In this research, we have presented the new network model for SIRS. The model has described seasonal influenza. We have discussed the dissipative feature for the SIRS model, the dynamic behaviors of the susceptible-infected-susceptible (SIS) model, the susceptible-infected-recovered (SIR) model, and the susceptible infected- recovered susceptible (SIRS) model have widely studied on complex networks. The model has described the diagram by the signal flow. We have given the Aboodh transform series decomposition method (ATSDM). Also, approach solutions of the nonlinear model for SIRS were procured via ATSDM: a procedure aimed to find the integral and the inverse transform of the troubles, augment the exponential function, and at a similar time, decompose the nonlinear condition. We have solved the SIRS model by using (ATSDM). We are showing the results with different initial conditions. The outcomes acquired from every one of the outlines considered are, without a bit of uncertainty, an authentication of the way that ATSDM is an amazing and believed rough technique that any specialist can utilize in getting an exact aftereffect of any issue of the sort thought about here in this current work.