Modeling the impact of migrated population on human-to-human transmission of Ebola virus disease

Abstract

A nonlinear SEIR mathematical model is developed to investigate the impact of migrated population, infected with Ebola virus, on human-to-human transmission of Ebola Virus Disease (EVD) in a disease-free area. In view of the dynamics of Ebola virus disease, here, the infected class is supposed to be divided into subclasses, viz. primary and secondary infected. The proposed model is analyzed qualitatively using the stability theory of differential equations and quantitatively using numerical simulation. The obtained results, qualitatively and quantitatively, suggest that migration and contact rates play an important role in controlling the spreading of disease. Critical values for migration and contact rates are evaluated and it is revealed that if these rates go beyond their critical values, it leads to delay in the stabilization of the system. It is also found that primary reproductive number increases with increase in migration rate. Besides this, the approximate time required to attain stability of the disease model system is also determined. The model analysis recommends quarantining the noninfected from the secondary infected in order to control the spreading out of disease.