MODEL EPIDEMI SEIR DENGAN SUMBER DAYA PENGOBATAN YANG TERBATAS; ( SEIR EPIDEMIC MODEL WITH A LIMITED TREATMENT RESOURCE )

Rifanti, Utti M, Lina Aryati

2015 | Disertasi | FMIPA

Treatment plays an important role to control or reduce the spread of infectious diseases, such as tuberculosis, influenza, and measles. In classical epidemic models, the level of treatment is assumed to be proportional to the number of infected individuals. However, in fact the treatment resources are relatively limited when comparing with the total population in a territory. Every country should have the appropriate capacity for treatment. The country will spend unnecessary costs if it is too large. On other hand, the country have the risk of disease outbreaks if it is too small. Type of treatment function with limited treatment resources more realistic because the number of treatment, medical personnel, and medicines in every country are limited. In this thesis, the existence and stability of the equilibrium point of this model will be analyzed. Basic reproduction number plays a very important role to the existence and stability of the equilibrium point. From the analysis of the existence of the equilibrium point of the model, we get a disease free equilibrium point and two endemic equilibrium point. Furthermore, mathematical analysis is used to study the dynamic behavior of this model

Kata Kunci : SEIR epidemic model; basic reproduction numbers; equilibrium point; stability.