One of basic model is SIR model which has a good potential for describing epidemics. In this model $S$ denotes suspection which are peoples that can be infected. The variable $I$ denotes the infected peoples and $R$ denotes the recovered ones. There are some dynamic equations that interprets the interaction of these three sets. Also, based on the virus behaviours, you can subdivide these sets and give them some sort of weights.

There is a pandemic parameter $R_0$ which plays a crucial rule in this model. For example, $1-\frac{1}{R_0}$ denotes the percent of population that must be quarantined or vaccinated. For example for COVID-19, this number belong to the interval $[0.5,0.75]$. In this model you can take many other conditions and see the effects.

You can search about $SIR$ model and find many valuable things. Specially in plus.math.org page.