KESTABILAN LOKAL TITIK EKUILIBRIUM MODEL PENYEBARAN PENYAKIT POLIO

Abstract

The fact shows that polio is very dangerous to humanity, it is necessary to study the dynamics of the spread of polio. One way, namely a mathematical approach in the form of a mathematical model for the spread of polio. The mathematical model used in this study is the SEIV model. This study aims to provide a description of the dynamics of the spread of polio. The results of this study are expected to be used as a reference to study the dynamics of the spread of polio in an area. The method used in the implementation of this research is literature study. The first stage starts with the model formulation. The second stage analyzes the model that has been formed and the last one makes a model simulation. The formed SEIV model is a system of nonlinear differential equations. The basic reproduction number parameter is obtained from the analysis of the system. If the basic reproduction number less than one, then there is a single point of free disease equilibrium that is locally stable asymptotically. Conversely, if the basic reproduction number more than one, then there are two points of equilibrium, namely the point of free equilibrium of disease and the endemic equilibrium point . When the basic reproduction number more than one endemic equilibrium point is stable asymptotically locally. Based on the simulation, if the basic reproduction number less than one for t → ∞ and value (S, E, I, V) are close enough to E*, the system solution will move to E*. This means that if the basic reproduction number less than one, the disease will not be endemic and tends to disappear in an infinite amount of time. Conversely, if the basic reproduction number more than one for t → ∞ and the value (S, E, I, V) are close enough to E^, then the system solution will move towards E^. This means that if the basic reproduction number more than one, then the disease will remain in the population but not reach extinction in an infinite amount of time

Keywords

• polio dynamics, polio model, numerical simulation