Modeling, analysis and simulations of MERS outbreak in Saudi Arabia

Abstract

This work describes a continuous differential equations model for the dynamics of Middle Eastern Respiratory Syndrome (MERS) and provides its computer simulations. It is a continuation of our previous paper Al-Asuoad et al. (Biomath, 2016) and it extends the simulations results provided there, which were restricted to the city of Riyadh, to the whole of Saudi Arabia. In addition, it updates the results for the city of Riyadh itself. Using an optimization procedure, the system coefficients were obtained from published data, and the model allows for the prediction of possible scenarios for the transmission and spread of the disease in the near future. This, in turn, allows for the application of possible disease control measures. The model is found to be very sensitive to the daily effective contact parameter, and the presented simulations indicate that the system is very close to the bifurcation of the stability of the Disease Free Equilibrium (DFE) and appearance of the Endemic Equilibrium (EE), which indicates that the disease will not decay substantially in the near future. Finally, we establish the stability of the DFE using only the stability number $\mathcal{R}_c$, which simplifies and improves one of the main theoretical results in our previous paper.

Keywords

• MERS model
• stability of DFE and EE
• simulations
• sensitivity analysis