Dengue is among the most important infectious diseases in the world. The main contribution of our paper is to present a mixed system of partial and ordinary differential equations. This combined model is a generalization of the two presented mathematical models (A. L. de Araujo, J. L. Boldrini and B. M. Calsavara, An analysis of a mathematical model describing the geographic spread of dengue disease, J. Math. Anal. Appl. 444 (2016) 298–325) and (L. Cai, X. Li, N. Tuncer, M. Martcheva and A. A. Lashari, Optimal control of a malaria model with asymptomatic class and superinfection, Math. Biosci. 288 (2017) 94–108), describing the geographic spread of dengue disease. Our model has the ability to consider the possibility of asymptomatic infection, which leads to investigate the effect of dengue asymptomatic individuals on disease dynamics and to go into the possibility of superinfection of asymptomatic individuals. In the light of considering these factors, as well as the movements of human and mature female mosquitoes, more realistic modeling of dengue disease can be achieved. We present a mathematical analysis and show the global existence of a unique non-negative solution to this model and then establish ways to control dengue disease using numerical simulations and sensitivity analysis of model parameters (which are related to the contact rates and death rate of winged mosquitoes). To show different biological behaviors, we provide several numerical results, showing the role of parameters in controlling dengue disease transmission. From our numerical simulations, it can also be concluded that local control of dengue transmission can be done at a lower cost.

中文翻译：

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具有数字季节控制的登革热疾病模型的三维传播分析

登革热是世界上最重要的传染病之一。我们论文的主要贡献是提出了偏微分方程和常微分方程的混合系统。该组合模型是对两个提出的数学模型（AL de Araujo、JL Boldrini 和 BM Calsavara，描述登革热地理传播的数学模型的分析）的概括，J.数学。肛门。应用程序。 444(2016) 298–325) 和 (L. Cai, X. Li, N. Tuncer, M. Martcheva 和 AA Lashari, 无症状类和重复感染疟疾模型的最佳控制,数学。生物科学。 288(2017) 94–108)，描述了登革热的地理传播。我们的模型能够考虑无症状感染的可能性，从而研究登革热无症状个体对疾病动态的影响，并研究无症状个体重复感染的可能性。考虑到这些因素，以及人类和成熟雌性蚊子的运动，可以实现更逼真的登革热疾病建模。我们提出了一个数学分析，并展示了该模型的唯一非负解的全局存在，然后使用数值模拟和模型参数的敏感性分析（与有翼的接触率和死亡率相关）建立控制登革热病的方法蚊子）。为了表现出不同的生物行为，我们提供了几个数值结果，显示了参数在控制登革热传播中的作用。从我们的数值模拟中，还可以得出结论，登革热传播的局部控制可以以较低的成本进行。