AbstractMass vaccinations are crucial public health interventions for curbing infectious diseases. Canine rabies control relies on mass dog vaccination campaigns (MDVCs) that are held annually across the globe. Dog owners must bring their pets to fixed vaccination sites, but sometimes target coverage is not achieved due to low participation.

摘要大规模疫苗接种是遏制传染病的关键公共卫生干预措施。犬类狂犬病的控制依赖于每年在全球范围内举行的大规模犬类疫苗接种活动（MDVCs）。养狗人必须将宠物带到固定的疫苗接种地点，但有时由于参与率低，无法实现目标覆盖率。

Travel distance to vaccination sites is an important barrier to participation. We aimed to increase MDVC participation in silico by optimally placing fixed-point vaccination locations. We quantified participation probability based on walking distance to the nearest vaccination site using regression models fit to participation data collected over 4 years.

到疫苗接种地点的旅行距离是参与的重要障碍。我们的目标是通过最佳地放置定点疫苗接种地点来增加MDVC在计算机上的参与。我们使用适合于4年内收集的参与数据的回归模型，根据步行距离到最近的疫苗接种地点来量化参与概率。

We used computational recursive interchange techniques to optimally place fixed-point vaccination sites and compared predicted participation with these optimally placed vaccination sites to actual locations used in previous campaigns. Algorithms that minimized average walking distance or maximized expected participation provided the best solutions.

我们使用计算递归交换技术来优化定点疫苗接种地点，并将这些最佳接种地点的预测参与率与之前活动中使用的实际地点进行比较。最小化平均步行距离或最大化预期参与度的算法提供了最佳解决方案。

Optimal vaccination placement is expected to increase participation by 7% and improve spatial evenness of coverage, resulting in fewer under-vaccinated pockets. However, unevenness in workload across sites remained. Our data-driven algorithm optimally places limited resources to increase overall vaccination participation and equity.

预计最佳疫苗接种位置将使参与率增加7%，并改善覆盖率的空间均匀性，从而减少接种不足的口袋。然而，各个地点的工作量仍然不均衡。我们的数据驱动算法优化了有限的资源，以增加总体疫苗接种参与率和公平性。

Field evaluations are essential to assess effectiveness and evaluate potentially longer waiting queues resulting from increased participation..

现场评估对于评估有效性和评估参与度增加可能导致的更长等待队列至关重要。。

IntroductionZoonotic epidemics and pandemics are an increasing public health threat worldwide. In Latin America, Asia, and Africa, epidemics of rabies and other zoonotic diseases are ongoing in major urban centers1,2,3,4,5,6,7,8. Vaccination efforts to eliminate canine rabies from Latin American countries have been mostly successful6.

引言人畜共患流行病和大流行是全球范围内日益严重的公共卫生威胁。在拉丁美洲，亚洲和非洲，狂犬病和其他人畜共患疾病正在主要城市中心流行1,2,3,4,5,6,7,8。拉丁美洲国家消除犬狂犬病的疫苗接种工作大多取得了成功6。

However, Peru is experiencing the first instance of canine rabies reintroduction into an area previously declared free of transmission in Latin America9. In the city of Arequipa and surrounding provinces, continued and increased transmission in free-roaming dogs10,11, the sole animal reservoir in the region, has put more than a million human inhabitants at risk of rabies, a fatal, but entirely preventable, disease12.

然而，秘鲁正在经历首次将犬类狂犬病重新引入拉丁美洲先前宣布不传播的地区9。在阿雷基帕市和周边省份，该地区唯一的动物水库自由流浪狗的传播持续增加10,11，使100多万人类居民面临狂犬病的风险，狂犬病是一种致命但完全可以预防的疾病12。

Annual mass dog vaccination campaigns (MDVCs) have been implemented in Peru to eliminate the epidemic without success13. The Pan American Health Organization recommends an annual canine mass vaccination coverage of 80%14; however, in Arequipa, this goal has not been attained in the past 8 years of vaccination campaigns, and rabies virus persists in the free-roaming dog population11,13,15.Most MDVCs in Latin America and Africa rely on fixed-location vaccination posts, where vaccinators wait for dog owners to bring their dogs to a set place15,16,17,18,19.

秘鲁已经实施了年度大规模犬类疫苗接种运动（MDVCs），以消除疫情，但没有取得成功13。泛美卫生组织建议每年犬类大规模疫苗接种率为80%14；然而，在阿雷基帕，在过去8年的疫苗接种运动中，这一目标尚未实现，狂犬病病毒在自由游荡的狗群中持续存在11,13,15。拉丁美洲和非洲的大多数MDVC依赖于固定地点的疫苗接种站，接种者在那里等待狗主人将他们的狗带到固定地点15,16,17,18,19。

The extensive application of fixed-location vaccination is due to its relative ease of implementation and lower cost compared to other strategies18,20,21. However, in some contexts, fixed-point MDVCs have failed to attain coverage targets13,22,23. Extensive behavioral research has been conducted to reduce refusal of human vaccines24,25,26,27,28,29; recent observational studies have focused on understanding non-participation in MDVCs13,15,16,18,19,30,31.

