Optimal Control and Cost-Effectiveness Analysis in An Epidemic Model with Viral Mutation and Vaccine Intervention

Abstract

This paper introduces an optimal control problem in a two-strain SIR epidemic model with viral mutation and vaccine administration. The purpose of this study was to investigate the efficacy and cost-effectiveness of two disease prevention strategies, namely restriction of community mobility to prevent disease transmission and vaccine intervention. We consider the time-dependent control case, and we use Pontryagin’s Maximum Principle to derive necessary conditions for the optimal control of the disease. We also calculate the Average Cost-Effectiveness Ratio (ACER) and the Incremental Cost-Effectiveness Ratio (ICER) to investigate the cost-effectiveness of all possible strategies of the control measures. The results of this study indicate that the most cost-effective disease control strategy is a combination of mobility restriction and vaccination.

Optimal Control and Cost Effectiveness Analysis for the Transmission Dynamics of Yaws Infection

“…The absence of new serologically confirmed indigenous cases for three years in a row, the absence of any case confirmed by PCR, and the lack of evidence of transmission for three years in a row as determined by sero-surveys conducted on children aged one to five years are the three requirements for the elimination of yaws (WHO, 2022). In order to examine the effectiveness and economics of two disease prevention strategies-community mobility restriction to stop disease transmission and vaccine intervention- Adi, Irsalinda, and Ndii (2022) introduce an optimal control problem in a two-strain SIR epidemic model with viral mutation and vaccine administration. We take into account the timedependent control scenario and construct the essential criteria for the best possible control of the disease using Pontryagin's Maximum Principle.…”

A survey on constructing Lyapunov functions for reaction-diffusion systems with delay and their application in biology

“…Many biological and ecological systems use the Lyapunov function as a key to show the local and global stabilities of the corresponding mathematical models, for example, see [1,2]. Many methods have been developed for constructing such functions associated to ordinary differential equations without/with delay, reaction-diffusion systems without/with delay, and many other systems, see [3][4][5][6][7][8][9]. But it was rare and difficult to determine a rigorous and general approach or method to find the Lyapunov function, and there are numerous works in the literature attempting to find Lyapunov function for various systems.…”