Optimal Treatment Strategy for Infectious Diseases with Two Treatment Stages

In this paper, a disease transmission model with two treatment stages is proposed and analyzed. The results indicate that the basic reproduction number is a critical threshold for the prevalence of the disease. If the basic reproduction number is less than one, the disease free equilibrium is globally asymptotically stable. Otherwise, the endemic equilibrium is globally asymptotically stable. Therefore, besides the basic reproduction number, a new marker for characterizing the seriousness of the disease, named as dynamical final infective size, is proposed, which differs from traditional final size because the proposed model includes the natural birth and death. Finally, optimization strategies for limited medical resources are obtained from the perspectives of basic reproduction number and dynamical final infective size, and the real-world disease management scenarios are given based on these finding.