Final size of a structured SIRD Model with active-population force of infection

TL;DR

This paper analyzes a two-group SIRD epidemic model where the infection force depends on active individuals, deriving the final size, its relation to the reproduction number, and comparing it with classical models through simulations.

Contribution

It introduces a novel active-population based SIRD model for two groups, characterizes the final size as a fixed point, and compares it with classical models.

Findings

Final susceptible size is always positive.

Final size decreases with higher transmission rates.

Numerical simulations show differences from classical models and multiple epidemic waves.

Abstract

We consider a SIRD epidemic model for a population composed of two groups of individuals with asymmetric interactions, where the force of infection depends on the active (alive) population in each group, rather than on the total population, as in the classical formulation. We prove that the final state for susceptible individuals is always positive and characterize it as the unique fixed point of a map. We also relate the final size to the basic reproduction number and show that the final number of susceptibles decreases when transmission rates increase. Numerical simulations compare the active-population and classical two-group SIRD models, showing differences in final size and the occurrence of multiple epidemic waves. The convergence of the fixed point approach is also illustrated.