In this paper, five different models for five different kinds of diseases occurring in wildlife populations are introduced. In all models, a logistic growth term is taken into account and the disease is transmitted to the susceptible population indirectly through an environment reservoir. The time evolution of these diseases is described together with its spatial propagation.The character of spatial homogeneous equilibria against the uniform and non-uniform perturbations together with the occurrence of Hopf bifurcations are discussed through a linear stability analysis. No Turing instability is observed.The partial differential field equations are also integrated numerically to validate the stability results herein obtained and to extract additional information on the temporal and spatial behavior of the different diseases.

中文翻译：

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间接传播的野生动物种群疾病的数学模型

本文介绍了针对野生动物种群中发生的五种不同疾病的五种不同模型。在所有模型中，都考虑了逻辑增长项，并且疾病通过环境水库间接传播给易感人群。描述了这些疾病的时间演化及其空间传播。通过线性稳定性分析讨论了空间均匀平衡对均匀和非均匀扰动的特性以及Hopf分岔的发生。没有观察到图灵不稳定性。偏微分场方程还进行了数值积分，以验证此处获得的稳定性结果，并提取有关不同疾病的时间和空间行为的其他信息。