Enacting caring presence in a conflicting environment: the case of state patients

Abstract

This study presents a novel predator-prey model that incorporates Susceptible-Infected (SI) disease dynamics within the predator population. In this model, infected predators face a higher risk of death due to hunger compared to disease-induced death. We introduce two control variables aimed at reducing disease transmission and mitigating the impact of hunger on infected predators. The optimal control problem is formulated using a smoothed prey penalty cost function to ensure the prey population remains above a critical threshold, thereby reducing predator mortality. Existence results for the optimal control are established, and numerical simulations illustrate the effectiveness of the proposed strategies. AMS Subject Classification (2020): 92D25, 92D30, 49N90, 34H05