Estimation Parameter of Susceptible – Infected – Susceptible (SIS) Model with Maximum Likelihood Method Using Steepest Descent Approach to Spread of Typhoid Disease

Abstract

Typhoid is a disease that can be spread through physical contact. Individuals who contract the disease can be re-infected depending on their immune system. This research uses the Susceptible Infected Susceptible (SIS) model to study the spread of typhoid disease with infection data that follows the Poisson distribution, so the infection rate is assumed to follow the Poisson distribution . The parameter is estimated with the Maximum Likelihood Estimator (MLE). Parameter estimation with MLE did not give exact results, so a numerical approach with the steepest descent method was used. After determining the parameter estimates through the steepest descent approach, the parameters are used to simulate the typhus disease spread model. The result of this research is the parameter estimation of SIS model with infection rate assumed to be Poisson distribution . Parameter estimates are used to predict infection rates based on historical data to understand how past changes affect the current condition of typhoid spread through data plotting.