Stability analysis of Rift Valley fever transmission model with efficient and cost-effective interventions

Rift Valley fever (RVF) is one of the neglected tropical diseases in Africa, likely to spread to other countries outside the continent, and capable of wreaking havoc on livestock and human populations. This study presents a novel mathematical model for RVF, taking into account time-dependent treatment, vaccination, and environmental sanitation controls. The existence of both RVF-free (disease-free) and RVF-present (endemic) equilibrium points are established analytically. Using the center manifold theory, the co-existence of both equilibrium points is characterized via bifurcation analysis. Castillo-Chavez's M-matrix approach and Lyapunov function are used to carry out the global stability analysis of the model around the disease-free and endemic equilibrium points, respectively. Furthermore, existence of triple optimal control is rigorously proved and characterized using Pontryagin's maximum principle. Consequently, the most efficient and cost-effective of each of the controls and several combinations of the controls are investigated through efficiency and cost-effectiveness analyses. The findings of the study provide insights into long term behavior of the RVF dynamics in the population, suggesting efficient prevention and optimal control measures at minimal cost of intervention.