Analisis Kestabilan Lokal pada Model SEIR Patogenesis Frambusia dengan Infeksi Primer-Sekunder dan Tersier

Fahri Alam Lasongke; Juni Wijayanti Puspita; Rina Ratianingsih; Vicya Utami; Salman Salman

doi:10.37905/euler.v12i2.27847

Analisis Kestabilan Lokal pada Model SEIR Patogenesis Frambusia dengan Infeksi Primer-Sekunder dan Tersier

Fahri Alam Lasongke, Juni Wijayanti Puspita, Rina Ratianingsih, Vicya Utami, Salman Salman

Abstract

Yaws is a skin disease characterized by red spots that can worsen if not treated promptly. This disease is caused by the bacteria Treponema Pallidum Pertenue. The symptoms of yaws have five stages, namely the primary stage, primary to secondary latent stage, secondary stage, secondary to tertiary latent stage, and tertiary stage. A mathematical model is one solution to describe the prognosis of yaws disease. Here, the population was divided into 5 sub-populations, namely susceptible sub-population, exposed sub-population, infected sub-population in the primary and secondary stages, infected sub-population in the tertiary stage, and recovered sub-population. The mathematical model of the spread of yaws disease is written as a system of nonlinear differential equations whose stability is analyzed around the critical point. From the system of differential equations, two critical points are obtained which describe the disease-free condition and the endemic condition. In this study, the existence and stability of both critical points can be guaranteed. Furthermore, numerical simulations were conducted using yaws disease data in Indonesia. Simulation results show that the transmission of yaws disease in Indonesia can be controlled by reducing contact between the primary-secondary infected population and the susceptible population.

Keywords

Yaws; Prognosis; SEIR Model; Local Stability

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DOI: https://doi.org/10.37905/euler.v12i2.27847

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