Investigation of some compartmental models under random effects

In this study, the dynamics of epidemic models are investigated under random effects. Epidemics, which are usually analyzed with deterministic compartmental models in literature, can produce random behavior. The scope of the study is to randomize deterministic compartmental models by using random effect terms to analyze such random structures. A modification of the random Differential Transformation Method, which is already available in literature, is presented along with Monte Carlo simulations to investigate the numerical characteristics of random models. The modified random Differential Transformation Method is used to obtain approximations for the moments of the models and the findings are compared with the results of the simulations. Random investigations of three SIR, SVEIR, SIIR type compartmental models are given by using these methods. The results of the models obtained with normal and Beta distributions are compared with deterministic and stochastic to comment on the random structure of the models. Comparison of numerical data is used to show that the modified random Differential Transformation Method decreases the amount of error in the approximations obtained for the moments of the random models.