Mathematical Model for Epidemic Disease in Two-patch Environment

Abstract

Abstract In this study, new mathematical model for assessing the impact of quarantine on the transmission dynamics of epidemic diseases in human populations living in two separated patches has been formulated. Historical remarks about epidemic diseases, controlling strategies has been briefly outlined. We presented conditions for positivity and boundedness of solutions. Furthermore, we proved the existence of disease-free equilibrium and endemic equilibrium, and we gave conditions for which these equilibrium are stable. We applied our model to measles disease and we presented some numerical simulation to investigate different parameter effects on the model dynamics.