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All Journal Zero : Jurnal Sains, Matematika, dan Terapan
David Prasetyo
Mathematics, Diponegoro University, Semarang, Indonesia
Agriculture, Biological Sciences & Forestry Chemistry Mathematics Physics

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Transmission Dynamics Model of Scabies in Islamic Boarding Schools David Prasetyo; Sunarsih Sunarsih; Sutrisno Sutrisno
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i1.28823

Abstract

Scabies continues to pose a major public health challenge in densely populated congregate settings such as Islamic boarding schools (pesantren) in Indonesia. This study develops a stage structured - - -  compartmental model (Susceptible, Early-stage Infected, Late-stage Infected, Recovered) that explicitly accounts for differences in mite burden, infectivity, and recovery rates between early and late-stage infections. Using qualitative analysis of the nonlinear differential equations, the basic reproduction number ( ) was derived via the Next Generation Matrix method, and stability analysis was performed. Results show that the diseasefree equilibrium is locally and globally asymptotically stable when . Under baseline parameters, , with late-stage infections accounting for approximately 88.3% of total transmission. Due to the model’s assumptions of a closed population and permanent immunity, no biologically meaningful endemic equilibrium exists; once the infection runs its course, the disease eventually dies out as susceptibles are exhausted. Sensitivity analysis highlights that reducing the late-stage transmission rate ( ) and increasing the early-stage recovery rate ( ) are the most effective intervention targets. This model provides a rigorous theoretical framework to guide evidencebased scabies control strategies in high-density residential institutions.
Co-Authors Sunarsih Sunarsih Sutrisno Sutrisno