We investigate a model for a vector-borne disease of susceptible-infected-removed type for the hosts in the presence of control measures and state constraints. The control is based on the use of textiles and household items treated with mosquito repellents which alter the mosquitos' host seeking behaviour. We perform a viability analysis of the model, which amounts to finding a viability kernel, or a set of initial conditions such that the proportion of infected individuals in the controlled system remains below a target infection cap for all future times. The viability kernel is characterised by a variational formulation. It is computed numerically from the sub-zero level-set of a value function that solves a Hamilton-Jacobi-Bellman equation.

我们研究了在存在控制措施和状态约束的情况下宿主易感性感染去除型载体传播疾病的模型。该控制措施是基于使用经驱蚊剂处理的纺织品和家庭用品的使用，从而改变了蚊子寻找宿主的行为。我们执行该模型的生存力分析，即找到一个生存力核或一组初始条件，以使受控系统中被感染个体的比例在未来所有时间内都保持在目标感染上限以下。生存力核心的特征在于变异配方。它是通过求解Hamilton-Jacobi-Bellman方程的值函数的次零级水平集进行数值计算的。