TITLE:
Mathematical Modelling of Conjunctivitis Viral Disease: Case of Burundi
AUTHORS:
Vianney Mbazumutima, Pascaline Nshimirimana, André Dembele, Fabiola Ndayiragije, Léonard Todjihounde
KEYWORDS:
Conjunctivitis, Basic Reproduction Number, Sensitivity Index, Ruth-Hurwitz Criteria
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.15 No.5,
May
28,
2025
ABSTRACT: In this paper, an SEIR mathematical model of conjunctivitis viral disease is formulated. The disease free equilibrium (DFE) and the endemic equilibrium points are investigated. The basic reproduction number is computed using the next generation matrix method and the local stability of the disease free equilibrium is investigated. This threshold characterizes the growth rate of an epidemic outbreak and shows that if
R
0
<1
the DFE is locally stable and unstable when
R
0
>1
. We analyze the sensitivity of the model according to its different parameters. Numerical simulations were performed using the defined parameters to support the theoretical results and compared to one from the real data. The results show the suitability of the chosen model of conjunctivitis viral disease that occurred in Burundi for the investigated period of one month.