Zika is a flavivirus that is transmitted to humans either through the bites of infected Aedes mosquitoes or through sexual transmission. Zika has been associated with congenital anomalies, like microcephalus. We developed and analyzed the fractional-order Zika virus model in this paper, considering the vector transmission route with human influence. The model consists of four compartments: susceptible individuals are x₁(t), infected individuals are x₂(t), x₃(t) shows susceptible mosquitos, and x₄(t) shows the infected mosquitos. The fractional parameter is used to develop the system of complex nonlinear differential equations by using Caputo and Atangana–Baleanu derivative. The stability analysis as well as qualitative analysis of the fractional-order model has been made and verify the non-negative unique solution. Finally, numerical simulations of the model with Caputo and Atangana Baleanu are discussed to present the graphical results for different fractional-order values as well as for the classical model. A comparison has been made to check the accuracy and effectiveness of the developed technique for our obtained results. This investigative research leads to the latest information sector included in the evolution of the Zika virus with the application of fractional analysis in population dynamics.

中文翻译：

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具有时间分数导数的寨卡病毒模型的数学分析与模拟

寨卡病毒是一种黄病毒，通过受感染的伊蚊叮咬或通过性传播传播给人类。寨卡与先天性异常有关，如小头症。我们在本文中开发和分析了分数阶寨卡病毒模型，考虑了具有人类影响的载体传播途径。该模型由四个部分组成：易感个体为x ₁ ( t )，感染个体为x ₂ ( t )，x ₃ ( t )表示易感蚊子，x ₄ ( t )显示受感染的蚊子。分数参数用于通过使用 Caputo 和 Atangana-Baleanu 导数来开发复杂的非线性微分方程组。对分数阶模型进行了稳定性分析和定性分析，验证了非负唯一解。最后，讨论了 Caputo 和 Atangana Baleanu 模型的数值模拟，以呈现不同分数阶值以及经典模型的图形结果。已经进行了比较，以检查所开发技术对我们获得的结果的准确性和有效性。通过在种群动态中应用分数分析，这项调查研究导致了寨卡病毒进化中包含的最新信息部门。