Backward bifurcation of a disease-severity-structured epidemic model with treatment

TL;DR

This paper models disease transmission considering severity and treatment capacity, revealing that limited treatment capacity can cause backward bifurcation, making disease control more complex than suggested by R0 alone.

Contribution

It introduces a disease-severity-structured epidemic model incorporating treatment capacity, demonstrating the occurrence of backward bifurcation under limited treatment resources.

Findings

Backward bifurcation occurs when treatment capacity is small.

A stable endemic equilibrium can coexist with a disease-free state for R0<1.

Limited treatment capacity undermines the sufficiency of R0<1 for disease eradication.

Abstract

This paper presents a disease-severity-structured epidemic model with treatment necessary only to severe infective individuals to discuss the effect of the treatment capacity on the disease transmission. It is shown that a backward bifurcation occurs in the basic reproduction number R0, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when R0 <1, if the capacity is relatively small. This epidemiological implication is that, when there is not enough capacity for treatment, the requirement R0 <1 is not sufficient for effective disease control and disease outbreak can happen to a high endemic level even though R0 <1.