Farming awareness is an important measure for pest controlling in agricultural practice. Time delay in controlling pest may affect the system. Time delay occurs in organizing awareness campaigns, also time delay may takes place in becoming aware of the control strategies or implementing suitable controlling methods informed through social media. Thus we have derived a mathematical model incorporating two time delays into the system and Holling type-II functional response. The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number and time delays. Stability changes occur through Hopf-bifurcation when time delays cross the critical values. Optimal control theory has been applied for cost-effectiveness of the delayed system. Numerical simulations are carried out to justify the analytical results. This study shows that optimal farming awareness through radio, TV etc. can control the delay induced bifurcation in a cost-effective way.

中文翻译：

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具有意识诱导干预的害虫控制多延迟模型——Hopf分岔和最优控制分析

农业意识是农业实践中害虫防治的重要措施。控制害虫的时间延迟可能会影响系统。在组织宣传活动时会出现时间延迟，在了解控制策略或实施通过社交媒体告知的适当控制方法时也可能会出现时间延迟。因此，我们推导出了一个数学模型，该模型将两个时间延迟纳入系统和 Holling II 型功能响应。根据基本再生数和时间延迟，得到平衡点的存在性和稳定性标准。当时间延迟超过临界值时，稳定性变化通过 Hopf 分岔发生。最优控制理论已应用于延迟系统的成本效益。进行数值模拟以证明分析结果的合理性。