与其他策略相比，固定地点疫苗接种的广泛应用是由于其相对易于实施且成本较低18,20,21。然而，在某些情况下，定点MDVC未能达到覆盖目标13,22,23。；最近的观察性研究集中在了解不参与MDVC 13,15,16,18,19,30,31。

Among the barriers repor.

在报告的障碍中。

Table 1 Regression analysis and cross-validation results.Full size tableOptimal placement of tentsWe simulated campaigns where placement of the vaccination tents was optimized using variants of the facility location problem. The goal in a facility location problem is to determine the placement of facilities (i.e., vaccination sites), among a pool of candidate sites, such that facility access for a set of demand points (i.e., houses) is optimized.

表1回归分析和交叉验证结果。全尺寸表帐篷的最佳放置我们模拟了活动，其中使用设施位置问题的变体优化了疫苗接种帐篷的放置。设施位置问题的目标是确定设施（即疫苗接种地点）在候选地点池中的位置，从而优化一组需求点（即房屋）的设施访问。

Towards this, we first implemented the Teitz and Bart’s algorithm for the “p-median problem,” which aims to find a subset of vaccination sites, S, of size p among a set of candidates, where the average distance of all houses to their nearest point in S is minimized44. To apply this to mass dog vaccination in Arequipa, we aimed to find a set of 20 optimized tent locations that minimized average walking distance to the nearest vaccination site; the number of tents (p = 20) was selected to match the number of tents annually run by the MOH in the MDVC.

为此，我们首先实施了Teitz和Bart的“p-中值问题”算法，该算法旨在在一组候选物中找到大小为p的疫苗接种位点s的子集，其中所有房屋到s中最近点的平均距离最小44。为了将其应用于阿雷基帕的大规模犬类疫苗接种，我们旨在找到一组20个优化的帐篷位置，以最大程度地减少到最近疫苗接种地点的平均步行距离；选择帐篷的数量（p=20）与卫生部在MDVC中每年经营的帐篷数量相匹配。

To find the optimized sites we then applied the Teitz and Bart algorithm. To describe the algorithm denote the set of all houses by \(H = \left\{ {h_{1} , h_{2} , \ldots , h_{N} } \right\}\), where N is the total number of houses. The Teitz and Bart algorithm for placing 20 vaccination sites proceeds as follows:.

为了找到优化的站点，我们应用了Teitz和Bart算法。为了描述该算法，将所有房屋的集合表示为\（H=\ left \{{H\u{1}，H\u{2}，\ldots，H\u{N}}\ right \}\），其中N是房屋总数。。

1.

1.

Select a random subset of 20 vaccination sites \(S = \left\{ {s_{1} , s_{2} , \ldots , s_{20} } \right\}\), out of all candidate sites A. For each house \(h_{i} \in H\), calculate \(d_{min} \left( i \right)\), the walking distance of \(h_{i}\) to the nearest site in S. Then calculate the average walking distance for all houses in the study area:$$\overline{{d_{min} }} = \frac{1}{N}\mathop \sum \limits_{i = 1}^{N} d_{min} \left( i \right)$$.

从所有候选地点a中选择20个疫苗接种地点的随机子集（S=\ left \{{S\u{1}，S\u{2}，\ldots，S\u{20}}\ right \}），对于每个房屋\（h中的h{i}\），计算\（d\umin}\ left（i \ right）\），步行距离\（h{i}\）到S中最近的地点。然后计算研究区域内所有房屋的平均步行距离：$$\ overline{{d\u{min}}=\frac{1}{N}\mathop\sum\limits\u{i=1}^{N}d\u{min}\ left（i \ right）$$。

2.

2.

Exchange \(s_{1}\) with each candidate site in \(A\backslash S\) and keep the one that minimizes \(\overline{{d_{min} }}\).

与\（反斜杠s \）中的每个候选站点交换\（s \{1}\），并保留最小化\（上划线{d \{min}}}\）的站点。

3.

3.

Repeat step 2 with the remaining 19 sites in S until the objective function stabilizes.

对S中剩余的19个位点重复步骤2，直到目标函数稳定。

The second optimization algorithm is an extension of the classic “p-center problem,” which aims to find the subset of facility sites that minimizes the maximum walking distance between any house and its nearest facility45. Classically, the p-center problem is formulated using Euclidean distance, and the solution involves drawing p circles whose union encloses all the demand points such that the maximum of the radii of the circles is minimized45.

