Motivated by the Feline immunodeficiency virus, the virus that causes AIDS in cat populations, we use discrete-time infectious disease models with demographic strong Allee effect to examine the impact of the fatal susceptible-infected (SI) infections on two different types of growth functions: Holling type III or modified Beverton–Holt per-capita growth function (compensatory density dependence), and Ricker per-capita growth function with mating (overcompensatory density dependence). The occurrence of the strong Allee effect in the disease-free equation renders the SI population model bistable, where the two coexisting locally asymptotically stable equilibrium points are either the origin (catastrophic extinction state) and the second fixed point (compensatory dynamics) or the origin and an intrinsically generated demographic period $k>1$ population cycle (overcompensatory dynamics). We use the basic reproduction number, ${\mathrm{ℛ}}_0$, and the spectral radius, ${\lambda }_k$, to examine the structures of the coexisting attractors. In particular, we use MATLAB simulations to show that the fatal disease is not only capable of enlarging or shrinking the basin of attraction of the catastrophic extinction state, but it is also capable of fracturing the basins of attraction into several disjoint sets. Thus, making it difficult to specify the asymptotic zoonotic SI disease outcome in terms of all initial infections. The complexity of the basins of attractions appears to increase with an increase in the period of the intrinsically generated demographic population cycles.

中文翻译：

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离散时间人畜共患病模型中的强 Allee 效应和吸引力盆地

受猫免疫缺陷病毒（在猫群中引起艾滋病的病毒）的启发，我们使用具有人口统计学强 Allee 效应的离散时间传染病模型来检查致命的易感感染 (SI) 感染对两种不同类型的生长功能的影响：Holling III 型或改良的 Beverton-Holt 人均生长函数（补偿性密度依赖性），以及具有交配的 Ricker 人均生长函数（过度补偿性密度依赖性）。无病方程中强 Allee 效应的出现使 SI 种群模型双稳态，其中两个并存的局部渐近稳定平衡点是原点（灾难性灭绝状态）和第二不动点（补偿动力学）或原点和内在产生的人口统计时期$ķ>1$人口周期（过度补偿动态）。我们使用基本再生数，${\mathrm{ℛ}}_0$, 和光谱半径,${\lambda }_{ķ}$，检查共存吸引子的结构。特别是，我们使用 MATLAB 模拟表明，致命疾病不仅能够扩大或缩小灾难性灭绝状态的吸引力盆地，而且还能够将吸引力盆地分裂成几个不相交的集合。因此，很难根据所有初始感染来指定渐近人畜共患病 SI 疾病的结果。景点盆地的复杂性似乎随着内在产生的人口周期周期的增加而增加。