Dynamical analysis and optimal control of a malaria transmission model with vaccination

Abstract

This study develops and analyzes a compartmental model for optimizing malaria control strategies, with particular emphasis on the role of vaccination. The model captures key epidemiological dynamics, including resusceptibility, drug resistance, and vaccination, and incorporates three time-dependent control interventions: preventive measures, vaccination enhancement, and treatment efforts. The basic reproduction number is analytically derived to characterize the threshold conditions for disease persistence. Local and global stability analyses of the nonendemic equilibrium are carried out, providing theoretical assurance that the disease can be eradicated when the reproduction number is below unity. Parameter values are obtained from regional data and literature sources. A local sensitivity analysis based on elasticity indices identifies the most influential parameters affecting the basic reproduction number, notably the transmission rates between humans and mosquitoes and the treatment rate for drug-sensitive infections. Contour plots further illustrate the joint effects of key parameters on disease transmission potential. Optimal control strategies are derived using Pontryagin’s Maximum Principle and validated through numerical simulations. The results demonstrate that vaccination significantly reduces the number of infected individuals and enhances overall disease suppression, particularly when implemented alongside prevention and treatment controls. These findings underscore the importance of integrating vaccination with other public health interventions to design effective and cost-efficient malaria control programs.