Studying Chaos in a Modified Dynamical Model: Some Applications

Many authors consider modified SIQR (susceptible, infected, isolated (quarantined), and recovered individuals) models for childhood diseases. In this paper, we examine a modified differential system with N free parameters that may be of interest to epidemiology experts. We pay special attention to the Melnikov function, which corresponds to the proposed new model. We create the Melnikov equation (M(t)=0) and analyze all of its roots using a specially designed software program. This gives the researcher the chance to accurately comprehend and articulate the classical Melnikov criterion for the potential appearance of chaos in the dynamical system. Additionally, we present a few specific modules for examining the new model’s dynamics. Additionally covered is a potential use of the Melnikov function that corresponds to the differential model under consideration, with particular potential in the modeling and synthesis of antenna diagrams. Last but not least, we consider the proposed generalization from a stochastic point of view.