Model Epidemi SIRS dengan Pertumbuhan Logistik

The phenomenon of the spread of infectious disease can be formed as an epidemic model. Simplest epidemic model is SI model which can be extended to SIR and SIS model. If recover person will not be susceptible to same disease until the immunity dies out, then the model will be SIRS model. If all person in SIRS model are in population which have restrictiveness of carrying capacity, then it will be formed SIRS model with logistic growth. This model can be presented mathematically using a system of differential equations. Based on SIRS model with logistic growth, it is obtained three disease-free equilibrium points and one endemic equilibrium point. Two disease-free equilibrium points are not stable, while one more point is asymptotically stable if modified reproduction ratio number more than one and the ratio between intrinsic growth rate with death rate which is caused of disease less than proportion of number of infected person with total population. Based on modified reproduction ratio number, loss of disease from population is affected by the interaction rate between susceptible person with infected person, recovery rate of infected person, death rate which is caused of disease, and birth rate. An endemic equilibrium point is asymptotically stable if basic reproduction ratio number more than one. Based on basic reproduction ratio number, epidemic case in population are affected by several things, they are the interaction rate between susceptible person with infected person, recovery rate of infected person, death rate which is caused of disease, birth rate, the factor which influence birth rate decrease, and intrinsic growth rate.