Transmission Dynamics Model of Scabies in Islamic Boarding Schools

David Prasetyo; Sunarsih Sunarsih; Sutrisno Sutrisno

doi:10.30829/zero.v10i1.28823

Transmission Dynamics Model of Scabies in Islamic Boarding Schools

David Prasetyo, Sunarsih Sunarsih, Sutrisno Sutrisno

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.

Keywords

Basic reproduction number; Mathematical epidemiology; Mathematical model; Scabies transmission dynamics; Stability analysis.

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DOI: http://dx.doi.org/10.30829/zero.v10i1.28823