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

Abstract

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.

Keywords: Bifurcation analysis; Economic analysis; Global stability; Mathematical model; Optimal control; Rift Valley fever.

Fig. 1

Global asymptotic stability of the RVF-free and RVF-present equilibrium points at different initial sizes.

Fig. 2

Behaviour of infected humans, infectious cattle, infectious mosquitoes and infected tissues in the environment and control profile with and without optimal combination of treatment in cattle and humans and vaccination .

Fig. 3

Behaviour of infected humans, infectious cattle, infectious mosquitoes and infected tissues in the environment and control profile with and without optimal combination of vaccination and environmental sanitation .

Fig. 4

Behaviour of infected humans, infectious cattle, infectious mosquitoes and infected tissues in the environment and control profile with and without optimal combination of treatment in cattle and humans and environmental sanitation .

Fig. 5

Behaviour of infected humans, infectious cattle, infectious mosquitoes and infected tissues in the environment and control profile with and without optimal combination of treatment in cattle and humans , vaccination and environmental sanitation .