Mathematical Model of an SIR Epidemic Switching with Zero Co-Infectives

Abstract

This paper studies the global dynamics of an SIR epidemic switching model with zero co-infectives and intervention programmes. The model considers two epidemics of nonspecific nomenclature in which the first epidemic is a precondition to the outbreak of the second epidemic. Analytical study of the model exposed the two epidemic steady states, namely, epidemic-free equilibrium (EFE) and epidemic endemic equilibrium (EEE). Both equilibrium states are shown to be globally attractive points with respect to the criteria of the basic reproduction number using Lyapunov stability theory. Some sufficient conditions on the model parameters are obtained to show the existence of the forward bifurcation. Finally, numerical simulations are done to exemplify the qualitative results and the impact of switching and intervention programmes. The numerical results shown that switching reduces the susceptibility and infectivity of the first epidemic and increases that of the second epidemic. Also, depending on the severity of the both epidemics, the different levels of intervention programmes are needed to reduce the number of infectives in both epidemics. However, equal intervention programmes are recommended for both epidemics to avoid neglecting one epidemic during outbreaks of the two epidemics. Contribution/Originality: This study is one of the few studies in mathematical epidemiology which have investigated the role of switching in an SIR model of two epidemics with zero co-infectives. In addition, Lyapunov functions theory and Center Manifold method is applied to the model for the global stability analysis and existence of forward bifurcation respectively.