HOMOCLINIC BIFURCATION IN AN DUAL SIQR MODEL FOR CHILDHOOD DISEASES: SOME SIMULATIONS AND APPLICATIONS, CHALLENGES FOR LEARNERS

Abstract

Many authors consider a system of ODEs which describes the transmissiondynamics of modified SIQR (susceptible, infected, isolated (quarantined), andrecovered individuals) models for childhood diseases. In this article, we study homoclinicbifurcation in a modified differential system (the so-called by us – dual SIQRmodel for childhood diseases) containing N number of free parameters, which couldbe of interest to specialists working in the field of epidemiology. With a specially developedsoftware product, we generate the Melnikov equation M(t) = 0 and examineall its zeros. This opens up an opportunity for the researcher to correctly understandand formulate the classical Andronov–Melnikov criterion for the possible occurrenceof chaos in the dynamical system. We demonstrate also some specialized modules forinvestigating the dynamics of the new model. A specialized module has been developedand implemented in CAS Mathematica for generating a Melnikov antenna factor.