Electron. J. Differential Equations, Vol. 2020 (2020), No. 62, pp. 1-29.
Stability and sensitivity analysis of the epidemiological
model Be-CoDiS predicting the spread of human diseases between countries
Benjamin Ivorra, Diene Ngom, Angel M. Ramos
Abstract:
The Ebola virus disease is a lethal human and primate disease that requires a
particular attention from the international health authorities due to important
recent outbreaks in some Western African countries and isolated cases in Europe
and North-America. Regarding the emergency of this situation, various decision
tools, such as mathematical models, were developed to assist the authorities to
focus their efforts in important factors to eradicate Ebola. In a previous work,
we proposed an original deterministic spatial-temporal model, called Be-CoDiS
(Between-Countries Disease Spread), to study the evolution of human diseases
within and between countries by taking into consideration the movement of people
between geographical areas. This model was validated by considering numerical
experiments regarding the 2014-16 West African Ebola Virus Disease epidemic.
In this article, we perform a stability analysis of Be-CoDiS. Our first objective
is to study the equilibrium states of simplified versions of this model, limited
to the cases of one or two countries, and determine their basic reproduction ratios.
Then, we perform a sensitivity analysis of those basic reproduction ratios regarding
the model parameters. Finally, we validate the results by considering numerical
experiments based on data from the 2014-16 West African Ebola Virus Disease epidemic.
Submitted April 24, 2020. Published June 18, 2020.
Math Subject Classifications: 92D30, 92C60, 34D20, 34K28.
Key Words: Epidemiological modelling; deterministic models; stability analysis;
sensitivity analysis; ebola virus disease; basic reproduction ratio.
DOI: 10.58997/ejde.2020.62
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Benjamin Ivorra
Instituto de Matemática Interdisciplinar (IMI)
Department of Applied Mathematics and Mathematical Analysis
and MOMAT Research Group
Complutense University of Madrid
Plaza de Ciencias, 3, 28040, Madrid, Spain
email: ivorra@ucm.es
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Diène Ngom
Département de Mathématiques
Université Assane Seck de Ziguinchor
UMI 2019-IRD \& UMMUSCO-UGB, BP 5233
Ziguinchor, Senegal
email: dngom@univ-zig.sn
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Angel M. Ramos
Instituto de Matemática Interdisciplinar (IMI)
Department of Applied Mathematics and Mathematical Analysis
and MOMAT Research Group
Complutense University of Madrid
Plaza de Ciencias, 3, 28040, Madrid, Spain
email: angel@mat.ucm.es
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