Reducing Sexual Violence by Increasing the Supply of Toilets in Khayelitsha, South Africa: A Mathematical Model

Background
Sexual violence is a major public health issue, affecting 35% of women worldwide. Major risk factors for sexual assault include inadequate indoor sanitation and the need to travel to outdoor toilet facilities. We estimated how increasing the number of toilets in an urban township (Khayelitsha, South Africa) might reduce both economic costs and the incidence and social burden of sexual assault.
Methods
We developed a mathematical model that links risk of sexual assault to the number of sanitation facilities and the time a woman must spend walking to a toilet. We defined a composite societal cost function, comprising both the burden of sexual assault and the costs of installing and maintaining public chemical toilets. By expressing total social costs as a function of the number of available toilets, we were able to identify an optimal (i.e., cost-minimizing) social investment in toilet facilities.
Findings
There are currently an estimated 5600 toilets in Khayelitsha. This results in 635 sexual assaults and US$40 million in combined social costs each year. Increasing the number of toilets to 11300 would minimize total costs ($35 million) and reduce sexual assaults to 446. Higher toilet installation and maintenance costs would be more than offset by lower sexual assault costs. Probabilistic sensitivity analysis shows that the optimal number of toilets exceeds the original allocation of toilets in the township in over 80% of the 5000 iterations of the model.
Interpretation
Improving access to sanitation facilities in urban settlements will simultaneously reduce the incidence of sexual assaults and overall cost to society. Since our analysis ignores the many additional health benefits of improving sanitation in resource-constrained urban areas (e.g., potential reductions in waterborne infectious diseases), the optimal number of toilets identified here should be interpreted as conservative.

### 背景
性暴力（Sexual violence）是一项重大公共卫生问题，全球范围内35%的女性深受其害。性侵犯的主要风险因素包括室内卫生设施不完善，以及需前往户外如厕设施。本研究评估了在南非城市乡镇Khayelitsha增加公厕数量，如何同时降低性侵犯相关经济成本、发生率及社会负担。

### 方法
本研究构建了一个数学模型（mathematical model），将性侵犯风险与卫生设施数量及女性步行至如厕地点所需时长相关联。我们定义了综合社会成本函数（composite societal cost function），该函数同时涵盖性暴力带来的社会负担，以及公共化学公厕（public chemical toilets）的安装与维护成本。通过将社会总成本表示为可用公厕数量的函数，本研究得以确定公厕设施的最优（即成本最小化）社会投入规模。

### 结果
目前Khayelitsha的公厕数量约为5600座，每年因此发生635起性侵犯事件，社会总成本达4000万美元。将公厕数量增至11300座时，可将社会总成本降至3500万美元，实现成本最小化，同时性侵犯事件数可降至446起。公厕安装与维护成本的增加，可通过性侵犯相关成本的降低得到超额抵消。概率敏感性分析（Probabilistic sensitivity analysis）结果显示，在5000次模型迭代中，超过80%的迭代结果表明，最优公厕数量超过该乡镇原有的公厕配置量。

### 解读
改善城市聚居区的卫生设施可及性，可同时降低性侵犯事件发生率与社会整体成本。由于本研究未考虑资源受限城市区域改善卫生设施所能带来的诸多额外健康收益（例如水源性传染病（waterborne infectious diseases）的潜在减少），因此本研究确定的最优公厕数量应被视为保守估计值。