第二种优化算法是经典“p中心问题”的扩展，该问题旨在找到设施场地的子集，以最小化任何房屋与其最近设施之间的最大步行距离45。经典地，p中心问题是使用欧几里德距离来描述的，解决方案涉及绘制p圆，其并集包围所有需求点，从而使圆半径的最大值最小化45。

However, the classic formulation of the p-center problem yields many redundant solutions for our case, which uses walking distance instead of Euclidean distance. As a result, we adapted the p-center problem to minimize the sum of the 10 largest maximal tent distances, which we define as follows. For each vaccination tent \(s \in S\), let \(C_{s}\) represent all houses in H for which the tent s is its closest facility.

然而，对于我们的案例，p中心问题的经典公式产生了许多冗余的解决方案，它使用步行距离而不是欧几里得距离。因此，我们调整了p中心问题，以最小化10个最大帐篷距离的总和，我们定义如下。对于每个疫苗接种帐篷（s中的s），让（C{s}）代表H中帐篷s是其最近设施的所有房屋。

Let \(D_{s} = \left\{ {d_{min} \left( i \right):i \in C_{s} } \right\}\) be the set of walking distances between the tent s and all houses in its catchment. Denote by$$max\left( {D_{s} } \right) = max_{{i \in C_{s} }} d_{min} \left( i \right),$$the maximal distance from the tent s to the houses in its catchment.

设\（D\u{s}=\ left \{D\u{min}\ left（i \ right）：i \ in C\u{s}\ right \}\）是帐篷与其流域中所有房屋之间的步行距离集。用$$max \ left（{D\u{s}}\ right）=max\u{i \ in C\u{s}}D\u{min}\ left（i \ right）表示，从帐篷到其集水区房屋的最大距离。

Now, denote by$$\left\{ {m_{1} ,m_{2} , \ldots ,m_{10} } \right\}$$the 10 maximal values among \(\left\{ {max\left( {D_{1} } \right), max\left( {D_{2} } \right), \ldots ,max\left( {D_{20} } \right)} \right\}.\) Our p-center algorithm is similar to the p-median algorithm outlined above; where, instead of minimizing the average walking distance \(\overline{{d_{min} }}\), our p-center algorithm minimizes \(\mathop \sum \limits_{i = 1}^{10} m_{i}\).In addition, we devised a third optimization algorithm that utilized our best-fit regression model that estimated MDVC participation probability as a function of the.

现在，用$$\ left \{{m\u{1}，m\u{2}，ldots，m\u{10}\ right \$$表示\（\ left \{max \ left（{D\u{1}\ right），max \ left（{D\u{2}\ right），\ ldots，max \ left（{D\u{20}\ right）}\ right \}）中的10个最大值我们的p中心算法类似于上面概述的p中值算法；其中，我们的p中心算法不是最小化平均步行距离（overline{d\uu{min}}}），而是最小化（mathop\sum\limits\u{i=1}^{10}m\u{i}）。此外，我们设计了第三种优化算法，该算法利用我们的最佳拟合回归模型来估计MDVC参与概率。

Table 2 Comparison of spatial evenness between current practice vaccination sites and vaccination sites optimized with different algorithms.Full size tableCompared to sites used in 2016, all the optimization algorithms considered produced a smaller D value, indicating that these algorithms improved the spatial evenness of expected vaccination coverage.

表2当前实践疫苗接种地点与使用不同算法优化的疫苗接种地点之间空间均匀性的比较。全尺寸表与2016年使用的站点相比，所有考虑的优化算法产生的D值都较小，表明这些算法改善了预期疫苗接种覆盖率的空间均匀性。

The p-median and p-probability algorithms, which performed best in terms of optimizing total vaccination coverage, also improved spatial evenness the most. The 33% reduction of D achieved by the p-median and p-probability algorithms can be interpreted as follows: compared to the actual vaccination sites used in 2016, if sites placed by these algorithms were used, one-third fewer participant and non-participant households would have to move to produce an even spatial distribution of vaccination coverage.DiscussionWe combine techniques used in facility location problems, combinatorial optimization, and statistical modeling to optimally place fixed-location vaccination points for the annual mass dog rabies vaccination campaigns in Arequipa, Peru.

在优化总疫苗接种覆盖率方面表现最佳的p-中值和p-概率算法也最大程度地改善了空间均匀性。通过p-中位数和p-概率算法实现的D减少33%可以解释如下：与2016年使用的实际疫苗接种地点相比，如果使用这些算法放置的地点，参与者和非参与者家庭将减少三分之一，以产生均匀的疫苗接种覆盖率空间分布。讨论我们结合设施选址问题，组合优化和统计建模中使用的技术，为秘鲁阿雷基帕的年度大规模犬类狂犬病疫苗接种活动最佳地放置固定位置的疫苗接种点。

In line with previous studies examining barriers to vaccination13,18,54,55,56, we found a significant negative association between walking distance from a vaccination location and household participation in the vaccination campaign. In order to maximize the coverage obtained from a fixed number of vaccination points in the city, we optimized the locations of the vaccination points by either minimizing walking distance to the vaccination tents (p-median and p-center) or maximizing overall participation probability (p-probability) The p-median and p-probability methods performed best at increasing estimated vaccination coverage and evening workload across vaccination sites.

