A mathematical model for the dynamics of COVID-19 pandemic involving the infective immigrants

Abstract

‎  Since the first outbreak in Wuhan, China, in December 31, 2019, COVID-19    pandemic  ‎has been spreading to many countries in the world. The ongoing COVID-19 pandemic has caused a ‎major global crisis, with 554,767 total confirmed cases, 484,570 total recovered cases, and ‎‎12,306 deaths in Iraq as of February 2, 2020. In the absence of any effective therapeutics or drugs ‎and with an unknown epidemiological life cycle, predictive mathematical models can aid in ‎the understanding of both control and management of coronavirus disease. Among the important ‎factors that helped the rapid spread of the epidemic are immigration, travelers, foreign workers, and foreign students. In this work, we develop a mathematical model to study the dynamical ‎behavior of COVID-19 pandemic, involving immigrants' effects with the possibility of re-infection. ‎Firstly, we studied the positivity and roundedness of the solution of the proposed model. The stability ‎results of the model at the disease-free equilibrium point were presented when . Further, it was proven that the pandemic equilibrium point will persist uniformly when . Moreover, we ‎confirmed the occurrence of the local bifurcation (saddle-node, pitchfork, and transcritical). Finally, ‎theoretical analysis and numerical results were shown to be consistent.