Buruli Ulcer Mathematical Modeling

Document Type : Research

Authors

1 Mathematics Department, Faculty of Science, Aswan University, Aswan, Egypt

2 Mathematics Department, Facultyof Science, Aswan University, Aswan, Egypt

Abstract

Buruli ulcer is classified as a neglected tropical disease that has emerged in various regions, including developed nations such as Australia. This condition primarily manifests as a skin disorder affecting the arms and legs. It has been detected in several mammalian species, notably in possums which in turn transmit the disease to humans. To effectively reduce the incidence and prevent the transmission of this disease to less developed countries, comprehensive eradication and control initiatives are essential before it escalates into an epidemic. This study introduces a SIR-type epidemic model specifically for humans. A detailed analysis of the model's properties has been conducted, leading to the establishment of its stability results. The stability at fixed points has been assessed, demonstrating that the model exhibits local asymptotic stability. The conditions for stability in the disease-free scenario are confirmed for R_0 < 1, while the endemic situation is analyzed for R_0 > 1.

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