In this paper we continue the stability analysis of the model for coinfection with density dependent susceptible population introduced in Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We consider the remaining parameter values left out from Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We look for coexistence equilibrium points, their stability and dependence on the carrying capacity K. Two sets of parameter value are determined, each giving rise to different scenarios for the equilibrium branch parametrized by K. In both scenarios the branch includes coexistence points implying that both coinfection and single infection of both diseases can exist together in a stable state. There are no simple explicit expression for these equilibrium points and we will require a more delicate analysis of these points with a new bifurcation technique adapted to such epidemic related problems. The first scenario is described by the branch of stable equilibrium points which includes a continuum of coexistence points starting at a bifurcation equilibrium point with zero single infection strain #1 and finishing at another bifurcation point with zero single infection strain #2. In the second scenario the branch also includes a section of coexistence equilibrium points with the same type of starting point but the branch stays inside the positive cone after this. The coexistence equilibrium points are stable at the start of the section. It stays stable as long as the product of K and the rate \({\bar{\gamma }}\) of coinfection resulting from two single infections is small but, after this it can reach a Hopf bifurcation and periodic orbits will appear.

在本文中，我们继续对 Andersson 等人引入的密度依赖性易感人群的共感染模型进行稳定性分析。（密度依赖性对共感染动力学的影响。arXiv:2008.09987, 2020）。我们考虑 Andersson 等人遗漏的其余参数值。（密度依赖性对共感染动力学的影响。arXiv:2008.09987, 2020）。我们寻找共存平衡点，它们的稳定性和对承载能力K 的依赖。确定了两组参数值，每组参数值都会引起由K参数化的平衡分支的不同场景. 在这两种情况下，分支都包括共存点，这意味着两种疾病的共感染和单一感染可以以稳定状态一起存在。这些平衡点没有简单的明确表达，我们将需要使用适用于此类流行病相关问题的新分叉技术对这些点进行更精细的分析。第一种情况由稳定平衡点的分支描述，该分支包括共存点的连续体，从具有零单个感染菌株 #1 的分叉平衡点开始，并在具有零单个感染菌株 #2 的另一个分叉点结束。在第二种情况下，分支还包括一段具有相同类型起点的共存平衡点，但此后分支停留在正锥内。共存平衡点在截面开始处是稳定的。只要产品是稳定的K和由两次单一感染引起的共感染率\({\bar{\gamma }}\)很小，但是在此之后它可以达到 Hopf 分叉并出现周期性轨道。