TITLE:
Theoretical Assessment of Environmental Factors and Untreated Infectious Individuals in the Transmission Dynamics of Buruli ulcer
AUTHORS:
Codjo Cesaire Yadouleton, Myriam Djoukwe Tapi, Judicael Deguenon, Ghislain Emmanuel Sopoh
KEYWORDS:
Buruli Ulcer, Mathematical Models, Equilibria, Stability
JOURNAL NAME:
Applied Mathematics,
Vol.15 No.8,
August
6,
2024
ABSTRACT: Buruli ulcer is the third most common mycobacterial disease worldwide, posing a significant public health burden, especially in impoverished regions of West and Central Africa, such as Benin. The management of Buruli ulcer (BU) in Africa is often hindered by limited resources, delays in treatment, and inadequate medical facilities. Additionally, a portion of the population does not seek hospital care, which facilitates the continued presence of the pathogen in the environment. This paper aims to investigate the role of environmental factors in the transmission of Buruli ulcer. We develop a mathematical model to describe the dynamics of Buruli ulcer transmission, incorporating the presence of the bacterium in the environment. Theoretical results are presented to demonstrate that the model is well-posed. We compute the equilibria, including the disease-free equilibrium and the endemic equilibrium, and study their stability. To achieve this, we derive a threshold parameter called the basic reproduction number
ℛ
0
, which determines whether the disease will persist in a human population. If
ℛ
0
is less than one, the disease will eventually die out; if
ℛ
0
is greater than one, the disease will persist. Sensitivity analysis is performed to understand the impact of various parameters on the dynamics of Buruli ulcer transmission and to identify the parameters that influence the basic reproduction number
ℛ
0
. Finally, numerical simulations are conducted to validate the theoretical results obtained from the mathematical analysis.