Abstract:
The epidemic model is a form of mathematical model in the field of epidemiology. Diarrhea is one
of the infectious diseases that can be prevented through treatment. The purpose of this study is to
explain the formation of an epidemic model for the spread of diarrheal disease, to analyze the
stability of the model, and to make a numerical simulation. This study uses the linearization method
to linearize the nonlinear model. The next generation matrix method is used to determine the Basic
reproduction number (𝑅
0
) and the fourth-order runge kutta method is used to simulate the model.
The results of this study, obtained an epidemic model of diarrheal disease in the form of a SIRT
(Susceptible, Infected, Treatment, Recovered) model with a type 2 Holling incidence function.
Furthermore, two equilibrium are obtained and it is shown that 𝑅
0
plays an important role in the
process of spreading the disease. If 𝑅
0
< 1 then the disease-free equilibrium is asymptotically stable
so that the population will be free from disease outbreaks. Conversely, if 𝑅
0
> 1 then the endemic
equilibrium is asymptotically stable so that the disease will always exist in the population. Based on
the value of the sensitivity index, it shows that the parameters of the effective contact rate and birth
rate are the most sensitive parameters (directly proportional) to changes in the value of 𝑅
0
.
Furthermore, a model simulation is given to provide an illustration of the stability analysis of the
model.
Keywords: epidemic model, equilibrium, sensitivity analysis, stability,
