Numerical and Chaotic Analysis of Proposed SIR Model

In this paper, we use the classic mathematical model SIR with the three differential equations as a non-linear system and combine it with the Runge-Kutta numerical method of the fourth order and the sixth and seventh order of the same method to generate simulated data in each of the mentioned ranks (for susceptible people, Infected and recovered from the disease) for the epidemic disease COVID-19 by giving the initial values (initial conditions) for the population in a certain country of the world, and we chose this country that is Iraq. Through this work the difference between the results for the three methods (4^th, 6^th, and 7^th order) was observed in terms of the error value, the time taken for each step and the total time to implement the solution in each rank, and this has been clarified in a table showing the comparison between the results for each rank for the numerical method. The binary test (0-1) was also used to study the chaotic behavior of the disease. The simulation data for the number of infected to solve in each rank was used to show the chaos of the dynamic system, and all methods of solution led to the results that the behavior of the disease is chaotic, the value of (Kc ≅ 1) and we explained that With a table showing the Kc values for the disease in each rank, also we used the Matlab system to write the important programs to obtain all the results and graphics required in this work.