Mathematical Modeling of Yellow Fever Transmission Dynamics with Multiple Control Measures
Tunde T. Yusuf *
Department of Mathematical Sciences, The Federal University of Technology Akure, Ondo state, Nigeria.
David O. Daniel
Department of Mathematical Sciences, The Federal University of Technology Akure, Ondo state, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Yellow-fever disease remains endemic in some parts of the world despite the availability of a potent vaccine and effective treatment for the disease. This necessitates continuous research to possibly eradicate the spread of the disease and its attendant burden. Consequently, a deterministic
model for Yellow-fever disease transmission dynamics within the human and vector population is considered. The model equilibrium solutions are obtained while the criteria for their existence and stability are investigated. The model is solved numerically using the forth order Runge- Kunta scheme and the results are simulated for different scenarios of interest. Findings from the simulations show that the disease will continue to be prevalent in our society (no matter how small) as long as the immunity conferred by the available vaccine is not lifelong and the Yellowfever infected mosquitoes continue to have unhindered access to humans. Thus, justifying the wisdom behind the practice of continuous vaccination and the use of mosquito net in areas of high Yellow-fever endemicity. However, it was equally found that the magnitude of the Yellowfever outbreak can be remarkably reduced to a negligible level with the adoption of chemical or biological control measures which ensure that only mosquitoes with minimal biting tendency thrive in the environment.
Keywords: Yellow-fever, Equilibrium solutions, Disease prevalence, Asymptotic stability, Basic reproduction number