An SEIR epidemic model with two infectious pathways

Abstract

In this research work, we present the mathematical framework of a SEIR epidemic model with two infectious pathways. The model is formulated by extending the classical SEIR mathematical model to involve two different but connected infectious states. The well posedness of the solutions of the system are shown. The basic reproduction number denoted by R₀ is computed through the next generation matrix method. The disease free equilibrium is asymptotically stable locally if R₀<1 and unstable otherwise while there exists a unique endemic equilibrium provided that R₀>1. The stability analysis for the disease free and endemic equilibrium is investigated by a suitable Lyapunov function globally. The effect of the parameters of the model on the basic reproduction number is measured by sensitivity analysis. Optimal control characterization analysis is also discussed. Some theoretical results obtained are also augmented through numerical simulation.