Applying a suitable approximate-simulation technique of an epidemic model with random parameters

In this research, a suitable numerical simulation method is used to solve a non-linear system that contains multi-variables and multi-parameters with absent real data. The solution to such type of system needs a long time with some difficulty. Mean Latin Hypercube\_Runge Kutta (MLH\_RK4) propused method solve such system that has random parameters easily and fast. In addition, it is the appropriate method for solving the change in the values of the system coefficients with time. The mentioned system has been given realistic results with MLH\_RK4 that has been applied to the epidemic model. The COVID-19 model from 2020 in Iraq is the application under the research. The comparison study between the numerical results with the proposed numerical simulation results is shown in tables, and more clear graphically. The COVID-19 pandemic in our study will vanish in the next few years, according to the behavior of the epidemic for all its stages mentioned in our study. The proposed method can lessen the number of iterations for the used numerical method, and the number of repetitions of the used simulation technique. As well as it is a faster technique in the generation of parameters that appears as random variables using the Latin Hypercube sampling technique. The MLH\_RK4 method has been confirmed to be reliable, and effective to solve linear and nonlinear problems. The proposed method can predict the behavior of phases of the epidemic in the future of some epidemiological models.