ANALISIS KESTABILAN MODEL SI UNTUK PENYAKIT MENULAR DENGAN ADANYA TRANSMISI VERTIKAL DAN TINGKAT KEJADIAN JENUH

Ana Rizki Mahmudah; Muhammad Ahsar Karim; Yuni Yulida

doi:10.20527/epsilon.v17i2.10826

ANALISIS KESTABILAN MODEL SI UNTUK PENYAKIT MENULAR DENGAN ADANYA TRANSMISI VERTIKAL DAN TINGKAT KEJADIAN JENUH

Ana Rizki Mahmudah, Muhammad Ahsar Karim, Yuni Yulida

Abstract

The transmission of infectious diseases can occur through two pathways: horizontal and vertical. Horizontal transmission occurs through direct or indirect physical contact with the infectious agent, while vertical transmission takes place when an infected mother transmits the disease to a fetus or a newborn. Within the context of disease transmission models, a critical feature is the saturation incidence rate, which refers to the impact of interventions that can reduce the rate of disease transmission among susceptible and infected individuals. This research aims to elucidate the formation of a model, determine equilibrium points, and calculate the basic reproduction number using the Next Generation Matrix method. The analysis involves assessing local stability through linearization methods and global stability using Lyapunov functions. Sensitivity analysis is conducted on the basic reproduction number, and numerical simulations are performed using the fourth-order Runge-Kutta method. The research findings indicate the establishment of an SIS (Susceptible-Infected) model for infectious diseases with vertical transmission and saturation incidence. This model depicts the spread of the disease in a population, where individuals can exist in susceptible or infected conditions. Equilibrium points include a disease-free equilibrium that is locally and globally stable when the basic reproduction number is less than one, and an endemic equilibrium that is locally and globally stable when the basic reproduction number exceeds one. Sensitivity analysis reveals that each parameter has varying influences on the basic reproduction number. An increase in the saturation incidence rate leads to a decrease in the number of infected subpopulations, while an increase in the vertical transmission rate results in a similar decline. Numerical simulations support stability analyses at equilibrium points. These findings provide a deeper understanding of the factors influencing the spread of diseases within a population.

Keywords

Mathematical Model, Vertical Transmission, Saturated Incidence Rate, Stability Analysis, Sensitivity Analysis.

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DOI: https://doi.org/10.20527/epsilon.v17i2.10826