Vasilyeva Olga, Oraby Tamer, Lutscher Frithjof
Department of Mathematics, Christopher Newport University, 1 Avenue of the Arts, Newport News, VA 23606, United States.
Math Biosci Eng. 2015 Feb;12(1):209-31. doi: 10.3934/mbe.2015.12.209.
Disease transmission depends on the interplay between the infectious agent and the behavior of the host. Some diseases, such as Chronic Wasting Disease, can be transmitted directly between hosts as well as indirectly via the environment. The social behavior of hosts affects both of these pathways, and a successful intervention requires knowledge of the relative influence of the different etiological and behavioral aspects of the disease. We develop a strategic differential equation model for Chronic Wasting Disease and include direct and indirect transmission as well as host aggregation into our model. We calculate the basic reproduction number and perform a sensitivity analysis based on Latin hypercube sampling from published parameter values. We find conditions for the existence of an endemic equilibrium, and show that, under a certain mild assumption on parameters, the model does not exhibit a backward bifurcation or bistability. Hence, the basic reproduction number constitutes the disease elimination threshold. We find that the prevalence of the disease decreases with host aggregation and increases with the lifespan of the infectious agent in the environment.
疾病传播取决于感染源与宿主行为之间的相互作用。一些疾病，如慢性消耗病，既可以在宿主之间直接传播，也可以通过环境间接传播。宿主的社会行为会影响这两种传播途径，而成功的干预措施需要了解疾病不同病因和行为方面的相对影响。我们为慢性消耗病开发了一个战略微分方程模型，并将直接和间接传播以及宿主聚集纳入我们的模型。我们计算基本再生数，并基于已发表参数值的拉丁超立方抽样进行敏感性分析。我们找到了地方病平衡点存在的条件，并表明，在对参数的某个温和假设下，该模型不会出现反向分岔或双稳性。因此，基本再生数构成了疾病消除阈值。我们发现，疾病的流行率随宿主聚集而降低，随感染源在环境中的寿命增加而增加。
