A nonautonomous epidemic model with general incidence and isolation

TL;DR

This paper develops a comprehensive nonautonomous SIQR epidemic model with general incidence functions, deriving threshold conditions for infection eradication and permanence that extend existing results to more general, time-dependent settings.

Contribution

It introduces new threshold conditions for nonautonomous epidemic models with various incidence functions, generalizing prior autonomous and periodic models.

Findings

Threshold conditions for infection eradication and permanence are established.

The model's thresholds coincide with known results in special cases.

Conditions are derived for models with mass-action, standard, and quarantine-adjusted incidence.

Abstract

We obtain conditions for eradication and permanence of infection for a nonautonomous SIQR model with time-dependent parameters, that are not assumed to be periodic. The incidence is given by functions of all compartments and the threshold conditions are given by some numbers that play the role of the basic reproduction number. We obtain simple threshold conditions in the autonomous, asymptotically autonomous and periodic settings and show that our thresholds coincide with the ones already established. Additionally, we obtain threshold conditions for the general nonautonomous model with mass-action, standard and quarantine-adjusted incidence.