Lee Sunmi, Castillo-Chavez Carlos
Department of Applied Mathematics, Kyung Hee University, Yongin-si, 446-701, Republic of Korea.
Simon A. Levin Mathematical, Computational, and Modeling Sciences Center, School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287-1804, USA.
J Theor Biol. 2015 Jun 7;374:152-64. doi: 10.1016/j.jtbi.2015.03.005. Epub 2015 Mar 17.
The reemergence and geographical dispersal of vector-borne diseases challenge global health experts around the world and in particular, dengue poses increasing difficulties in the Americas, due in part to explosive urban and semi-urban growth, increases of within and between region mobility, the absence of a vaccine, and the limited resources available for public health services. In this work, a simple deterministic two-patch model is introduced to assess the impact of dengue transmission dynamics in heterogeneous environments. The two-patch system models the movement (e.g. urban versus rural areas residence times) of individuals between and within patches/environments using residence-time matrices with entries that budget within and between host patch relative residence times, under the assumption that only the human budgets their residence time across regions. Three scenarios are considered: (i) resident hosts in Patch i visit patch j, where i≠j but not the other way around, a scenario referred to as unidirectional motion; (ii) symmetric bi-directional motion; and (iii) asymmetric bi-directional motion. Optimal control theory is used to identify and evaluate patch-specific control measures aimed at reducing dengue prevalence in humans and vectors at a minimal cost. Optimal policies are computed under different residence-matrix configurations mentioned above as well as transmissibility scenarios characterized by the magnitude of the basic reproduction number. Optimal patch-specific polices can ameliorate the impact of epidemic outbreaks substantially when the basic reproduction number is moderate. The final patch-specific epidemic size variation increases as the residence time matrix moves away from the symmetric case (asymmetry). As expected, the patch where individuals spend most of their time or in the patch where transmissibility is higher tend to support larger patch-specific final epidemic sizes. Hence, focusing on intervention that target areas where individuals spend "most" time or where transmissibility is higher turn out to be optimal. Therefore, reducing traffic is likely to take a host-vector system into the world of manageable outbreaks.
媒介传播疾病的再度出现和地理扩散给全球卫生专家带来了挑战，尤其是登革热在美洲造成的困难日益增加，部分原因是城市和半城市的迅猛发展、区域内和区域间人口流动的增加、缺乏疫苗以及公共卫生服务可用资源有限。在这项工作中，引入了一个简单的确定性双斑块模型，以评估登革热在异质环境中传播动态的影响。双斑块系统使用停留时间矩阵对个体在斑块/环境之间以及斑块/环境内部的移动（例如城市与农村地区的停留时间）进行建模，该矩阵的元素记录了宿主斑块内部和之间的相对停留时间，前提是只有人类会规划其跨区域的停留时间。考虑了三种情况：（i）斑块i中的常住宿主访问斑块j，其中i≠j，但反之则不然，这种情况称为单向移动；（ii）对称双向移动；以及（iii）非对称双向移动。最优控制理论用于识别和评估旨在以最小成本降低人类和病媒中登革热流行率的斑块特异性控制措施。在上述不同的停留矩阵配置以及以基本再生数大小为特征的传播性情景下计算最优策略。当基本再生数适中时，最优的斑块特异性策略可以显著减轻疫情爆发的影响。随着停留时间矩阵偏离对称情况（非对称性），最终的斑块特异性疫情规模变化会增加。正如预期的那样，个体花费大部分时间的斑块或传播性较高的斑块往往会出现更大的斑块特异性最终疫情规模。因此，将干预重点放在个体花费“最多”时间或传播性较高的区域被证明是最优的。所以，减少交通流量可能会使宿主-病媒系统进入可控制疫情爆发的状态。
