The Impact of Relapse Rate on Deterministic Epidemiological Models with Pseudo-recovery

Abstract

Abstract The deterministic epidemiological model with pseudo-recovery called the SEIRI model is a model that describes disease transmission in a population. Pseudo-recovery is a term for individuals who have recovered of infection, but some of them might be re-infected. This research aims to reconstruct the model, to analyse stability of fixed point and sensitivity of parameters. Also, to carry out numerical simulations upon combination of parameter values. The stability itself was determined using the Lyapunov functions. In this work, the sensitivity analysis was focussed on the effects of the effective contact rate and relapse rate on basic reproduction numbers. Both the effective contact rate and relapse rate increase with basic reproduction number. This may suggest that controlling the spread of the diseases can be done by decreasing both the effective contact rate or the relapse rate.