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

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