Nonlinear dynamics of an epidemic compartment model with asymptomatic infections and mitigation

TL;DR

This paper introduces a compartmental epidemic model accounting for asymptomatic and symptomatic infections, deriving analytic bounds on infection peaks and analyzing the impact of mitigation strategies.

Contribution

It presents a novel epidemic model with separate compartments for asymptomatic and symptomatic cases, and provides analytic bounds on infection peaks considering mitigation.

Findings

Analytic bounds on peak infections derived

Model captures effects of asymptomatic transmission

Mitigation strategies reduce peak infection levels

Abstract

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.