Analisa Kestabilan Bebas Penyakit Model SITRS pada Penyebaran Diare

Widayati, Ratna
Hamim Muntoha, Renal
Ma'rifah, Umi
Yulianti, Nita

Diophantine Journal of Mathematics and Its Applications
Vol. 3 No. 1 (2024)

This study discusses the spread of diarrhea accompanied by complications resulting in death among sufferers. It is assumed that people with diarrhea can transmit the disease to susceptible individuals. Additionally, deaths occurred due to diarrhea when treatment was not administered. Individuals who have contracted diarrhea may acquire temporary immunity and then become susceptible again. The model used is SITRS. Based on the model, disease-free equilibrium points and endemic equilibrium points are obtained. The analysis was conducted around the disease-free equilibrium point, and it was concluded that the disease-free equilibrium point is locally asymptotically stable if R0<1. Furthermore, based on the simulation results, it is shown that the model's solution tends towards a disease-free equilibrium point if R0<1. . This implies that diarrhea will disappear from the population at some point if the infection level R0<1. is met.