Spreading dynamic of infectious disease in two interacting areas

The spread of infectious disease in a heterogeneous area can be grouped as a homogeneous group. The graph theory approach to analyze the spread of infectious disease in the group using a mathematical model. Heterogeneity in a population can be caused by many factors. Within a group can be divided into several homogeneous groups based on clusteritation, such as grouping the population based on age in the spread of infectious diseases. Population heterogeneity can be described as a network where each vertex represents a homogeneous group and an edge (j, i) exists if and only if the disease can be transmitted from group i to group j. The system of mathematical differential equations is formed based on the graph theory approach and the infectios disease distribution compartment diagram. Based on the numerical solution that we have obtained, the rate of change in the exposed population increases as the increasing of the disease transmission. And the rate of change in the infected population increases as the endemic appears.