Stability analysis of an eight parameter SIR-type model including loss of immunity, and disease and vaccination fatalities

TL;DR

This paper analyzes a generalized SIR model with eight parameters, including vaccination effects and fatalities, providing a comprehensive stability analysis that reveals the complex dynamics and potential failure modes of vaccination strategies.

Contribution

It extends a classical five-parameter SIR model by incorporating vaccination and death parameters, offering a complete stability characterization of the resulting model.

Findings

Complete stability conditions for all parameter cases.

Identification of bistability and complex dynamics.

Insights into vaccination failure scenarios.

Abstract

We revisit here a landmark five parameter SIR-type model of [DvdD93, Sec. 4], which is maybe the simplest example where a complete picture of all cases, including non-trivial bistability behavior, may be obtained using simple tools. We also generalize it by adding essential vaccination and vaccination-induced death parameters, with the aim of revealing the role of vaccination and its possible failure. The main result is Theorem 5, which describes the stability behavior of our model in all possible cases.