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Compartmental models have long served as important tools in mathematicalepidemiology, with their usefulness highlighted by the recent COVID-19pandemic. However, most of the classical models fail to account for certainfeatures of this disease and others like it, such as the ability of exposedindividuals to recover without becoming infectious, or the possibility thatasymptomatic individuals can indeed transmit the disease but at a lesser ratethan the symptomatic.  In the first part of this paper we propose two new compartmentalepidemiological models and study their equilibria, obtaining an endemicthreshold theorem for the first model. In the second part of the paper, wetreat the second model as an affine control system with two controls:vaccination and mitigation. We show that this system is static feedbacklinearizable, present some simulations, and investigate of an optimal controlversion of the problem. We conclude with some open problems and ideas forfuture research.

A look at endemic equilibria of compartmental epidemiological models and model control via vaccination and mitigation