Abstract This paper deals with an optimal control problem for a general reaction-diffusion predator-prey model with disease in prey population. Infected prey will recover from a medication considered as a control strategy. Our primary goal is to characterize an optimal control which minimizes the total density of infected prey and the costs of treatment. Firstly, we obtain the existence and some estimates of the unique strong solution for the controlled system by applying semigroup theory. Subsequently, the existence of optimal pair is proved by means of the technique of minimizing sequence. Furthermore, by proving the differentiability of the control-to-state mapping, we derive the first-order necessary optimality condition, and point out that the optimal is a Bang-Bang control in a special case. Finally, several numerical simulations are performed to illustrate the concrete realization and practical application of the theoretical results obtained in this contribution.

中文翻译：

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具有猎物疾病的一般反应-扩散生态流行病学模型的最优控制问题

摘要 本文研究了具有疾病的猎物种群的一般反应-扩散捕食者-猎物模型的最优控制问题。受感染的猎物将从被视为控制策略的药物中恢复。我们的主要目标是确定一个最佳控制，以最大限度地减少受感染猎物的总密度和治疗成本。首先，应用半群理论得到受控系统唯一强解的存在性和一些估计。随后，通过最小化序列的技术证明了最优对的存在。此外，通过证明控制到状态映射的可微性，我们推导出一阶必要最优条件，并指出最优是特殊情况下的Bang-Bang控制。最后，