Optimal impulse control of West Nile virus
Optimal impulse control of West Nile virus
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DOI：
10.3934/math.20221075
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发表时间：
2022
期刊：
影响因子：
2.2
通讯作者：
F. Agusto;Daniel Bond;Adira Cohen;Wandi Ding;R. Leander;Allis Royer
中科院分区：
文献类型：
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作者：
F. Agusto;Daniel Bond;Adira Cohen;Wandi Ding;R. Leander;Allis Royer
我们构建了一个西尼罗河病毒流行模型，其中包括鸟类宿主和蚊媒之间的相互作用，蚊子的生活阶段(卵、幼虫、成虫)，以及杀幼虫和杀鼠剂的动态。我们得到了流行病的基本再生数作为下一代矩阵的谱半径。我们提出了两个脉冲最优控制问题，寻求在杀虫剂使用成本(包括时间和使用水平)与(1)媒介控制：减少蚊子数量或(2)疾病控制：减少疾病负担之间取得平衡。我们将这些脉冲最优控制问题转化为非线性优化问题，并推导出相应的最优控制必要条件。数值模拟被用来解决三个问题：控制及其对系统的影响如何随着目标类型的变化而变化？是否有利于优化治疗时机？使用的杀虫剂种类不同，控制措施及其对种群的影响有何不同？
We construct a West Nile virus epidemic model that includes the interaction between the bird hosts and mosquito vectors, mosquito life stages (eggs, larvae, adults), and the dynamics of both larvicide and adulticide. We derive the basic reproduction number for the epidemic as the spectral radius of the next generation matrix. We formulate two impulsive optimal control problems which seek to balance the cost of insecticide applications (both the timing and application level) with the benefit of (1) vector control: reducing the number of mosquitoes or (2) disease control: reducing the disease burden. We reformulate these impulsive optimal control problems as nonlinear optimization problems and derive associated necessary conditions for the optimal controls. Numerical simulations are used to address three questions: How does the control and its impact on the system vary with the objective type? Is it beneficial to optimize the treatment timing? How does the control and its impact on the population vary with the type of pesticide used?