Stability and Control of a Vector-Host Disease Model with Time Delay and Saturated Treatment

This paper studies the dynamics of a vector-host illness model with a time-based delay and a saturated treatment function. The human population is divided into three compartments, while the vector population is categorized into two groups. A treatment function is introduced to account for the limited capacity of the healthcare system. Four control strategies are identified to reduce the infected population and increase the number of susceptible and recovered individuals. The analysis demonstrates endemic and disease-free equilibria exhibit stability depending on the basic reproduction number. Additionally, the study addresses optimal control with time delays, revealing the impact of delayed therapies on disease dynamics and control strategies. Numerical simulations are used to support and complement the theoretical conclusions.