Global analysis for a modified SEIR model with general non-linear incidence function.

In this paper we study a modified SEIR model with general incidence function of the form f (s) [ g (I 1) + h (I 2) ] where I 1 and I 2 are two infection categories different and the migration is constant in all compartments. The model admits neither a disease-free equilibrium point nor a basic reproduction number. Using a suitable Lyapunov function and under sufficient conditions on the functions f, g and h we show that the endemic equilibrium point is globally asymptotically stable. The considered model without migration has a disease-free equilibrium, at least one endemic equilibrium and a basic reproduction number. We show according to the values of R 0 that these equilibria are globally asymptotically stable. To illustrate the results obtained we use a non-linear incidence function given by β S I 1 1 + α 1 I 1 + η I 2 1 + α 2 I 2 where I 1 modeling uneducated infected individuals and I 2 modeling educated infected individuals. Next, we performed sensitivity analysis to determine how each parameter of the model may affect disease transmission. Finally, using reasonably chosen numerical data, we confirm our analytical results. [ABSTRACT FROM AUTHOR]