Stability and Sensitivity Analysis of Yellow Fever Dynamics

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  •   Henry Otoo

  •   S. Takyi Appiah

  •   D. Arhinful

Abstract

 Several West African countries have recently reported of Yellow Fever outbreaks. Ghana recently recorded an outbreak which lead to the death of three (3) people in the West Gonja District of the Northern Region. These indicate the re-emergence of the deadly disease. This research proposes a deterministic mathematical model through non-linear ordinary differential equations in order to gain an accurate insight into the dynamics of yellow fever between human beings and the vector Aedes mosquito in an unvaccinated area for the purpose of controlling the disease. The disease threshold parameter was obtained using the next generation matrix. The Gerschgorin theorem proved the disease-Free equilibrium and the Endemic equilibrium to be locally asymptotically stable for  and  respectively. The Lyapunov function proved the disease-Free Equilibrium to be globally asymptotically stable for . In order to study the effect of the model parameters to , the sensitivity analysis of the basic reproduction number with respect to epidemiological parameters was performed.


Keywords: Endemic Equilibrium, Reproduction Number, Sensitivity Analysis, Transmission Rate

References

Staple J. E., Bocchini J. A., Rubin L., and Fischer M. (2010), “Yellow Fever Vaccine: Recommendations of the Advisory Committee on Immunization Practices (ACIP)”, Recommendations and Reports, 59(RR07), 27pp

Barnett, E. D. (2007), “Yellow Fever: Epidemiology and Prevention”, Infectious Disease Society of America, pp. 850-856

Kung’aro, M., Luboobi, L. S., Shahada, F. (2014), “Reproduction Number for Yellow Fever Dynamics between Primates and Human Beings”, Commun. Math. Biol. Neurosci. 2014, 2014:5, 24pp.

Kung’aro, M., Luboobi, L. S., Shahada, F. (2015), “Modelling and Stability Analysis of SVEIRS Yellow Fever Two Host Model”, Gulf Journal of Mathematics, vol. 3, Issue 3 (2015), pp. 106-129.

Mussad, E., Burattini, M. N., Continho, F.A., and Lopez, L.F., (2003), “The risk of Yellow Fever in a Dengue-Infested area”, Trans R. Soc. Trop med Higg, Vol.95, pp. 370-374

Raimundo, S. M., Amaku, M., and Massad, E. (2015) “Equilibrium Analysis of a Yellow Fever Dynamical Model with Vaccination”, Hindawi Publishing Corporation, Computational and Mathematical Methods in Medicine, Vol. 2015, Article ID 482091, 12pp.

Khanh, N. H. (2015), “Stability Analysis of an Influenza virus model with disease resistance”, Journal of the Egyptian Mathematical Society, (2015), 7pp

Chitnis, N. R. (2005), “Using Mathematical Models in Controlling the Spread of Malaria”, 118pp

Side, S. and Noorani, S. M. (2013), “A SIR Model for Spread of Dengue Fever Disease (Simulation for South Sulawesi, Indonesia and Selanger, Malaysia)”, World Journal of Modelling and Simulation, Vol. 9, No. 2, pp. 96-105.

Anon,(2016a),“HealthNews”,http:www.mobile.Ghanaweb.com/GhanaHomepage/heath/Yellow-fever-kills-3-in-Gonja-406024 Accessed :February 20, 2016.

Anon, (2016b), “Malheur County Vector Control district” http: www.malheurvector.com Accessed: April 18, 2016.

Anon,(2016c), “Yellow Fever Facts sheet” http: www.who.int/topics/yellow fever/en Accessed: March 4, 2016.

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How to Cite
[1]
Otoo, H., Appiah, S. and Arhinful, D. 2019. Stability and Sensitivity Analysis of Yellow Fever Dynamics. European Journal of Engineering and Technology Research. 4, 12 (Dec. 2019), 159-166. DOI:https://doi.org/10.24018/ejers.2019.4.12.1666.