Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah 711103, West Bengal, India.
J Theor Biol. 2012 Oct 7;310:187-98. doi: 10.1016/j.jtbi.2012.06.032. Epub 2012 Jul 6.
In this paper, we propose and analyze a prey-predator system. Here the prey population is taken as pest and the predators are those eat the pests. Moreover we assume that the prey species is infected with a viral disease forming into susceptible and infected classes and infected prey is more vulnerable to predation by the predator. The dynamical behavior of this system both analytically and numerically is investigated from the point of view of stability and bifurcation. Then we explicitly introduce a control variable for pest control into the analysis by considering the associated control cost. In the nonconstant control case, we use Pontrygin's Maximum principle to derive necessary conditions for the optimal control of the pest. Then we demonstrated the analytical results by numerical analysis and characterized the effects of the parameter values on optimal strategy.
本文提出并分析了一个捕食者-被捕食者系统。这里的被捕食者种群被视为害虫，而捕食者则是那些捕食害虫的物种。此外，我们假设被捕食物种感染了病毒性疾病，形成易感染和感染两个类别，而感染的猎物更容易受到捕食者的捕食。从稳定性和分岔的角度，对该系统的动力学行为进行了分析和数值研究。然后，我们通过考虑相关的控制成本，明确地将一个害虫控制的控制变量引入到分析中。在非恒定控制的情况下，我们使用庞特里亚金极大值原理推导出害虫最优控制的必要条件。然后，我们通过数值分析验证了分析结果，并对最优策略的参数值的影响进行了特征化描述。
