Itao Kenji, Omata Fumiya, Nishikawa Yoshitaka, Oda Tetsuro, Sasaki Toshiharu, Zhang Cherri, Maninang John Solomon, Yamaguchi Takayuki
Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, Japan.
Kurihara Central Hospital 3-1-1 Miyano-Chuo Tukidate Kurihara city, Miyagi, Japan.
Math Biosci Eng. 2019 Jun 25;16(5):5931-5946. doi: 10.3934/mbe.2019297.
Depopulation is one of the important interventions for the outbreak of animal diseases. Simulation models using actual case scenarios conclude that early depopulation is the most efficient in preventing the spread of foot-and-mouth disease (FMD). However, the long delay in its initiation was often seen in the actual cases and the theoretical analyses of FMD epidemiology with depopulation needs further elaboration. Here, we investigated the qualitative features of epidemic models when depopulation at a fixed capacity was delayed. We built a simple deterministic model for FMD based on state-transition, the SEIIR model whose unit is a single farm. The model settings and parameters were determined using the data from the 2010 epidemic in Miyazaki, Japan. By numerical calculation, we showed the existence of the threshold phenomenon with respect to delays in the initiation of depopulation and if the initiation of full-fledged depopulation surpasses the certain critical timing, the final size of the epidemic rapidly increases leading to a "catastrophic situation". We also revealed the mechanism of the threshold phenomenon from the relationship between the depopulation capacity and the increasing rate of infection. Although it can be delayed with lower transmission coefficients, the threshold phenomenon still exists. Thus, the existence of the critical timing for depopulation appears to be a universal feature of FMD epidemiology when depopulation is used as the main treatment for disease control.
扑杀是动物疾病爆发时的重要干预措施之一。使用实际病例情景的模拟模型得出结论，早期扑杀在预防口蹄疫（FMD）传播方面最为有效。然而，在实际病例中经常出现扑杀启动的长时间延迟，并且对口蹄疫流行病学与扑杀的理论分析需要进一步阐述。在此，我们研究了固定容量扑杀延迟时流行模型的定性特征。我们基于状态转换构建了一个简单的口蹄疫确定性模型，即单位为单个农场的SEIIR模型。模型设置和参数使用来自日本宫崎2010年疫情的数据确定。通过数值计算，我们展示了扑杀启动延迟方面阈值现象的存在，并且如果全面扑杀的启动超过某个关键时间点，疫情的最终规模会迅速增加，导致“灾难性情况”。我们还从扑杀能力与感染增加率之间的关系揭示了阈值现象的机制。尽管它可以通过较低的传播系数延迟，但阈值现象仍然存在。因此，当扑杀用作疾病控制的主要治疗方法时，扑杀关键时间点的存在似乎是口蹄疫流行病学的一个普遍特征。
