A mathematical model of the COVID-19 pandemic dynamics with dependent variable infection rate: Application to the Republic of Korea

Abstract

This work constructs, analyzes, and simulates a new compartmental SEIR-type model for the dynamics and potential control of the current COVID-19 pandemic. The novelty in this work is two-fold. First, the population is divided according to its compliance with disease control directives (lockdown, shelter-in-place, masks/face coverings, physical distancing, etc.) into those who fully comply and those who follow the directives partially, or are necessarily mobile (such as medical staff). This split, indirectly, reflects on the quality and consistency of these measures. This allows the assessment of the overall effectiveness of the control measures and the impact of their relaxing or tightening on the disease spread. Second, the adequate contact rate, which directly affects the infection rate, is one of the model unknowns, as it keeps track of the changes in the population behavior and the effectiveness of various disease treatment modalities via a differential inclusion. Existence, uniqueness and positivity results are proved using a nonstandard convex analysis-based approach. As a case study, the pandemic outbreak in the Republic of Korea (South Korea) is simulated. The model parameters were found by minimizing the deviation of the model prediction from the reported data over the first 100 days of the pandemic in South Korea.The simulations show that the model captures accurately the pandemic dynamics in the subsequent 75 days, which provides confidence in the model predictions and its future use. In particular, the model predicts that about 40% of the infections were not documented, which implies that asymptomatic infections contribute silently but substantially to the spread of the disease indicating that more widespread asymptomatic testing is necessary.