An integrated optimization control model of combining epidemic and production–inventory models and its numerical simulations

Abstract

This paper explores the integration and harmonization of an epidemic dynamics model and a resource production–inventory management model, aiming to identify optimal control strategies of epidemic containment. We begin with establishing a generalized optimal control model for epidemic dynamics, which offers a unified framework to verify the sufficient conditions for the existence of the optimal solutions to a class of epidemic optimal control models. Based on the model, a resource production–inventory dynamic model with learning ability is proposed to find optimal strategies of the medical resource management. Subsequently, we propose the optimal control model for a dynamics system of COVID-19 and explore the optimal strategies of the combined applications of vaccine and recommended treatment in comprehensive control of the epidemic. Finally, the viability of effective integration and coordination between the optimal control models of the epidemic dynamics and the resource production–inventory system is verified by numerical simulation and analytical analysis, and a new method is implemented for finding the optimal management strategy for epidemic control. Therefore, this study advances a more comprehensive understanding of the interplay between epidemic dynamics and resource management, illustrating the feasibility and efficacy of integrating multiple models to achieve optimal decisions in both theoretical and practical aspects of epidemic control.