An SEIR model with modified saturated incidence rate and Holling type II treatment function

Abstract

In this article, the behavior of an susceptible exposed infected recovered (SEIR) epidemic model with nonlinear incidence rate and Holling type II treatment function is presented and analyzed. Reproduction number of the model is calculated. Equilibrium points are determined. Disease-free equilibrium exists when R0 is below 1. Behavior of disease-free equilibrium is examined at R0 = 1. Endemic equilibrium exists when R0 crosses 1. Stability of both equilibrium points is investigated locally and globally. Simulation is provided to support the result.

Keywords

• seir, basic reproduction number
• holling type ii function
• lyapunov function
• 34d23
• 93a30
• 93d20