Global dynamics for a discrete quarantine/isolation model

Abstract

We propose in the present paper a discrete mathematical model by obtaining it from a continuous time model. We present in brief the mathematical formulation of the model using Euler-backward differences. The discrete model is then analyzed and present its mathematical results. The fundamental results for the discrete mathematical model are explored. We present the stability of the fixed points for our proposed model whenever the threshold R0 less or greater than one. We provide mathematically that the system is globally asymptotically stable whenever R0<1. We show the existences of the endemic equilibria by showing the system has the solution which is unique. Further, we propose suitable Lyapunov function to discuss and analyze the global stability for the endemic case whenever R0>1. We solve the discrete mathematical model numerically and present various graphical results. The effect of quarantine and without quarantine in combinations with some suitable parameters are shown. The results show the significance of the use of the backward differences for an epidemic model. Finally, we provide summarize conclusion based on the achieved results.