Dynamics of SEIR model: A case study of COVID-19 in Italy

Abstract

COVID-19 takes a gigantic form worldwide in a short time from December, 2019. For this reason, World Health Organization (WHO) declared COVID-19 as a pandemic outbreak. In the early days when this outbreak began, the coronavirus spread rapidly in the community due to a lack of knowledge about the virus and the unavailability of medical facilities. Therefore it becomes a significant challenge to control the influence of the disease outbreak. In this situation, mathematical models are an important tool to employ an effective strategy in order to fight against this pandemic. To study the disease dynamics and their influence among the people, we propose a deterministic mathematical model for the COVID-19 outbreak and validate the model with real data of Italy from 15th Feb 2020 to 14th July 2020. We establish the positivity and boundedness of solutions, local stability of equilibria to examine its epidemiological relevance. Sensitivity analysis has been performed to identify the highly influential parameters which have the most impact on basic reproduction number (R0). We estimate the basic reproduction number (R0) from available data in Italy and also study effective reproduction numbers based on reported data per day from 15th Feb 2020 to 14th July 2020 in Italy. Finally, the disease control policy has been summarized in the conclusion section.

Keywords

• COVID-19
• Transcritical bifurcation
• Model validation
• Parameter estimation
• Sensitivity analysis
• Effective reproduction number