与之前研究疫苗接种障碍的研究13,18,54,55,56一致，我们发现距离疫苗接种地点的步行距离与家庭参与疫苗接种运动之间存在显着的负相关。为了最大限度地提高城市固定数量疫苗接种点的覆盖率，我们通过最小化到疫苗接种帐篷的步行距离（p-中位数和p-中心）或最大化总体参与概率（p-概率）来优化疫苗接种点的位置。p-中位数和p-概率方法在增加疫苗接种地点的估计疫苗接种覆盖率和夜间工作量方面表现最佳。

In additio.

此外

Data availability

数据可用性

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

在当前研究期间生成和/或分析的数据集可根据合理要求从通讯作者处获得。

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Download referencesAcknowledgementsWe gratefully acknowledge the members of the Zoonotic Disease Research Laboratory who helped with annual surveys of households in the study area, as well as the Gerencia Regional de Salud de Arequipa and Red de Salud Arequipa Caylloma who ran the annual mass dog vaccination campaigns and shared their expertise with our team.FundingThis project was supported by NIH-NIAID grants K01AI139284 (RCN), R01AI168291 (RCN), and 1R01AI146129 (MZL).

。资助该项目得到了NIH-NIAID拨款K01AI139284（RCN），R01AI168291（RCN）和1R01AI146129（MZL）的支持。

The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Author informationAuthors and AffiliationsDepartment of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USARicardo Castillo-Neyra, Sherrie Xie, Brinkley Raynor Bellotti & Michael Z.

资助者在研究设计，数据收集和分析，决定发表或准备手稿方面没有任何作用。作者信息作者和附属机构宾夕法尼亚大学佩雷尔曼医学院生物统计学，流行病学和信息学系，宾夕法尼亚州费城，USARDO Castillo Neyra，谢丽，Brinkley Raynor Bellotti＆Michael Z。

LevyZoonotic Disease Research Lab, One Health Unit, School of Public Health and Administration, Universidad Peruana Cayetano Heredia, Lima, PeruRicardo Castillo-Neyra, Elvis W. Diaz, Amparo M. Toledo, Gian Franco Condori-Luna & Michael Z. LevyThe Wharton School, University of Pennsylvania, Philadelphia, PA, USAAris Saxena, Maria Rieders & Bhaswar B.

利马秘鲁卡耶塔诺·埃雷迪亚大学公共卫生与管理学院一个健康单位的LevyZoonotic疾病研究实验室，秘鲁卡斯蒂略·内拉，埃尔维斯·W·迪亚兹，安帕罗·M·托莱多，吉安·弗兰科·康多里·卢纳和迈克尔·Z·莱维思宾夕法尼亚大学沃顿商学院，宾夕法尼亚州费城，USARIS Saxena，玛利亚·里德斯和Bhaswar B。

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PubMed Google ScholarContributionsR.C., S.X. and M.Z.L. wrote the main manuscript text; R.C., E.W.D. and A.M.T. collected the data; S.X. and A.S. prepared figures S.X., B.R.B., G.F.C.L., M.R., B.B.B. and A.S. performed the analyses, R.C., M.R., B.B.B. and M.Z.L. conceived and designed the study.

PubMed谷歌学术贡献。C、 ，S.X.和M.Z.L.撰写了主要的手稿文本；R、 ；S、 X.和A.S.准备了数字S.X.，B.R.B.，G.F.C.L.，M.R.，B.B.B.和A.S.进行了分析，R.C.，M.R.，B.B.B.和M.Z.L.构思并设计了这项研究。

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里卡多·卡斯蒂略·内拉。道德宣言

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Reprints and permissionsAbout this articleCite this articleCastillo-Neyra, R., Xie, S., Bellotti, B.R. et al. Optimizing the location of vaccination sites to stop a zoonotic epidemic.

转载和许可本文引用本文Castillo Neyra，R.，Xie，S.，Bellotti，B.R.等人优化疫苗接种地点的位置以阻止人畜共患流行病。

Sci Rep 14, 15910 (2024). https://doi.org/10.1038/s41598-024-66674-xDownload citationReceived: 21 September 2023Accepted: 03 July 2024Published: 10 July 2024DOI: https://doi.org/10.1038/s41598-024-66674-xShare this articleAnyone you share the following link with will be able to read this content:Get shareable linkSorry, a shareable link is not currently available for this article.Copy to clipboard.

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