Stability analysis of mathematical model new corona virus (COVID-19) disease spread in population

Abstract

The New Corona Virus epidemic is the most serious epidemic that the international community had known in 2019 and this is manifested by the deaths it claimed and in a short time. Its risk is much greater than (MERS) disease that emerged in the Republic of Korea and it is spreading largely more than SARS disease which appeared in Saudi Arabia and the Middle East. This deadly disease caught the public’s attention and caused terror in many societies around the world. We are building a dynamic model based on the detailed data of mortality from the World Health Organization (WHO) and the actual spread of the epidemic. By using Routh-Hurwitz criteria and constructing Lyapunov functions, the local and the global stability of the disease-free equilibrium and the disease equilibrium are obtained. We also study the sensitivity analysis of model parameters to know the parameters that have a high impact on the reproduction number R0. Finally, numerical simulations are performed to verify the theoretical analysis using Matlab.