Treatment and delay control strategy for a non-linear rift valley fever epidemic model

Rift Valley Fever (RVF) is a viral disease affecting animals and humans, causing symptoms such as fever, liver damage, and bleeding, particularly prevalent in Africa. This study focuses on numerical solutions for a non-linear delayed dynamic epidemiological model of RVF. It extends a control problem incorporating the susceptible, infected, treated, recovered vector to analyze the impact of measures such as mosquito repellent and treatment. The goal is to examine how time delays in implementing control measures affect the dynamics of an epidemic. The model considers delay factors such as mosquito replication, hospitalization, travel restrictions, and isolation due to the lack of proper vaccination. The study explores the model's aspects, including the reproduction number, equilibrium points, and stability. Local and global implications are examined using techniques such as the Lyapunov function and the Brauer-F lemma. Numerical analysis employs the non-standard finite difference method, establishing the local stability of the equilibrium through the effective reproduction number Rrvf and sensitivity analysis. The research highlights the importance of treatment and delay strategies in reducing RVF transmission, emphasizing the critical need for immunization and preventive measures.