity. Future research is necessary to compare ARV allocation strategies based upon the principle of efficiency (i.e., allocating ARVs to maximize epidemic reduction) in order to determine whether utilizing different principles for optimization would result in similar (or different) allocation strategies.

The World Health Organization and the Joint United Nations Programme on HIV/AIDS have identified three core principles that should underlie the effort to fairly distribute ARVs, namely: urgency, equity, and sustainability [

Although we have focused on one equitable strategy, there are many other ARV allocation strategies that are ethical. Uneven access to HIV treatment has the very real potential to fracture social and political structures and could lead to intrastate and/or interstate conflict [

Treatment priority decisions for individuals could be based on many different criteria, including disease progression (CD4 cell counts and viral load), socioeconomic status, ethnicity, and who is thought to have the greatest risk of transmitting infections (for example, pregnant women with HIV or female sex workers). Although it could be argued that behavioral core groups should be targeted to receive ARVs because this may have the greatest epidemiological impact, such an allocation strategy would be neither feasible nor practical to implement. For example, sex workers are an obvious behavioral core group, but many women would likely claim to be sex workers if they knew that ARVs were only available to sex workers. Additionally, the ethics of targeting such groups in favor of other societal groups must be questioned. It could also be argued that, to maximize the preventative effect of ARV therapy, ARVs should be concentrated in virological core groups (i.e., people with the highest viral load) [

Our model has been applied to the South African province of KwaZulu–Natal, but it can be applied by government health officials in any resource-constrained country. In many of the countries worst affected by the HIV pandemic, scarcity of resources will mean that not everyone that could potentially benefit from ARVs will be able to access them. Many of the decisions that must be made to develop an effective response to the HIV/AIDS epidemic are inevitably underpinned by ethical considerations. Leadership in most resource-constrained regions cannot avoid these decisions. Whilst there has been considerable attention given to South Africa, many other countries worldwide either have plans in place (e.g., Brazil, Thailand, and Botswana) or are in the process of developing national programs for ARV distribution through the public health system (e.g., Mozambique, Malawi, and Kenya) [

The authors acknowledge the financial support of the National Institutes of Health National Institute of Allergy and Infectious Diseases (RO1 AI041935). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

antiretroviral

health-care facility

optimal equitable allocation strategy