Mathematical model, analysis and simulations of the COVID-19 pandemic with variable infection rate: Application to South Korea

The talk describes a substantial extension of the Middle East Respiratory Syndrome (MERS) model constructed, analyzed and simulated in Al-Asuoad et. al. BIOMATH 5 (2016)1, Al-Asuoad, Oakland University Dissertation (2017), and Al-Asuoad and Shillor, BIOMATH 7(1)(2018)2 to the case of the current COVID-19 Respiratory Syndrome pandemic that is sweeping the globe. It is caused by the new SARS-CoV-2 coronavirus that has been identified in December 2019 and since then outbreaks have been reported in all parts of the world. To help predict the dynamics and possible controls of the pandemic we developed a mathematical model for the pandemic. The model has a compartmental structure similar but more complex to the SARS and MERS models. It is a coupled system of nonlinear ordinary differential equations (ODEs) and a differential inclusion for the contact rate parameter. The talk will describe the model in detail, mention some of its analysis, and describe our computer simulations of the pandemic in South Korea. The main modeling novelties are in taking into account the shelter-in-place directives, the rates at which the populations obey them and the observed changes in the infectiveness of ‘contact number’ of the SARS-CoV-2 virus. The model predictions are fitted to some of the data from the outbreak in South Korea. Since the DFE (in South Korea) is found to be asymptotically stable, the pandemic will eventually die out (as long as some control measures remain in place). And, indeed, the model simulations show that the COVID-19 will in the near future be contained. However, the containment time and the severity of the outbreak depend crucially on the contact coefficients and the isolation or shelter-in-place rate constant. The simulations show that when randomness is added to the model coefficients the model captures the pandemic dynamics very well. Finally, the model highlights the importance of isolation of infected individuals and may be used to assess other control measures. It is general and will be used to analyze outbreaks in other parts of the world.

*with Aycil Cesmelioglu and Anna M. Spagnuolo

1 http://dx.doi.org /10.11145/j.biomath.2016.12.141
2 http://dx.doi.org/10.11145/j.biomath.2018.02.277