In this paper we develop a compartmental model of SIR type (the abbreviation refers to the number of Susceptible, Infected and Recovered people) that models the population dynamics of two diseases that can coinfect. We discuss how the underlying dynamics depends on the carrying capacity K: from a simple dynamics to a more complex. This can also help in understanding the appearance of more complicated dynamics, for example, chaos and periodic oscillations, for large values of K. It is also presented that pathogens can invade in population and their invasion depends on the carrying capacity K which shows that the progression of disease in population depends on carrying capacity. More specifically, we establish all possible scenarios (the so-called transition diagrams) describing an evolution of an (always unique) locally stable equilibrium state (with only non-negative compartments) for fixed fundamental parameters (density independent transmission and vital rates) as a function of the carrying capacity K. An important implication of our results is the following important observation. Note that one can regard the value of K as the natural ‘size’ (the capacity) of a habitat. From this point of view, an isolation of individuals (the strategy which showed its efficiency for COVID-19 in various countries) into smaller resp. larger groups can be modelled by smaller resp. bigger values of K. Then we conclude that the infection dynamics becomes more complex for larger groups, as it fairly maybe expected for values of the reproduction number \(R_0\approx 1\). We show even more, that for the values \(R_0>1\) there are several (in fact four different) distinguished scenarios where the infection complexity (the number of nonzero infected classes) arises with growing K. Our approach is based on a bifurcation analysis which allows to generalize considerably the previous Lotka-Volterra model considered previously in Ghersheen et al. (Math Meth Appl Sci 42(8), 2019).

在本文中，我们开发了一个 SIR 类型的分区模型（缩写是指易感人群、感染人群和康复人群的数量），该模型模拟了可以同时感染的两种疾病的人口动态。我们讨论了潜在的动态如何取决于承载能力K：从简单的动态到更复杂的动态。这也有助于理解更复杂的动力学的出现，例如，对于较大的K值，混沌和周期性振荡。还提出病原体可以在人群中入侵，其入侵取决于携带能力K这表明人群中疾病的进展取决于承载能力。更具体地说，我们建立了所有可能的场景（所谓的转换图），描述了固定基本参数（与密度无关的传输和生命速率）的（总是唯一的）局部稳定平衡状态（只有非负隔室）的演变承载能力K的函数。我们的结果的一个重要含义是以下重要观察。请注意，可以将K的值视为作为栖息地的自然“大小”（容量）。从这个角度来看，将个人（在各个国家/地区显示其对 COVID-19 的效率的策略）隔离为较小的相应。较大的组可以通过较小的resp来建模。K的较大值。然后我们得出结论，对于较大的群体，感染动态变得更加复杂，因为对于繁殖数\(R_0\approx 1\)的值来说，这是完全可以预期的。我们展示了更多，对于值\(R_0>1\)，有几个（实际上是四个不同的）不同的场景，其中感染复杂性（非零感染类的数量）随着K的增长而出现. 我们的方法基于分岔分析，该分析允许在很大程度上概括先前在 Ghersheen 等人中考虑的 Lotka-Volterra 模型。(Math Meth Appl Sci 42(8), 2019)。