Analisis Kestabilan Model Matematika Penyebaran Penyakit Schistosomiasis dengan Saturated Incidence Rate

Schistosomiasis is a disease caused by infections of the genus Schistosoma. Schistosomiasis can be transmitted through schistosoma worms that contact human skin. Schistosomiasis is a disease that continues to increase in spread. Saturated incidence rates pay attention to the ability to infect a disease that is limited by an increase in the infected population. This thesis formulates and analyzes a mathematical model of the distribution of schistosomiasis with a saturated incidence rate. Based on the analysis of the model, two equilibrium points are obtained, namely non-endemic equilibrium points (E₀) and endemic equilibrium points (E₁). Both equilibrium points are conditional asymptotically stable. The nonendemic equilibrium point will be asymptotically stable if r_h > d_h, r_s > d_s and R₀ < 1, while the endemic equilibrium point will be asymptotically stable if R₀ > 1. Sensitivity analysis shows that there are parameters that affect the spread of the disease. Based on numerical simulation results show that when R₀ < 1, the number of infected human populations (H_i), the number of infected snail populations (S_i), the amount of cercaria density (C) and the amount of miracidia density (M) will tend to decrease until finally extinct. Otherwise at the time R₀ > 1, the number of the four populations tends to increase before finally being in a constant state.