Analisis Model Matematika Penyebaran Penyakit Kolera Dengan Mempertimbangkan Masa Inkubasi - Nuha, A R; Resmawan (JURNAL ILMIAH MATEMATIKA DAN TERAPAN, 2020)
Cholera is a type of diarrheal disease caused by the presence of Vibrio cholerae in the patient's intestine. Bacteria V. cholerae has the ability to survive in water so that it will easily transmit disease to humans. This study discusses the dynamics of the spread of cholera caused by V. cholerae bacteria. The incubation period in the disease transmission system is a factor that considered in a compiled mathematical model. Besides giving the vaccine is considered a powerful way to reduce the rate of transmission. This study aims to modify the mathematical model of the spread of cholera, carry out the analysis of the stability of the modified model, and carry out numerical simulations. The modified model will be determined by its equilibrium and then stability analysis will be carried out at the equilibrium by considering the basic reproduction number (R0). Modification of the model with consideration of the incubation period produces a mathematical model of the spread of cholera type SVEIR-B. The stability of a fixed point is influenced by R0. The condition value R0 < 1 resulting in a disease-free equilibrium that is asymptotically stable, whereas the condition R0 > 1 results in an endemic equilibrium being asymptotically stable. Numerical simulations show an increase in the rate of vaccine delivery can decrease the value while increasing the rate of vaccine shrinkage and the incubation rate of each can increase the value.