Malaria prevalence in sub-Saharan Africa remains high. Kenya for example, records about 3.5 million new cases and 11 thousand deaths each year.1 Most of these cases and deaths are among children under five. The main control method in malaria endemic regions has been through the use of insecticide-treated nets (ITNs). Although this approach has been fairly successful, the gains are threatened by mosquito-resistance to pyrethroids (insecticides on nets), physical and chemical degradation of ITNs that reduce their efficacy, inconsistent and improper use by humans, etc. We present a model to investigate the effects of ITN use and mosquito-resistance and adaptation to pyrethroids used to treat bed nets on malaria prevalence and control in malaria endemic regions. The model captures the development and loss of resistance to insecticides, the effects of ITN use on malaria control in a setting where proper and consistent use is not guaranteed, as well as differentiated biting of human hosts by resistant and sensitive mosquitoes. Important thresholds, including the basic reproduction number [Formula: see text], and two parameter groupings that are important for disease control and for establishing the existence of endemic equilibria to the model are calculated. Furthermore, a global sensitivity analysis is carried out to identify important parameters such as insecticide treated bed-net coverage, ITN, the maximum biting rate of resistant mosquitoes, etc., that drive the system and that can be targeted for disease control. Threshold levels of ITN coverage and ITN efficacy required for containing the disease are identified and shown to depend on the type of insecticide-resistance. For example, when mosquito-resistance to insecticides is not permanent and is acquired only through recruitment and the efficacy of ITNs is [Formula: see text], about [Formula: see text] net coverage is required to contain malaria. However, for the same ITN efficacy, i.e., [Formula: see text], approximately [Formula: see text] net coverage is required to contain the disease when resistance to insecticides is permanent and is acquired through recruitment and mutation in mosquitoes. The model exhibits a backward bifurcation, which implies that simply reducing [Formula: see text] slightly below unity might not be enough to contain the disease. We conclude that appropriate measures to reduce or eliminate mosquito-resistance to insecticides, ensure that more people in endemic areas own and use ITNs properly, and that the efficacy of these nets remain high most of the time, as well as educating populations in malaria endemic areas on how to keep mosquito densities low and minimize mosquito bites are important for containing malaria.

中文翻译：

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适应性蚊子行为和经杀虫剂处理的蚊帐对疟疾流行的影响

撒哈拉以南非洲的疟疾流行率仍然很高。例如，肯尼亚每年记录约 350 万新病例和 11000 人死亡。1大多数病例和死亡病例发生在五岁以下的儿童中。疟疾流行地区的主要控制方法是使用驱虫蚊帐 (ITN)。尽管这种方法相当成功，但其收益受到蚊子对拟除虫菊酯（蚊帐上的杀虫剂）的抗性、ITN 的物理和化学降解降低其功效、人类使用不一致和不当等的威胁。我们提出了一个模型来调查ITN 使用和蚊虫抗性以及对用于治疗蚊帐的拟除虫菊酯的适应对疟疾流行地区疟疾流行和控制的影响。该模型记录了对杀虫剂的抗药性的发展和丧失，在无法保证正确和一致使用的环境中使用 ITN 对疟疾控制的影响，以及抵抗和敏感的蚊子对人类宿主的不同叮咬。计算重要阈值，包括基本繁殖数 [公式：见正文]，以及对疾病控制和建立模型的地方性平衡存在很重要的两个参数组。此外，还进行了全局敏感性分析，以确定驱动系统并可以针对疾病控制的重要参数，例如杀虫剂处理的蚊帐覆盖率、ITN、抗性蚊子的最大叮咬率等。确定并显示控制该疾病所需的 ITN 覆盖率和 ITN 功效的阈值水平取决于杀虫剂抗性的类型。例如，当蚊子对杀虫剂的抗药性不是永久性的，只能通过招募获得，并且 ITN 的功效是 [公式：见文本]，关于 [公式：见文本] 需要网络覆盖才能遏制疟疾。然而，对于相同的 ITN 功效，即 [公式：见正文]，当对杀虫剂的抗性是永久性的并且通过蚊子的招募和突变获得时，大约需要 [公式：见正文] 净覆盖率来遏制疾病。该模型表现出后向分叉，这意味着简单地将 [公式：见文本] 略低于统一可能不足以控制疾病。我们得出的结论是，采取适当措施减少或消除蚊子对杀虫剂的抗药性，确保流行地区更多的人拥有并正确使用 ITN，