Department of Applied Mathematics, Indian School of Mines, Dhanbad, Jharkhand, India.
Math Biosci. 2013 Apr;242(2):172-87. doi: 10.1016/j.mbs.2013.01.002. Epub 2013 Feb 8.
In this paper, we have proposed and analysed a mathematical model to figure out possible ways to rescue a damaged eco-epidemiological system. Our strategy of rescue is based on the realization of the fact that chaotic dynamics often associated with excursions of system dynamics to extinction-sized densities. Chaotic dynamics of the model is depicted by 2D scans, bifurcation analysis, largest Lyapunov exponent and basin boundary calculations. 2D scan results show that μ, the total death rate of infected prey should be brought down in order to avoid chaotic dynamics. We have carried out linear and nonlinear stability analysis and obtained Hopf-bifurcation and persistence criteria of the proposed model system. The other outcome of this study is a suggestion which involves removal of infected fishes at regular interval of time. The estimation of timing and periodicity of the removal exercises would be decided by the nature of infection more than anything else. If this suggestion is carefully worked out and implemented, it would be most effective in restoring the health of the ecosystem which has immense ecological, economic and aesthetic potential. We discuss the implications of this result to Salton Sea, California, USA. The restoration of the Salton Sea provides a perspective for conservation and management strategy.
本文提出并分析了一个数学模型，以找出可能的方法来拯救受损的生态流行病学系统。我们的救援策略基于这样一个事实，即混沌动力学通常与系统动力学向灭绝密度的漂移有关。模型的混沌动力学通过二维扫描、分岔分析、最大李雅普诺夫指数和基区边界计算来描述。二维扫描结果表明，为了避免混沌动力学，应降低总感染猎物死亡率μ。我们进行了线性和非线性稳定性分析，并得到了所提出模型系统的Hopf 分岔和持久性准则。这项研究的另一个结果是建议定期清除受感染的鱼类。清除工作的时间和周期性的估计将取决于感染的性质，而不是其他任何因素。如果这个建议被认真考虑并实施，它将是恢复生态系统健康最有效的方法，因为生态系统具有巨大的生态、经济和美学潜力。我们讨论了这一结果对美国加利福尼亚州索尔顿海的影响。索尔顿海的恢复为保护和管理策略提供了一个视角。
