Despite centuries of enormous control efforts, mosquito-borne diseases continue to show upward trend of morbidity. According to WHO reports, malaria caused 438000 deaths in the year 2015 and dengue cases have been increased 30-fold over the last five decades. To control these diseases, it is necessary to understand the transmission dynamics of them among mosquitoes. There are some vertically transmitted mosquito-borne diseases which can also be spread among mosquitoes through sexual contact (e.g., dengue, zika, chikungunya). Recent experimental observations indicate that for virus persistence in mosquito population, the role of venereal transmission cannot be ignored. It is therefore important to investigate which transmission route is more responsible for the persistence of the virus when there is no host. To this aim, we propose and analyze a novel compartmental model considering mosquito population only. To the best of authors knowledge, this is the first attempt to take into account both vertical and sexual transmission of the virus in a mathematical model. Expression representing the basic reproduction number is derived using Jacobian approach. Local stability conditions for disease-free equilibrium and complete infection equilibrium are obtained. Global sensitivity analysis of the system is performed with respect to an epidemiologically important response. While investigating the impact of sexual transmission in presence of vertical transmission, we observed that sexual transmission route has the potential to drive the equilibrium from disease free to endemic states. Further numerical experiments reveal that the virus will have higher half life in fertilized infected female mosquitoes for vertical transmission only than for venereal transmission alone. Furthermore, when both transmission pathways are active, a variety of parameters indicate threshold like behavior of the infection.

中文翻译：

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性病传播对蚊子垂直传播病毒疾病动力学的影响。

尽管经过数百年的巨大努力，蚊子传播的疾病继续呈上升趋势。根据世卫组织的报告，疟疾在2015年造成438000人死亡，在过去的五十年中，登革热病例已增加30倍。为了控制这些疾病，有必要了解它们在蚊子之间的传播动态。有一些垂直传播的蚊媒疾病，也可以通过性接触（例如登革热，寨卡病毒，基孔肯雅热）在蚊子中传播。最近的实验观察表明，对于蚊子种群中的病毒持久性而言，性传播途径的作用不可忽视。因此，重要的是研究在没有宿主的情况下哪种传播途径对病毒的持久性负责。为此，我们提出并分析了仅考虑蚊子种群的新型隔室模型。据作者所知，这是首次尝试在数学模型中考虑病毒的垂直传播和性传播。使用雅可比方法导出表示基本再现编号的表达式。获得了无病平衡和完全感染平衡的局部稳定性条件。针对流行病学上重要的反应对系统进行全局敏感性分析。在调查存在垂直传播的情况下性传播的影响时，我们观察到性传播途径具有将平衡从无病状态转移到流行状态的潜力。进一步的数值实验表明，该病毒在受精感染的雌性蚊子中仅垂直传播比单独的性传播具有更高的半衰期。此外，当两个传播路径均处于活动状态时，各种参数会指示阈值，如感染行为。