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

Abstract

This study introduces a segmented mathematical model, crafted for dissecting the spread mechanisms of a specific disease. It refines the classic SEIR framework by bifurcating the infected segment (I) into two subcategories: the uneducated infected (Iu) and the educated infected (Ie). Central to this model is a complex infection rate function, delineated as f (S) (g(Iu) + h(Ie)). Critical to our analysis are certain presumptions regarding the functions f , g, and h. By utilizing the next generation matrix technique, we successfully derived the fundamental reproduction rate, denoted as R0. The research confirms the existence of two vital states of equilibrium within the model: one signifying the absence of disease and the other, its persistent presence. The global asymptotic stability of these equilibriums is validated using Lyapunov's direct method coupled with LaSalle's invariance principle. To reinforce our theoretical findings, we executed a series of numerical simulations, applying specific variations of the functions f , g, and h.