Mathur Kunwer Singh, Srivastava Abhay, Dhar Joydip
Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, Sagar, Madhya Pradesh 470003 India.
ABV - Indian Institute of Information Technology & Management, Gwalior, Madhya Pradesh 474015 India.
J Eng Math. 2021;127(1):1. doi: 10.1007/s10665-021-10089-4. Epub 2021 Feb 20.
In this work, an eco-epidemic predator-prey model with media-induced response function for the interaction of humans with adulterated food is developed and studied. The human population is divided into two main compartments, namely, susceptible and infected. This system has three equilibria; trivial, disease-free and endemic. The trivial equilibrium is forever an unstable saddle position, while the disease-free state is locally asymptotically stable under a threshold of delay parameter as well as . The sufficient conditions for the local stability of the endemic equilibrium point are further explored when . The conditions for the occurrence of the stability switching are also determined by taking infection delay time as a critical parameter, which concludes that the delay can produce instability and small amplitude oscillations of population masses via Hopf bifurcations. Further, we study the stability and direction of the Hopf bifurcations using the center manifold argument. Furthermore, some numerical simulations are conducted to validate our analytical findings and discuss their biological inferences. Finally, the normalized forward sensitivity index is used to perform the sensitivity analysis of and .
在这项工作中，我们建立并研究了一个具有媒体诱导响应函数的生态流行病捕食者 - 猎物模型，用于描述人类与掺假食品相互作用的情况。人群被分为两个主要部分，即易感人群和感染人群。该系统有三个平衡点：平凡平衡点、无病平衡点和地方病平衡点。平凡平衡点始终是一个不稳定的鞍点，而无病状态在延迟参数阈值以及 下是局部渐近稳定的。当 时，进一步探讨了地方病平衡点局部稳定性的充分条件。通过将感染延迟时间作为关键参数，确定了稳定性切换发生的条件，结果表明延迟可通过霍普夫分岔产生种群数量的不稳定性和小振幅振荡。此外，我们使用中心流形理论研究了霍普夫分岔的稳定性和方向。此外，进行了一些数值模拟以验证我们的分析结果并讨论其生物学推断。最后，使用归一化正向灵敏度指数对 和 进行灵敏度分析。
