A Graph-Theoretic Method on HBY Epidemic Model

Abstract

In this paper, we present an epidemic model with non-monotonic incidence function. This epidemic model is investigated for different classes of infectious diseases. Mathematical analyses are carried out to determine the positivity of solution and the Graph-Theoretic method is used in calculating the Basic reproduction number. In addition, we obtained the numerical simulation to verify the model predictions. The results suggested that the model is approaching equilibrium with increase immunization program.