We introduce novel epidemic models with single and two strains described by systems of delay differential equations with a periodic time-dependent disease transmission rate, and based on the number of newly infected individuals. Transitions between infected, recovered, and returning to susceptible compartments due to waning immunity are determined by the accompanying time delays. Positiveness, existence and uniqueness of solutions are demonstrated with the help of fixed point theory. Reducing delay differential equations to integral equations facilitates determining the analytical estimation of the equilibrium solutions. When there are two strains, they compete with each other, and the strain with a larger basic reproduction number dominates in the population. However, both strains coexist, and the magnitudes of epidemic outbreaks are governed by the basic reproduction numbers. The results of this work are verified through comparison with seasonal influenza data.

中文翻译：

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具有周期性传播率的延迟流行模型动力学


我们引入了新的流行模型，其中单毒株和双毒株由延迟微分方程系统描述，具有周期性时间依赖性疾病传播率，并基于新感染者的数量。由于免疫力减弱，感染、康复和返回易感隔室之间的过渡由伴随的时间延迟决定。在定点理论的帮助下证明了解决方案的积极性、存在性和唯一性。将延迟微分方程简化为积分方程有助于确定平衡解的解析估计。当有两个品系时，它们会相互竞争，具有较大基本繁殖数的品系在种群中占主导地位。然而，这两种菌株共存，流行病爆发的程度由基本繁殖数决定。通过与季节性流感数据的比较验证了这项工作的结果。