Assessing the effect of migration and immigration rates on the transmission dynamics of infectious diseases.

This paper explores the effect of immigration in a generalized model that considers susceptibles, infected, chronic carriers, and recovered, the incidence rate is considered as a general function and the immigration as a constant in all its populations. This model has the characteristic that carriers and infected can transmit the disease, besides it has not a disease-free equilibrium point and no basic reproductive number when the immigration is considered. Using an appropriate Lyapunov function and with suitable conditions on the functions involved in the general incidence, we show that the endemic equilibrium point is globally asymptotically stable. When the immigration is not considered the model has a disease-free equilibrium point, endemic equilibrium and basic reproductive number which are globally asymptotically stable depending on the magnitude of this threshold. Through numerical simulations we show that even having a good vaccination rate, recovery rate, diagnosis rate cannot stop the transmission of the disease if migration or immigration is considered. [ABSTRACT FROM AUTHOR]