We study a general multi-host model of visceral leishmaniasis including both humans and animals, and where host and vector characteristics are captured via host competence along with vector biting preference. Additionally, the model accounts for spatial heterogeneity in human population and heterogeneity in biting behaviour of sandflies. We then use parameters for visceral leishmaniasis in the Indian subcontinent as an example and demonstrate that the model exhibits backward bifurcation, i.e. it has a human infection and a sandfly population threshold, characterized by a bi-stable region. These thresholds shift as a function of host competence, host population size, vector feeding preference, spatial heterogeneity, biting heterogeneity and control efforts. In particular, if control is applied through human treatment a new and lower human infection threshold is created, making elimination difficult to achieve, before eventually the human infection threshold no longer exists, making it impossible to control the disease by only reducing the infection levels below a certain threshold. A better strategy would be to reduce the human infection below a certain threshold potentially by early diagnosis, control animal population levels and keep the vector population under check. Spatial heterogeneity in human populations lowers the overall thresholds as a result of weak migration between patches.

我们研究了内脏利什曼病的一般多宿主模型，包括人和动物，其中宿主和载体的特征是通过宿主能力以及载体咬合偏好来捕获的。此外，该模型说明了人类种群的空间异质性和沙蝇咬人行为的异质性。然后，我们以印度次大陆的内脏利什曼病参数为例，证明该模型表现出向后分叉，即它具有人类感染和以双稳态区域为特征的沙蝇种群阈值。这些阈值随宿主能力，宿主种群大小，媒介饲养偏好，空间异质性，咬合异质性和控制工作而变化。特别是，如果通过人的治疗进行控制，则会创建一个新的较低的人类感染阈值，从而难以实现消除，最终人类感染阈值将不复存在，从而无法通过仅将感染水平降低到一定阈值以下来控制疾病。更好的策略是可以通过早期诊断将人类感染降低到一定阈值以下，控制动物种群水平并使载体种群受到控制。由于斑块之间的弱迁移，人口中的空间异质性降低了总体阈值。仅通过将感染水平降低到一定阈值以下就不可能控制疾病。更好的策略是可以通过早期诊断将人类感染降低到一定阈值以下，控制动物种群水平并使载体种群受到控制。由于斑块之间的弱迁移，人口中的空间异质性降低了总体阈值。仅通过将感染水平降低到一定阈值以下就不可能控制疾病。更好的策略是可以通过早期诊断将人类感染降低到一定阈值以下，控制动物种群水平并使载体种群受到控制。由于斑块之间的弱迁移，人口中的空间异质性降低了总体阈值。