Analysis of Stability in a Delay Differential Equation Model for Malaria InfectionWith Treatment

In this paper, we introduce a biological model employing delay differential equations to explore the evolution of malaria within a host undergoing drug treatment. Our analysis focuses on the stability of equilibrium points, leveraging the critical case theorem, an extension of the Lyapunov-Malkin theorem, which is particularly useful for scenarios involving zero roots in the characteristic equation. By determining equilibrium points and assessing their stability through the eigenvalues of the linearized system, we ensure the applicability of the theorem via translations to zero. The results highlight the significant influence of treatment-induced delays on the stability of malaria dynamics, offering valuable insights for optimizing control strategies and improving disease management.