Model Simulation of Continuous Time Markov Chain Susceptible Infected Recovered-Bacterial Population for Cholera Disease

Abstract

Epidemic is an outbreak of an infectious disease rapidly in a population at a certain place and time. Epidemic models are used to explains the spread pattern of disease. The continuous time Markov chain susceptible infected recovered-bacterial population in the aquatic reservoir (CTMC SIR-B) model is a stochastic model, which considers the effect of bacterial population. The human population are classified into 3 groups. There are susceptible, infected, and recovered groups. Then, there are bacterial population which can infectious the cholera disease to human. CTMC SIR-B model considers treatment and water sanitation parameters. The spread of cholera disease can be modeled as CTMC SIR-B. Cholera is an acute intestinal infectious disease caused by the bacterium Vibrio cholerae. Cholera can be transmitted through the human digestive system. The symptoms of cholera disease are diarrhea, vomiting, and dehydration. The dehydration if not handled properly, may cause death. The aims of this research are to build and simulate the CTMC SIR-B model for cholera disease. The result of the model simulation shows that there is no significant difference between various values of treatment and water sanitation parameters. The pattern of the cholera disease spread describes that the transmission of cholera can occur from human to human even though there is no population of bacteria in the aquatic reservoir.

Keywords: cholera; ctmc sir-b; epidemic model; stochastic.