Mathematical model and simulations of MERS outbreak: Predictions and implications for control measures

Abstract

The Middle East Respiratory Syndrome (MERS) has been identified in 2012 and since then outbreaks have been reported in various localities in the Middle East and in other parts of the world. To help predict the possible dynamics of MERS, as well as ways to contain it, this paper develops a mathematical model for the disease. It has a compartmental structure similar to SARS models and is in the form of a coupled system of nonlinear ordinary differential equations (ODEs). The model predictions are fitted to data from the outbreaks in Riyadh (Saudi Arabia) during 2013-2016. The results reveal that MERS will eventually be contained in the city. However, the containment time and the severity of the outbreaks depend crucially on the contact coefficients and the isolation rate constant. When randomness is added to the model coefficients, the simulations show that the model is sensitive to the scaled contact rate among people and to the isolation rate. The model is analyzed using stability theory for ODEs and indicates that when using only isolation, the endemic steady state is locally stable and attracting. Numerical simulations with parameters estimated from the city of Riyadh illustrate the analytical results and the model behavior, which may have important implications for the disease containment in the city. Indeed, the model highlights the importance of isolation of infected individuals and may be used to assess other control measures. The model is general and may be used to analyze outbreaks in other parts of the Middle East and other areas.

Modeling, analysis and simulations of MERS outbreak in Saudi Arabia

“…We use the basic model of MERS dynamics developed in [2], where full details of the model and its underlying assumptions can be found so, the description of the model here follows very closely the one in [2]. The model represents the disease dynamics of five populations of individuals: susceptible S(t), asymptomatic E(t), symptomatic I(t), isolated J(t), and recovered R(t), where the time t is measured in days.…”

“…1. The mathematical model for the MERS disease (the basic model in [2]), which consists of five rate equations for the dynamics of S, E, I, J and R, is as follows.…”

“…These individuals carry the virus but have not yet developed clinical symptoms of MERS, which means that they can infect susceptibles unintentionally. Following [2], k (1/day) is the rate of development of clinical symptoms in asymptomatic population. The last term on the right-hand side of (3) describes both the mortality rate due to development of clinical symptoms at rate k and the natural mortality rate.…”

“…This work uses the mathematical model constructed in [2] to study the dynamics of the Middle East Respiratory Syndrome (MERS) in Saudi Arabia. It also expands the study that was performed there of the disease in the city of Riyadh, since new data became available since the publishing of the paper.…”

“…Moreover, the new proof of the global stability of the EE is simpler and more elegant than the one in Proposition 4 in [2], since it uses only the effective reproduction number or the stability control parameter R c . Second, the model is used for simulations of the overall outbreak in Saudi Arabia, and it also extends the study of MERS done in [2] of the city of Riyadh, as more data has been collected since its publication. Indeed, currently there exists data that spans 1550 days, [25].…”