We propose new single and two-strain epidemic models represented by systems of delay differential equations and based on the number of newly exposed individuals. Transitions between exposed, infectious, recovered, and back to susceptible compartments are determined by the corresponding time delays. Existence and positiveness of solutions are proved. Reduction of delay differential equations to integral equations allows the analysis of stationary solutions and their stability. In the case of two strains, they compete with each other, and the strain with a larger individual basic reproduction number dominates the other one. However, if the basic reproduction number exceeds some critical values, stationary solution loses its stability resulting in periodic time oscillations. In this case, both strains are present and their dynamics is not completely determined by the basic reproduction numbers but also by other parameters. The results of the work are illustrated by comparison with data on seasonal influenza.

中文翻译：

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由潜伏期、感染和免疫持续时间决定的延迟流行病模型

我们提出了新的单株和双株流行病模型，以时滞微分方程组为代表，并基于新暴露个体的数量。暴露区、传染区、恢复区和返回易感区之间的过渡由相应的时间延迟决定。证明了解的存在性和正性。将时滞微分方程简化为积分方程可以分析稳态解及其稳定性。在两个菌株的情况下，它们相互竞争，个体基本繁殖数较大的菌株占主导地位。然而，如果基本再生数超过某些临界值，平稳解就会失去稳定性，导致周期性时间振荡。在这种情况下，两种菌株都存在，并且它们的动态并不完全由基本繁殖数决定，还由其他参数决定。通过与季节性流感数据的比较来说明工作结果。