Real-world models, like those used in social studies, epidemiology, energy transport, engineering, and finance, are often called "multi-layer networks." In this work, we have described a controller that connects the paths of synchronized models that are grouped together in clusters. We did this using Lyapunov theory and a variety of coupled matrices to look into the link between the groups of chaotic systems based on influenza and covid-19. Our work also includes the use of external synchrony in biological systems. For example, we have explained in detail how the pandemic disease covid-19 will get weaker over time and become more like influenza. The analytical way to get these answers is to prove a theorem, and the numerical way is to use MATLAB to run numerical simulations.
Copyright: © 2023 Marwan et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.