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Susceptible Exposed Infected Recovery (SEIR) with Immigration: Equilibrium Points and its Application

Last modified: 2017-07-19

#### Abstract

Infectious deseases such as rubelle, mumps, measles, pertussis are caused by viruses or bacterias. There is a period of incubation in the spread of these diseases. The incubation period is a period in which individuals who are attacked by viruses or bacterias began shows clinical symptoms but have not been able to transmit the disease. The spread of disease by observing the period of incubation can be represented by the susceptible exposed infected recovery (SEIR) model. Immigration has an influence on the spread of disease. This caused by immigrants who could carry the disease from their areas to other places. For this reason, the SEIR model with immigration to be considered. Here we will discribe the SEIR model with immigration, determine a equilibrim point. The model is then applied to the measles disease. The SEIR model with immigration can be represented as system of the first ordinary differential equations. The model has two endemic equilibrium points. It means that there is still disease at the equilibrium point. Fom the application on the measles desease, the spread of measles is the solution of the model. This spread has the endemic equilibrium population with the number of infected individuals is 142 person.