A Mathematical Model for the Transmission Dynamics of Yellow Fever with Vaccination and Vector Control

Yellow fever, a mosquito borne viral hemorrhagic disease endemic in sub Saharan Africa, remains a significant public health challenge due to insufficient vaccination coverage and inadequate vector control. This study proposes a deterministic model for the transmission dynamics of yellow fever, explicitly incorporating the effect of vaccination alongside vector control as intervention strategies. The model categorized the human population into susceptible, exposed, infectious, and recovered classes, while the vector population is partitioned into susceptible, exposed and infectious compartments, capturing the human-mosquito-human transmission pathway. The model's mathematical wellposedness is established by proving the positivity, boundedness, and uniqueness of solutions. Equilibrium analysis reveals the existence of both disease free and endemic steady states. The effective reproduction number , is derived using the next generation matrix method. Local stability of the disease free equilibrium is examined by linearizing the Jacobian matrix at the disease free state, while the endemic equilibrium is analyzed using the Routh Hurwitz criterion. Global stability results are established via the Castillo Chavez theorem for the disease free equilibrium and an appropriate Lyapunov function for the endemic equilibrium. Sensitivity analysis identifies key parameters influencing , with vaccination coverage and vector control exhibiting strong negative impacts on transmission. Numerical simulations demonstrate that increasing vaccination rates and intensifying mosquito control efforts can reduce below unity, thereby preventing outbreaks. This study emphasizes the importance of combined vaccination and vector control strategies in reducing the burden of yellow fever.