Dynamical Analysis of a Modified Epidemic Model with Saturated Incidence Rate and Incomplete Treatment

Abstract

This paper addresses a modified epidemic model with saturated incidence and incomplete treatment. The existence of all equilibrium points is analyzed. A reproduction number R0 is determined. Next, it is found that the non-endemic point P0 is stable in case R0 < 1, but unstable in case R0 > 1. The special conditions to analyze the local and global stability of the non-endemic and endemic points are investigated. Globally, the sensitivity analysis of the system is studied by combining the Latin Hypercube Sampling and Partial Rating Correlation Coefficients methods. By using the Pontryagins maximum principle, the optimal control problem is studied. Various numerical results are given to support our analysis.