Multi-step Adomian decomposition method for solving a delayed Chikungunya virus system

‎This paper is an extension of work [M‎. ‎Chamekh‎, ‎M‎. ‎A‎. ‎Latrach‎, ‎F‎. ‎Jday‎, ‎J‎. ‎Umm Al-Qura Univ‎. ‎Appll‎. ‎Sci.‎, \(\bf 9\) (2023)‎, ‎123--131] in which we proposed a multi-step semi-analytical solution for a chikungunya virus system without delay‎. ‎Accordingly‎, ‎this work targets the same problem but with delay‎. ‎We first used the Lyapunov function method to present the theoretical stability analysis of the Chikungunya virus model with latency and with delay‎. ‎Afterwards‎, ‎we discussed the use of the Adomian decomposition method with a technique of multi-step to obtain a solution to a delayed Chikungunya problem in particular‎, ‎and we aimed in general at some problems of dynamical systems with delay‎. ‎To validate the accuracy and efficiency of this method‎, ‎the numerical results were discussed by comparing them to the Runge-Kutta method‎.