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

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.