The final size and critical times of an SIVR epidemic model

TL;DR

This paper analyzes an SIVR epidemic model incorporating impulsive vaccination, focusing on the final epidemic size, peak infection, and critical stopping times, extending classical SIR model results.

Contribution

It introduces a novel SIVR model with impulsive vaccination and derives estimates for final size, peak, and critical times, advancing epidemic modeling techniques.

Findings

Derived estimates for epidemic final size.

Analyzed peak infection value and timing.

Identified critical stopping times for infection control.

Abstract

To understand the impact of vaccination, we consider a SIVR (susceptible-infected-vaccinated-recovered) model which combines impulsive vaccination into the classical SIR model. The final size is firstly defined and estimated, and then the peak value and peak time are considered. Finally, the critical times for a given infected number is studied, and it can be used to define and estimate the stopping time. Our results extend those for the well-understood SIR model.