The role of explicit solutions in the analysis of epidemic models

Sammanfattning: In this thesis, we will study basic mathematical epidemic models SIR, SIS, and SEIR. Then we will construct a modified model as a combination of SIR and SIS models. First, we will find the explicit solutions for the SIS model. and show no exact solution for the SIR model. Also, find the parametric solution for the SIR model and find a numerical solution by using Euler’s method. Then we find an approximate explicit form of the epidemic curve. Also, we will study parametric influences on the SIR and SIS models. Finally, we will suggest some recommendations to decrease the epidemic’s spread.