Mathematical Modeling of Yellow Fever Transmission Dynamics with Multiple Control Measures
Asian Research Journal of Mathematics,
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.
- Equilibrium solutions
- Disease prevalence
- Asymptotic stability
- Basic reproduction number
How to Cite
Luz PM, Struchiner CJ, Galvani AP. Modeling transmission dynamics and control
of vector-borne neglected tropical diseases. PLoS Negl Trop Dis. 2010;4(10):e761.
Kermack WO, McKendrick AG. Contribution to the mathematical theory of epidemics. Proc.
Royal Society London, A Contain Pap Math Phys Character.1927;115:700?21.
Ross R. An application of the theory of probabilities to the study of a priori pathometry. Proc
Royal Society London. 1916;92:204-230.
Barrett AD, Higgs S. Yellow fever: A disease that has yet to be conquered. Annual Review of
Raimundo SM, Yang HM, Engel AB. Modelling the eects of temporary immune protection
and vaccination against infectious diseases. Applied Mathematics and Computation.
Yusuf TT, Benyah B. Optimal control of vaccination and treatment for an SIR epidemiological
model. World Journal of Modelling and Simulation. 20128(3):194-204.
Amaku M, Coutinho FA, Raimundo SM, Lopez LF, Burattini MN, Massad E. A comparative
analysis of the relative ecacy of vector-control strategies against dengue fever. Bulletin of
Mathematical Biology. 2014;76(3):697-717.
Yusuf and Daniel; ARJOM, 13(4): 1-15, 2019; Article no.ARJOM.48683
Monath TP, Vasconcelos PF. Yellow fever. Journal of Clinical Virology. 2015;64:160 - 73.
Raimundo SM, Amaku M, Massad E. Equilibrium analysis of a yellow fever dynamical
model with vaccination. Computational and Mathematical Methods in Medicine; 2015.
Wu JT, Peak CM, Leung GM, Lipsitch M. Fractional dosing of yellow fever vaccine to
extend supply: A modelling study. Lancet; 2016. Available:https://doi.org/10.1016/S0140-
Ijalana CO, Yusuf TT. Optimal control strategy for hepatitis B virus epidemic in areas of
high endemicity. International Journal of Scientific and Innovative Mathematical Research.
Zhao S, Stone L, Gao D, He D. Modelling the large-scale yellow fever outbreak in Luanda,
Angola, and the impact of vaccination. PLoS Negl Trop Dis. 2018;12(1): e0006158.
Kung’aro M, Luboobi LS, Shahada F. Reproduction number for yellow fever dynamics between
primates and human beings. Commun. Math. Biol. Neurosci. 2014;1(5):1-24.
Van den Driessche P, Watmough J. Reproduction numbers and sub threshold endemic equilibria
for compartmental models of disease transmission. Mathematical Biosciences. 2002;180:29-48.
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