  A significant proportion of the infections driving the current {SARS-CoV-2}
pandemic are transmitted asymptomatically. Here we introduce and study a simple
epidemic model with separate compartments comprising asymptomatic and
symptomatic infected individuals. The linear dynamics determining the outbreak
condition of the model is equivalent to a renewal theory approach with
exponential waiting time distributions. Exploiting a nontrivial conservation
law of the full nonlinear dynamics, we derive analytic bounds on the peak
number of infections in the absence and presence of mitigation through
isolation and testing. The bounds are compared to numerical solutions of the
differential equations.
