the SEIRS model is rescaled with the total time varying population and analyzed according to its epidemic condition R_0 for two cases of no epidemic 〖(R〗_0≤1) and epidemic 〖(R〗_0>1) using the time series and phase portraitsof the susceptible S, exposed E, infected I, and recovered R individuals.Based on the experimental results using a set of arbitrarily defined parameters for horizontal transmission of the infectious diseases, the proportional population of the SEIRS model consisted primarily of the recovered R (0.7–0.9) individuals and susceptible S (0.0–0.1) individuals (epidemic) and recovered R (0.9) individuals with only a small proportional population for the susceptible S (0.1) individuals (no epidemic).