Nur Asiyah, Basuki Widodo : Analysis of Diphtheria Dissemination By Using Multi Groups of Dynamic System Method Approach
Prof. Dr. Basuki Widodo M.Sc.
5th ISERD INTERNATIONAL CONFERENCE
multi-grup analysis; stability analysis; basic reproduction
Diphtheria Dissemination is an infectious disease on a region which is become endemic or not, it can be analyzed by using a mathematical model approach in the form of differential equation systems. The disease dissemination in those populations can be clustered into some groups including group of under 15 years old and group of above 15 years old. Therefore, the diphtheria dissemination that occurred is cross-analyzed between the groups. This research consideres about analyzing multi-grup epidemic model with rate of nonlinear transmission for preventing the occurrence of endemic and evaluating the threshold, i.e. the basic reproduction values R0, through stability of the free disease equilibrium point and the endemic equilibrium point in East Java areas. Data is taken from the year of 2013. The result of this research is expected to be able to give information about the characteristics of diphtheria patient through multi group of dynamic system model. The criteria of Routh ? Hurwitz is used to analyze the local stability and construct Liapunov function for the global stability by applying directed graph. Based on the theory of graph approach, the system can be described as a network, where each vertex is a homogeneus group and an edge(j,i)is existsif only if can be transmitted from group i to group j. Keywords- multi-grup analysis, stability analysis, basic reproduction