Analysis of a Multiscale Model of Ebola Virus Disease

Main Article Content

Duncan O. Oganga
George O. Lawi
Colleta A. Okaka

Abstract

Multiscale models are ones that link the epidemiological processes dealing with the transmission between hosts and the immunological processes dealing with the dynamics within one host. In this study, a multiscale model of Ebola Virus Disease linking epidemiological and immunological processes has been developed and analysed. The model has considered two infectious classes ; the exposed and the infected individuals. Local and global stability analyses of the Disease Free Equilibrium and the Endemic Equilibrium points of the model show that the disease dies out if the basic reproduction number Rc0 < 1 and persists in the population when Rc0 > 1 respectively. Sensitivity analysis shows that the rate of vaccination, v , is the most sensitive parameter. This indicates that effort should be directed towards implementing an effective vaccination strategy to control the spread of the disease. It has also been established that when treatment efficacy is scaled up, the viral load goes down and consequently, the transmission between hosts is also reduced. The impact of treatment on the disease spread has also been established through the coupling function (L∗) . The study indicates that a higher percentage of the exposed and the infected individuals should be treated to control the spread of the disease within the population.

Keywords:
Ebola virus disease, viral load, local and global stability, disease free and endemic equilibrium, sensitivity analysis, simulations

Article Details

How to Cite
Oganga, D. O., Lawi, G. O., & Okaka, C. A. (2020). Analysis of a Multiscale Model of Ebola Virus Disease. Asian Research Journal of Mathematics, 16(6), 53-69. https://doi.org/10.9734/arjom/2020/v16i630197
Section
Original Research Article

References

Martyushev A, Nakaoka S, Sato K, Noda T, Shingo I. Modelling Ebola virus dynamics: Implications for therapy. Antiviral Research. 2016;135:62e73. Science Direct
DOI.org/10.1016/j.antiviral.2016.10.004
WHO. Ebola virus disease.
Available:www.who.int/mediacenter/factsheet/fs103/en/.2016

Amira R, Delfim FMT. Mathematical modelling, simulation and optimal control of the 2014 Ebola outbreak in West Africa. Hindawi Publishing Corporation; 2015.

Majumder MS, Kluberg S, Santillana M, Mekaru S, Brownstein JS. Ebola outbreak: Media events track changes in observed reproductive number. PLOS Currents Outbreaks. Edition 1;
DOI:10.1371/currents.outbreaks.e6659013c1d7f11bdab6a20705d1e865

Zhilan F, Jorge V, Brenda T, Maria C. A model for Coupling Within-host and Between-host Dynamics in an infectious Disease. Springer Science; 2011.
DOI;10.1007/s 11071-011-0291-0

Amira R, Delfim FMT. Analysis, simulation and optimal control of a SEIR model for Ebola virus with demographic effects. Commun. Fac. Sci.Univ. Ank. Ser. A1 Math. Stat; 2017.
ISSN: 1303-5991.

Durojaye MO, Ajie IJ. Mathematical model of the spread and control of Ebola virus disease.

Applied Mathematics. 2017;7(2): 23-31.
DOI:10.5923/j.am.20170702.02

Harout B. Modeling the spread of Ebola with SEIR and optimal control. SIAM Journal of Mathematical Analysis; 2016.

Oduro FT, George A, Joseph B. Optimal control of Ebola transmission dynamics with interventions. Science Domain International. 2016;19(1):1-19. Article no. BJMCS. 29372 Shen M, Yanni X, Libin R. Modelling the effects of comprehensive interventions on ebola virus transmission. Scientific Report. 2015;5:15818.
DOI:10.1038/srep 15818

Sophia B, Zvi R, Mirjana P. Mathematical modeling of Ebola virus dynamics as a step towards rational vaccine design. IFMBE proceedings. 2010;32:196-200.

Thomas W. Analysis and simulation of a mathematical model of Ebola virus dynamics in vivo . SIAM; 2015.

Vincent M, Lisa O, Frederick G,Thi H,Tram N, Xavier L, France M, Stephan G, Jeremie G.

Ebola virus dynamics in mice treated with favipiravir . Antiviral Research. 2015;123:70-77. Science Direct
DOI:10-1016/j.antiviral.2015.08.015

Alexis ESA,Van KN, Esteban AHV. Multiscale model of within-host and between-host for viral infectious diseases. bioRxiv; Journal of Mathematical Biology. 2017;77:10351057.
DOI: 10.1101/174961

Alexis ESA, Esteban AHV. Coupling multiscale within-host dynamics and Between-host transmission with recovery (SIR) dynamics.Elsevier; Mathematical Biosciences. 2019;309:34-
DOI.org/10.1016/j.mbs.2019.01.001

Tae SD, Young SL. Modeling the spread of Ebola. Osong Public Health Res Perspect.
;7(1):43-48.
Available:http://dx.doi.org/10.1016/j.phrp.2015.12.012p
ISSN 2210-9099-ISSN 2233-6052

Muhammad T, Syed IAS, Gul Z, Sher M. Ebola virus epidemic disease its modeling and stability analysis required abstain strategies. Cogent Biology. 2018;4.
DOI.org/10.1080/23312025.2018.1488511

Dieckmann U, Metz J, Sabelis M, Sigmund K. Adaptive dynamics of infectious diseases: In pursuit of virulence management. New York, Cambridge University Press; 2002.

James W, Van D. Further notes on the basic reproduction number. In: Brauer F, Van
Den Driessche P, Wu J. (Eds) Mathematical Epidemiology. Lecture Notes in Mathematics.
;1945. Springer, Berlin, Heidelberg

Chitnis N, Hyman J, Cushing J. Residual viremia in treated HIV+ individuals Epidemiology.

PLOS Computational Biology. 2008;12:597-677.