On the role of vaccination, health education, and hygiene compliance in the elimination and control of Hepatitis A Virus: An optimal control approach

Abstract

A deterministic mathematical model for Hepatitis A infection is established and subsequently examined to optimize control strategies. The model incorporates three time-dependent controls: vaccination, health education, and hygiene compliance, focusing on mitigating disease transmission in the community. The derivation of the basic reproduction number was conducted using the Next-Generation Matrix (NGM) technique, which was subsequently utilized to analyze the stability of the equilibria of the model. The optimal control problem is established and analyzed using Pontryagin’s Maximum principle. The numerical simulation of the optimal control problem is achieved via Runge–Kutta fourth-order schemes (forward and backward sweeps). The numerical findings demonstrate a significant reduction in Hepatitis A cases by implementing at least one control measure. Besides that, it has been established that coupling vaccination, health education and hygiene compliance results in the lowest number of cases, making it an optimal option for eradicating Hepatitis A in the community. However, applying this strategy could be more costlier. As such, the cost-effective analysis was carried out via an incremental cost-effectiveness ratio approach to ascertain the most cost-effective strategy. The findings confirmed that the vaccination strategy was the most cost-effective approach among the strategies under consideration because it offers the minimum number of cases at the minimum cost. This approach is particularly applicable in situations with constrained resources, a circumstance prevalent in many developing nations.