Typically, infectious diseases are modelled via SIR-type systems. SIR stands for Susceptible-Infected-Recovered, but possibly further compartments can be introduced. See
1) since then, a lot of research has been done, especially on the issue of spatial propagation of epidemics
2) applying simple models like SIR is deceptively simple and relies on an accurate estimation of the parameters involved, which are usually subject to major uncertainties; as a consequence, extreme caution should be exercised when employing these models to make 'predictions' or compute 'scenarios'.
An assessment of different epidemics containment policies has been proposed in
Preprint Can the COVID-19 epidemic be managed on the basis of daily data?
Also, many papers published in medical engineering journals such as NEJM, Nature Methods and even Nature, also concern about some math models about COVID-19. You can search the papers published not only in Mathematical journals but also in the medical journals.